Case Study SSG110 Lean Six Sigma

gfergy77

SSG110AdditionalLeanSixSigmaTools1.xlsx

Home >Business & Finance homework help >Operations Management homework help >Case Study SSG110 Lean Six Sigma

DMAIC_Roadmap

Lean Six Sigma DMAIC Roadmap

Purpose

Key Tools

Key Outputs

Define

To establish a quantified problem statement, objective and business case that will become the foundation to your Six Sigma project. Conduct stakeholder analysis, select team members and kick-off your project.

Primary Metric

Process Map

Project Charter

Project Plan

* Process Map * Gather VOC * Translate VOC to CTQ's * QFD/HOQ * COPQ * Primary & Secondary Metrics * Establish Project Charter * Stakeholder Analysis * Team Selection * Project Plan

Measure

Refine your understanding of the process. Assess process capability relative to customer specifications. Validate measurement systems. Brainstorm potential x's.

C&E

SIPOC

FMEA

Cpk

* Early Y=f(x) Hypothesis * Detailed Process Map * SIPOC * Cause & Effect Diagram * Cause & Effect Matrix * FMEA * Basic Statistics * Normality Test * Capability Analysis * Gage R&R

Analyze

Conduct data collection and planned studies in order to eliminate non-critical x's and validate critical x's. Establish a stronger and quantified Y=f(x) equation.

Normality Test

ANOVA

2 Sample t-test

Equal Variances

* Narrowed Y=f(x) * 1 & 2 Sample t-tests * 1 & 2 Proportions tests * Equal variance tests * Normality tests * ANOVA * Moods Median * Mann Whitney * Paired t-test * Chi-Squared test

Improve

Design, test and implement your new process or product under live operating conditions. Pilot solutions if feasible before broadly deploying expensive improvements or products.

Pugh Matrix

Linear Regression

Binary Logistic Regression

DOE

* Refined Y=f(x) * Pugh Matrix * Correlation * Simple Linear Regression * Multiple Linear Regression * Binary Logistic Regression * Full Factorial DOE * Fractional Factorial DOE

Control

Plan, communicate, train and implement your product or process solutions. Ensure control mechanisms are established. Use Poke Yoke, visual controls, SOP's and SPC wherever possible.

Control Plan

SOP's

Communication Plan

SPC

* Control Plan * Training Plan * Refined FMEA * Communication Plan * Standard Operating Procedures * Five-S Audit * Poke Yoke * Visual Controls * Statistical Process Control

VILLANOVA UNIVERSITY

DMAIC_Project_Checklist

D.M.A.I.C Project Checklist
	DEFINE		IMPROVE
	2	Projecct Charter	2	Potential Solutions Developed
	2	Business Case (why is this project important)	2	Potential Solutions Prioritized
	3	Problem Statement & Objective	2	Solution Selected
	2	Baseline Data (Primary Metric "Y")	2	Improvement Pilot/Test Plan
	2	Target	2	Improvement Pilot/Test Execution
	2	COPQ Estimate	2	Improvement Verified
	2	Project Team	2	New Process Capability
	2	Project Scope	2	Updated Process Map
	2	Project Timeline	2	Solution Implementation Plan
	2	Project Constraints/Dependencies	2	Primary Metric Updated
	2	High Level Process Map	2	COPQ Revision
	2	Customer Requirements Identified	2	Improve Phase Report
	2	Define Phase Report
	MEASURE		CONTROL
	2	Detailed Process Map	2	Full Solution Implementation
	2	SIPOC	2	Standard Operating Procedures Developed
	3	Data Collection Plan (Potential X's)	2	Communication Plan
	2	Measurement Systems Analysis (Primary Y)	2	Training Plan
	2	Process Capability Analysis	2	Audit Plan
	2	List of Possible X's	2	Control Charts
	2	Prioritized List of X's to be Analyzed	2	Control Plan
	2	Primary Metric Updated	2	Primary Metric Updated
	2	COPQ Revision	2	COPQ Revision
	2	Measure Phase Report	2	Full Project Report
	ANALYZE
	2	Sources of Variation Identified
	2	Potential X's Eliminated
	2	Root Causes Confirmed (Critical X's Identified)
	2	Primary Metric Updated
	2	COPQ Revision
	2	Analyze Phase Report

VILLANOVA UNIVERSITY

Solution Selection Matrix

Solution Selection Matrix								GO HOME!!
Project Goal	Please rank each solution for each criteria by using the 1-5 Scale as indicated below
Increase IISE SDD Membership Engagement by 10%
	Very Low (less good)		Moderate		Very High (best)
	1	2	3	4	5
Potential Solution (Provide Brief Description)	Potential to Meet Goal	Positive Customer Impact	Cost to Implement (1 = $$$ & 5 = $)	Stakeholder Buy-in	Time to Implement (1 = Long 5 = Quick)	Total Score	Implement? Yes/No
Weighted Criteria	10	9	8	7	5
IISE Sustainable Development Division Membership Engagement
Coffee talks with Lean topics	5	3	2	4	5	146	Yes
More interactive sessions, instead of standard panel discussions	5	4	4	3	1	144	Yes
Board meetings, problem solving discussion groups	5	4	4	3	1	144	Yes
Tracks for problem solving – interactive session less directive	5	4	4	3	1	144	Yes
Could we utilize the app to gain feedback?	5	5	2	3	1	137	Yes
IISE Connect?	5	4	5	5	5	186	Yes
Discussions with TVP's and Track Chairs	2	3	2	3	1	89	Yes
Can we do this outside of the conference?	4	4	3	3	2	131	Yes
Survey – VOC	3	3	5	3	5	143	Yes

&"Arial,Bold"&10Solution Selection Matrix &"Arial,Regular"&8v1.0

A3

Project XYZ
Location				Date:					Project Leader:		Tina Agustiady				Team Members																																																										GO HOME!!
																Project XYZ
Strategic Project		Critical Project			X	Issue Resolution
1. Project Goal												3. Action Plan
													Action					Owner	Due Date		2017 - Week Beginning
																					Dec				Jan					Feb				Mar				Apr				May					Jun				Jul					Aug				Sep				Oct					Nov
																					5	12	19	26	2	9	16	23	30	6	13	20	27	6	13	20	27	3	10	17	24	1	8	15	22	29	5	12	19	26	3	10	17	24	31	7	14	21	28	4	11	18	25	2	9	16	23	30	6	13	20	27
2. Project/Problem Analysis (Project: Objectives; Problem: Root Cause, Barriers, Roadblocks)

	Out of scope items:
4. Results (Impact on Targets to Improve)
	For each line item determine % completion
	Element		Item					% complete sitewide
										Comment
								0%
								0%
								0%
								0%
								0%
								0%
								0%
								0%
								0%
								0%
								0%
								0%
5. Unresolved Issues - Risks:
Legend
		Planned Timeline to Complete Action					Planned Due Date			Planned Action "ON TARGET"				Planned Action "OFF TARGET"			Planned Action "Past Due"			Planned Action Complete

CounterMeasureTemplate

Countermeasure for Project

Data Table

Plant:

Reasons (Root Cause Short Description. This MUST come from a root cause analysis tool)

Impact

Month

Enter KPI

Target

Savings Target

Gap Closure Target

Actual

Better

Worse

GO HOME!!

Date of Review:

Enter Date of Review

Start Month:

Enter 1st Month Counter Measure Form Is Used

Jan

Feb

Mar

Apr

May

June

July

Aug

Sep

Oct

Nov

Dec

Problem Statement:

Enter Problem Statement

Overall Impact (Note: Should Exceed "Gap to Close")

0.00%

Reasons (Enter Reason Being Addressed from Above)

What (Describe actions being taken to address this Root Cause)

Who (Resp for action and impact)

When (Date Complete)

Impact (Target Benefit by the Complete Date)

Status (P,D,C,A)

Planned Impact Improvement (Note: This must equal or exceed the gap closure target)

0.00%

Enter Title

Better Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec 0 0 0 0 0 0 0 0 0 0 0 0 Worse Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec 0 0 0 0 0 0 0 0 0 0 0 0 Target Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Actual

0 0 0 0 0 0 0 0 0 0 0 0 Gap Closure

PFMEA

#	Process Function (Step)	Potential Failure Modes (process defects)	Potential Failure Effects (KPOVs)	SEV	Class	Potential Causes of Failure (KPIVs)	OCC	Current Process Controls	DET	RPN	Recommend Actions	Responsible Person & Target Date	Taken Actions	SEV	OCC	DET	RPN	GO HOME!!
1										0
2										0
3										0
4										0
5										0
6										0
7										0
8										0
9										0
10										0
11										0
12										0
13										0
14										0
15										0
16										0
17										0
18										0
19										0
20										0
21										0
22										0
23										0
24										0
25										0
26										0
27										0
28										0
29										0
30										0
30										0
31										0
32
33
34
35

Severity

Effect	Criteria: Severity of Effect Defined	Ranking	GO HOME!!
Hazardous: Without Warning	May endanger operator. Failure mode affects safe vehicle operation and / or involves noncompliance with government regulation. Failure will occur WITHOUT warning.	10
Hazardous: With Warning	May endanger operator. Failure mode affects safe vehicle operation and / or involves noncompliance with government regulation. Failure will occur WITH warning.	9
Very High	Major disruption to production line. 100% of product may have to be scrapped. Vehicle / item inoperable, loss of primary function. Customer very dissatisfied.	8
High	Minor disruption to production line. Product may have to be sorted and a portion (less than 100%) scrapped. Vehicle operable, but at a reduced level of performance. Customer dissatisfied.	7
Moderate	Minor disruption to production line. A portion (less than 100%) may have to be scrapped (no sorting). Vehicle / item operable, but some comfort / convenience item(s) inoperable. Customers experience discomfort.	6
Low	Minor disruption to production line. 100% of product may have to be reworked. Vehicle / item operable, but some comfort / convenience item(s) operable at reduced level of performance. Customer experiences some dissatisfaction.	5
Very Low	Minor disruption to production line. The product may have to be sorted and a portion (less than 100%) reworked. Fit / finish / squeak / rattle item does not conform. Defect noticed by most customers.	4
Minor	Minor disruption to production line. A portion (less than 100%) of the product may have to be reworked on-line but out-of-station. Fit / finish / squeak / rattle item does not conform. Defect noticed by average customers.	3
Very Minor	Minor disruption to production line. A portion (less than 100%) of the product may have to be reworked on-line but in-station. Fit / finish / squeak / rattle item does not conform. Defect noticed by discriminating customers.	2
None	No effect.	1

Occurrence

Probability of Failure	Possible Failure Rates	Cpk	Ranking	GO HOME!!
Very High:	³ 1 in 2	< 0.33	10
Failure is almost inevitable	1 in 3	³ 0.33	9
High: Generally associated with processes similar to previous	1 in 8	³ 0.51	8
processes that have often failed	1 in 20	³ 0.67	7
Moderate: Generally associated with processes similar to	1 in 80	³ 0.83	6
previous processes which have	1 in 400	³ 1.00	5
experienced occasional failures, but not in major proportions	1 in 2,000	³ 1.17	4
Low: Isolated failures associated with similar processes	1 in 15,000	³ 1.33	3
Very Low: Only isolated failures associated with almost identical processes	1 in 150,000	³ 1.5	2
Remote: Failure is unlikely. No failures ever associated with almost identical processes	£ 1 in 1,500,000	³ 1.67	1

Detection

Detection	Criteria: Liklihood the existence of a defect will be detected by test content before product advances to next or subsequent process	Ranking	GO HOME!!
Almost Impossible	Test content detects < 80 % of failures	10
Very Remote	Test content must detect 80 % of failures	9
Remote	Test content must detect 82.5 % of failures	8
Very Low	Test content must detect 85 % of failures	7
Low	Test content must detect 87.5 % of failures	6
Moderate	Test content must detect 90 % of failures	5
Moderately High	Test content must detect 92.5 % of failures	4
High	Test content must detect 95 % of failures	3
Very High	Test content must detect 97.5 % of failures	2
Almost Certain	Test content must detect 99.5 % of failures	1

Scorecard

Villanova Basic Scorecard
																		GO HOME!!
							Calculate
Status			Q1'15			Q2'15			Q3'15			Q4'15			Full Year 2015
Current	FYF	Key Business Metrics	Goal	Fcst	Actual	Goal	Fcst	Actual	Goal	Fcst	Actual	Goal	Fcst	Actual	Goal	Fcst	Actual
1.16	0.97	Operating Expense Reduction	$15.0	$12.0	$8.0	$25.0	$25.0	$29.0	$35.0	$36.0		$25.0	$24.0		$100.0	$97.0
0.9672131148	ERROR:#DIV/0!	Customer Satisfaction	$61.0	$58.0	$57.0	$61.0	$58.0	$59.0	$61.0	$59.0	$59.0	$61.0	$61.0
ERROR:#DIV/0!	ERROR:#DIV/0!	Net Income
0	1.05	OWT				$10.0	$10.0	$0.0	$10.0	$10.0	$13.1	$40.0	$40.0		$60.0	$63.0
		Operating Metrics
3	3	Recall Open Cases
3	3	Recall Open Case Dollars
3	3	Recall Cases w/Purchasing
3	3	Recall Case Dollars w/Purchasing
3	3	Legacy Open Cases
3	3	Legacy Open Case Dollars
3	3	Legacy Cases w/Purchasing
3	3	Legacy Case Dollars w/Purchasing
1	1	OWT Cumulative Parts Reviewed							31,200	3,802		52,800	4,967		52,800	4,967
1	1	OWT Cumulative Recovery Groups w/TF							1,213	189		1,933	195		1,933	195
Status Rules: Current status based on forecst vs. goal for future periods and based on actual vs. goal for past period. FYF status based on full year forecast vs.goal untill the year completes.
Status Conditions: Green >=100% of Goal, Yellow 95%-99% of Goal, Red <95% of Goal
$dollars represented in Millions

VILLANOVA UNIVERSITY

Gantt Chart Instructions

GO HOME!!

Project Plan Guide: •To delete these instructions, select this text box and then hit [Delete]. Date Cells (H6:GU7) These cells power much of the conditional formatting and allow the project plan to "float." All the cells are indirectly referenced to cell G6, which can be set to a firm date (ex. 2/1/2010) or a reference (ex. =MIN([project dates])). Adjusting cell G6 will shift the entire calendar. Task Cells (A10:F40) The tasks have three levels, deliverable, task and sub task. Each has a different conditional format in the Gantt chart area. Deliverable Sections The deliverable section(s) (ex. 15:19) can be copied and pasted as rows to add new deliverable sections below the existing sections if needed. Within each deliverable section you can add additional room for tasks by inserting a row above the light blue row (ex. 13). This way the appropriate conditional formatting is added and no formulas are compromised. Task s By entering a task in the B column the conditional formatting will make the associated bar a medium blue. By entering a task in the C column the associated bar will be light blue. The bar is shown via conditional formatting based on the dates entered (Cols D:E) cross referenced with the calendar across the top. Task dependence/precedence can be managed by creating formulas between the data cells instead of firm dates (ex. =E11+5 vs. 2/10/2010). Special Events (B2:E7) Functionality was added to allow for up to five "special events" that will highlight the background color. This was intended for non-task events that may need to be included. Misc. - There is a current date indicator that will show the current date on the Gantt chart. - The Gantt chart bars and the task list will highlight according to % complete status. - The Page Setup includes repeating rows of 2:9 and repeating columns of A:G. To print a small section of the chart simply select the area of the Gantt chart (ex. H10:AZ41) and set it as the Print Area. - Hypothetically additional days can be added to the calendar by copy and inserting columns to the left of Column GU. Be sure to check that the formulas in 6:7 and 4:5 have been copied appropriately.

Gantt Chart

Special Events

Start

End

Project Plan Template

Time off

4/27

5/10

GO HOME!!

Holiday

3/12

Feb

Mar

Apr

May

Jun

Jul

Aug

1/28

1/29

1/30

1/31

2/1

2/2

2/3

2/4

2/5

2/6

2/7

2/8

2/9

2/10

2/11

2/12

2/13

2/14

2/15

2/16

2/17

2/18

2/19

2/20

2/21

2/22

2/23

2/24

2/25

2/26

2/27

2/28

2/29

3/1

3/2

3/3

3/4

3/5

3/6

3/7

3/8

3/9

3/10

3/11

3/12

3/13

3/14

3/15

3/16

3/17

3/18

3/19

3/20

3/21

3/22

3/23

3/24

3/25

3/26

3/27

3/28

3/29

3/30

3/31

4/1

4/2

4/3

4/4

4/5

4/6

4/7

4/8

4/9

4/10

4/11

4/12

4/13

4/14

4/15

4/16

4/17

4/18

4/19

4/20

4/21

4/22

4/23

4/24

4/25

4/26

4/27

4/28

4/29

4/30

5/1

5/2

5/3

5/4

5/5

5/6

5/7

5/8

5/9

5/10

5/11

5/12

5/13

5/14

5/15

5/16

5/17

5/18

5/19

5/20

5/21

5/22

5/23

5/24

5/25

5/26

5/27

5/28

5/29

5/30

5/31

6/1

6/2

6/3

6/4

6/5

6/6

6/7

6/8

6/9

6/10

6/11

6/12

6/13

6/14

6/15

6/16

6/17

6/18

6/19

6/20

6/21

6/22

6/23

6/24

6/25

6/26

6/27

6/28

6/29

6/30

7/1

7/2

7/3

7/4

7/5

7/6

7/7

7/8

7/9

7/10

7/11

7/12

7/13

7/14

7/15

7/16

7/17

7/18

7/19

7/20

7/21

7/22

7/23

7/24

7/25

7/26

7/27

7/28

7/29

7/30

7/31

8/1

8/2

8/3

8/4

8/5

8/6

8/7

8/8

8/9

8/10

Start

End

% Compl.

Project Deliverable 1

2/17

3/1

Task 1

2/17

3/1

80%

Task 2

2/20

2/27

60%

Task 3

3/1

3/5

10%

Project Deliverable 2

3/3

3/23

Task 1

3/3

3/23

25%

Sub task 1

3/4

3/17

40%

Sub task 2

3/17

3/23

Project Deliverable 3

3/23

4/18

Task 1

3/23

4/5

Task 2

3/23

4/12

Task 3

4/12

4/18

Project Deliverable 4

5/10

5/22

Task 1

4/19

5/22

Sub Task 1

5/2

5/22

Task 2

5/10

5/30

Task 3

5/31

6/20

Task 4

6/13

7/4

Project Deliverable 5

7/5

8/15

Task 1

7/5

7/18

Task 2

7/19

8/1

Task 3

8/2

8/8

Task 4

8/9

8/15

&"-,Bold"Example Project Plan Template

Page &P of &N

Data Collection Sheet

FLOW CHART

SUBJECT

FORM NO.

DATE

GO HOME!!

FILE NO.

PAGE NO. OF PAGES

CHARTED BY

SUMMARY OF STEPS IN PROCESS

OPERATIONS

TRANSPORTS

INSPECTIONS

DELAYS

STORAGE

TOTAL STEPS

TOTAL DIST.

TOTAL MINS

PRESENT

PROPOSED

SAVINGS

LINE

DETAILS OF PRESENT/PROPOSED METHOD (CIRCLE ONE)

Operation

Transport

Inspection

Delay

Storage

TIME

DISTANCE

Possibilities

Notes

Simplify

Eliminate

Alt Sequence

Reg.

Combine

Other

[

RACI - People

RACI Matrix

Count of Assignments

Project Structure

Organization Development

Daily Accountability

Lean Tools

Role

Names

Project Leader

Project Management

Communication Plan

Roles & Responsibilities

Talent Selection

Goal Alignment

Structure Support Functions

4 - Tier Structure

Steering Team

Coaching Structure

Daily Tier Accountability

Leader Standard Work

Escalation Process

Problem Solving

5S + 1

Visual Management

Total Productive Maintenance

Value Stream Mapping/ Flow

Responsible

Accountable

Consulting

Inform

GO HOME!!

Sponsor

SENIOR

VP of CI

HR Director Americas

MBB

ACCOUNTABLES

MBB

HR Director

Plant Manager

Lean Manager

Operations Mgr

Team Members

Quality Manager

Support

EH&S Manager

Responsible 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SENIOR ACCOUNTABLES BB Team Members Support 0 0 0 9 9 7 9 4 8 0 8 8 8 5 5 5 5 0 0 0 0 0 0 0 Accountable 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SENIOR ACCOUNTABLES BB Team Members Support 0 2 0 2 2 1 1 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Consulting 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SENIOR ACCOUNTABLES BB Team Members Support 0 1 3 7 7 5 1 7 1 0 8 8 9 0 0 0 0 0 0 0 0 0 0 0

CTQ

GO HOME!!

Instructions:

Step 1: Define the problem. Place it at the top.

Step 2: Ask: 'What causes this?" or "Why did this happen?"

Brainstorm all possible answers and write each below the problem

Step 3: Determine if all items from Step 2 are sufficient and necessary.

Ask: "are all items at this level necessary for the one on the level above?"

Step 4: Using each item from Step 2, repeat Step 2 & 3. In other words, treat

each response from Step 2 as the new problem and repeat Step 2 & 3

Step 5: Repeat the process until specific actions can be taken

Step 6: Identify Root Cause

Problem

Cause

Communication_Plan

Communication Plan Template

Process/Function Name

Project/Program Name

Project Lead

Project Sponsor/Champion

GO HOME!!

Communication Purpose:

Target Audience

Key Message

Message Dependencies

Delivery Date

Location

Medium

Follow up Medium

Messenger

Escalation Path

Contact Information

VILLANOVA UNIVERSITY

Training_Plan

Training Plan Template

Project

Process

Project Lead

Business Division

Sponsor

GO HOME!!

Who

Where

When

How Many

Key Change/Process

Training Medium

Supporting Docs

Technology Requirements

Other Requirements

Trainer

Status

VILLANOVA UNIVERSITY

Pugh_Matrix

Pugh Matrix Template

Pugh Matrix

Owner:

GO HOME!!

Measures|CTQ's|Factors etc.

Importance Rating

Baseline

Option 1

Option 2

Option 3

Option 4

Option 5

Option 6

Option 7

Hard Dollar Savings

Operating Expenses

Cost Avoidance

Ongoing Maintenance Expense

ROI (NPV)

Incremental Capital

Operational Stability

Brand/Reputation

Sum of +'s

Sum of -'s

Sum of Sames

Weighted Sum of +'s

Weighted Sum of -'s

Highest Score Wins

Baseline = "write your description of the basline here"

Option1 = "description of option 1"

Option2 = "description of option 2"

Option3 = "description of option 3"

Option4 = "description of option 4"

Option5 = "description of option 5"

Key

"+" = Better than baseline

"-" = Worse than baseline

"s" = Same as baseline

VILLANOVA UNIVERSITY

CandE_Matrix

Cause & Effect Matrix

GO HOME!!

Date:

Project:

Matrix Owner:

Output Measures (Y's)*

Y10

Weighting (1-10):

Input Variables (X's)#

For each X, score its impact on each Y listed above (use a 0,3,5,7 scale)

Score

X10

X11

X12

X13

X14

X15

X16

X17

X18

X19

X20

X21

X22

X23

X24

X25

X26

X27

X28

X29

X30

Matrix Premise: The Matrix or "Cause & Effect Matrix functions on the premise of the Y=f(x) equation.

*Rate each "Y" on a scale of 1 to 10 with 1 being the least important output measure

#For each X rate its impact on each Y using a 0,3,5,7 scale (0=No impact, 3=Weak impact, 5=Moderate impact, 7=Strong impact).

VILLANOVA UNIVERSITY

Risk_Mgt_Plan

Risk Management Plan

Company

Project/Program Name

Project Lead

Project Sponsor/Champion

Last Updated

Risk ID

Risk Category

Risk Description

Risk Impact

ImpactRating

Mitigation Action

Responsible

Status

GO HOME!!

VILLANOVA UNIVERSITY

DPMO_Sigma_Level

	Without 1.5 sigma shift			With 1.5 sigma shift
Sigma Level	DPMO	Yield	Defect Rate	DPMO	Yield	Defect Rate	GO HOME!!
1	317310	68.2690000%	31.7310000%	697612	30.23880%	69.76120%
1.1	271332	72.8668000%	27.1332000%	660082	33.99180%	66.00820%
1.2	230139	76.9861000%	23.0139000%	621378	37.86220%	62.13780%
1.3	193601	80.6399000%	19.3601000%	581814	41.81860%	58.18140%
1.4	161513	83.8487000%	16.1513000%	541693	45.83070%	54.16930%
1.5	133614	86.6386000%	13.3614000%	501349	49.86510%	50.13490%
1.6	109598	89.0402000%	10.9598000%	461139	53.88610%	46.11390%
1.7	89130	91.0870000%	8.9130000%	421427	57.85730%	42.14270%
1.8	71860	92.8140000%	7.1860000%	382572	61.74280%	38.25720%
1.9	57432	94.2568000%	5.7432000%	344915	65.50850%	34.49150%
2	45500	95.4500000%	4.5500000%	308770	69.12300%	30.87700%
2.1	35728	96.4272000%	3.5728000%	274412	72.55880%	27.44120%
2.2	27806	97.2194000%	2.7806000%	242071	75.79290%	24.20710%
2.3	21448	97.8552000%	2.1448000%	211927	78.80730%	21.19270%
2.4	16395	98.3605000%	1.6395000%	184108	81.58920%	18.41080%
2.5	12419	98.7581000%	1.2419000%	158686	84.13140%	15.86860%
2.6	9322	99.0678000%	0.9322000%	135686	86.43140%	13.56860%
2.7	6934	99.3066000%	0.6934000%	115083	88.49170%	11.50830%
2.8	5110	99.4890000%	0.5110000%	96809	90.31910%	9.68090%
2.9	3731	99.6269000%	0.3731000%	80762	91.92380%	8.07620%
3	2699	99.7301000%	0.2699000%	66810	93.31900%	6.68100%
3.1	1935	99.8065000%	0.1935000%	54801	94.51990%	5.48010%
3.2	1374	99.8626000%	0.1374000%	44566	95.54340%	4.45660%
3.3	966	99.9034000%	0.0966000%	35931	96.40690%	3.59310%
3.4	673	99.9327000%	0.0673000%	28716	97.12840%	2.87160%
3.5	465	99.9535000%	0.0465000%	22750	97.72500%	2.27500%
3.6	318	99.9682000%	0.0318000%	17864	98.21360%	1.78640%
3.7	215	99.9785000%	0.0215000%	13903	98.60970%	1.39030%
3.8	144	99.9856000%	0.0144000%	10724	98.92760%	1.07240%
3.9	96	99.9904000%	0.0096000%	8197	99.18030%	0.81970%
4	63	99.9937000%	0.0063000%	6209	99.37910%	0.62090%
4.1	41	99.9959000%	0.0041000%	4661	99.53390%	0.46610%
4.2	26	99.9974000%	0.0026000%	3467	99.65330%	0.34670%
4.3	17	99.9983000%	0.0017000%	2555	99.74450%	0.25550%
4.4	10	99.9990000%	0.0010000%	1865	99.81350%	0.18650%
4.5	6	99.9994000%	0.0006000%	1349	99.86510%	0.13490%
4.6	4	99.9996000%	0.0004000%	967	99.90330%	0.09670%
4.7	2	99.9998000%	0.0002000%	687	99.93130%	0.06870%
4.8	1	99.9999000%	0.0001000%	483	99.95170%	0.04830%
4.9	0.96	99.9999040%	0.0000960%	336	99.96640%	0.03360%
5	0.574	99.9999426%	0.0000574%	232	99.97680%	0.02320%
5.1	0.34	99.9999660%	0.0000340%	159	99.98410%	0.01590%
5.2	0.2	99.9999800%	0.0000200%	107	99.98930%	0.01070%
5.3	0.116	99.9999884%	0.0000116%	72	99.99280%	0.00720%
5.4	0.067	99.9999933%	0.0000067%	48	99.99520%	0.00480%
5.5	0.038	99.9999962%	0.0000038%	31	99.99690%	0.00310%
5.6	0.021	99.9999979%	0.0000021%	20	99.99800%	0.00200%
5.7	0.012	99.9999988%	0.0000012%	13.35	99.99867%	0.00134%
5.8	0.007	99.9999993%	0.0000007%	8.55	99.99915%	0.00086%
5.9	0.004	99.9999996%	0.0000004%	5.42	99.99946%	0.00054%
6	0.002	99.9999998%	0.0000002%	3.4	99.99966%	0.00034%

VILLANOVA UNIVERSITY

Sample_Size_Calculator

			GO HOME!!
	Sample Size Calculator
Continuous	Data Type:	Discrete
Discrete	Enter Proportion Defective:	0.50
	Acceptable Margin of Error:	0.05
	Required Sample Size @ 99% CI	666
	Required Sample Size @ 95% CI	385
	Required Sample Size @ 90% CI	271

VILLANOVA UNIVERSITY

Takt Time Calculator

GO HOME!!

Please enter data in boxes marked yellow

Working shifts / day

shifts

Hours / shift

hours

Gross Available time / shift

480

minutes

Break time / shift

minutes

Lunch time / shift

minutes

Planned downtime / shift

minutes

Net Available time / shift

420

minutes

Net Available time / shift

25200

seconds

Net Available time / day

25200

seconds

Customer Demand / day

800

units

Takt Time =

seconds / unit

VILLANOVA UNIVERSITY

Z_Distribution_Table

Table of Probabilities for the Standard Normal (Z) Distribution
Right Tailed Distribution											GO HOME!!
Z	0	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.500000	0.496011	0.492022	0.488034	0.484047	0.480061	0.476078	0.472097	0.468119	0.464144
0.1	0.460172	0.456205	0.452242	0.448283	0.444330	0.440382	0.436441	0.432505	0.428576	0.424655
0.2	0.420740	0.416834	0.412936	0.409046	0.405165	0.401294	0.397432	0.393580	0.389739	0.385908
0.3	0.382089	0.378280	0.374484	0.370700	0.366928	0.363169	0.359424	0.355691	0.351973	0.348268
0.4	0.344578	0.340903	0.337243	0.333598	0.329969	0.326355	0.322758	0.319178	0.315614	0.312067
0.5	0.308538	0.305026	0.301532	0.298056	0.294599	0.291160	0.287740	0.284339	0.280957	0.277595
0.6	0.274253	0.270931	0.267629	0.264347	0.261086	0.257846	0.254627	0.251429	0.248252	0.245097
0.7	0.241964	0.238852	0.235762	0.232695	0.229650	0.226627	0.223627	0.220650	0.217695	0.214764
0.8	0.211855	0.208970	0.206108	0.203269	0.200454	0.197663	0.194895	0.192150	0.189430	0.186733
0.9	0.184060	0.181411	0.178786	0.176186	0.173609	0.171056	0.168528	0.166023	0.163543	0.161087
1.0	0.158655	0.156248	0.153864	0.151505	0.149170	0.146859	0.144572	0.142310	0.140071	0.137857
1.1	0.135666	0.133500	0.131357	0.129238	0.127143	0.125072	0.123024	0.121000	0.119000	0.117023
1.2	0.115070	0.113139	0.111232	0.109349	0.107488	0.105650	0.103835	0.102042	0.100273	0.098525
1.3	0.096800	0.095098	0.093418	0.091759	0.090123	0.088508	0.086915	0.085343	0.083793	0.082264
1.4	0.080757	0.079270	0.077804	0.076359	0.074934	0.073529	0.072145	0.070781	0.069437	0.068112
1.5	0.066807	0.065522	0.064255	0.063008	0.061780	0.060571	0.059380	0.058208	0.057053	0.055917
1.6	0.054799	0.053699	0.052616	0.051551	0.050503	0.049471	0.048457	0.047460	0.046479	0.045514
1.7	0.044565	0.043633	0.042716	0.041815	0.040930	0.040059	0.039204	0.038364	0.037538	0.036727
1.8	0.035930	0.035148	0.034380	0.033625	0.032884	0.032157	0.031443	0.030742	0.030054	0.029379
1.9	0.028717	0.028067	0.027429	0.026803	0.026190	0.025588	0.024998	0.024419	0.023852	0.023295
2.0	0.022750	0.022216	0.021692	0.021178	0.020675	0.020182	0.019699	0.019226	0.018763	0.018309
2.1	0.017864	0.017429	0.017003	0.016586	0.016177	0.015778	0.015386	0.015003	0.014629	0.014262
2.2	0.013903	0.013553	0.013209	0.012874	0.012545	0.012224	0.011911	0.011604	0.011304	0.011011
2.3	0.010724	0.010444	0.010170	0.009903	0.009642	0.009387	0.009137	0.008894	0.008656	0.008424
2.4	0.008198	0.007976	0.007760	0.007549	0.007344	0.007143	0.006947	0.006756	0.006569	0.006387
2.5	0.006210	0.006037	0.005868	0.005703	0.005543	0.005386	0.005234	0.005085	0.004940	0.004799
2.6	0.004661	0.004527	0.004396	0.004269	0.004145	0.004025	0.003907	0.003793	0.003681	0.003573
2.7	0.003467	0.003364	0.003264	0.003167	0.003072	0.002980	0.002890	0.002803	0.002718	0.002635
2.8	0.002555	0.002477	0.002401	0.002327	0.002256	0.002186	0.002118	0.002052	0.001988	0.001926
2.9	0.001866	0.001807	0.001750	0.001695	0.001641	0.001589	0.001538	0.001489	0.001441	0.001395
3.0	0.001350	0.001306	0.001264	0.001223	0.001183	0.001144	0.001107	0.001070	0.001035	0.001001
3.1	0.000968	0.000935	0.000904	0.000874	0.000845	0.000816	0.000789	0.000762	0.000736	0.000711
3.2	0.000687	0.000664	0.000641	0.000619	0.000598	0.000577	0.000557	0.000538	0.000519	0.000501
3.3	0.000483	0.000466	0.000450	0.000434	0.000419	0.000404	0.000390	0.000376	0.000362	0.000349
3.4	0.000337	0.000325	0.000313	0.000302	0.000291	0.000280	0.000270	0.000260	0.000251	0.000242
3.5	0.000233	0.000224	0.000216	0.000208	0.000200	0.000193	0.000185	0.000178	0.000172	0.000165
3.6	0.000159	0.000153	0.000147	0.000142	0.000136	0.000131	0.000126	0.000121	0.000117	0.000112
3.7	0.000108	0.000104	0.000100	0.000096	0.000092	0.000088	0.000085	0.000082	0.000078	0.000075
3.8	0.000072	0.000069	0.000067	0.000064	0.000062	0.000059	0.000057	0.000054	0.000052	0.000050
3.9	0.000048	0.000046	0.000044	0.000042	0.000041	0.000039	0.000037	0.000036	0.000034	0.000033
4.0	0.000032	0.000030	0.000029	0.000028	0.000027	0.000026	0.000025	0.000024	0.000023	0.000022
4.1	0.000021	0.000020	0.000019	0.000018	0.000017	0.000017	0.000016	0.000015	0.000015	0.000014
4.2	0.000013	0.000013	0.000012	0.000012	0.000011	0.000011	0.000010	0.000010	0.000009	0.000009
4.3	0.000009	0.000008	0.000008	0.000007	0.000007	0.000007	0.000007	0.000006	0.000006	0.000006
4.4	0.000005	0.000005	0.000005	0.000005	0.000004	0.000004	0.000004	0.000004	0.000004	0.000004
4.5	0.000003	0.000003	0.000003	0.000003	0.000003	0.000003	0.000003	0.000002	0.000002	0.000002
4.6	0.000002	0.000002	0.000002	0.000002	0.000002	0.000002	0.000002	0.000002	0.000001	0.000001
4.7	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001
4.8	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001	0.000001
4.9	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	Standard Normal (Z) Distribution:

VILLANOVA UNIVERSITY

t_Distribution_Table

Table of Probabilities for Student's t-Distribution
df	0.600	0.700	0.800	0.900	0.950	0.975	0.990	0.995
1	0.325	0.727	1.376	3.078	6.314	12.706	31.821	63.657	GO HOME!!
2	0.289	0.617	1.061	1.886	2.920	4.303	6.965	9.925
3	0.277	0.584	0.978	1.638	2.353	3.182	4.541	5.841
4	0.271	0.569	0.941	1.533	2.132	2.776	3.747	4.604
5	0.267	0.559	0.920	1.476	2.015	2.571	3.365	4.032
6	0.265	0.553	0.906	1.440	1.943	2.447	3.143	3.707
7	0.263	0.549	0.896	1.415	1.895	2.365	2.998	3.499
8	0.262	0.546	0.889	1.397	1.860	2.306	2.896	3.355
9	0.261	0.543	0.883	1.383	1.833	2.262	2.821	3.250
10	0.260	0.542	0.879	1.372	1.812	2.228	2.764	3.169
11	0.260	0.540	0.876	1.363	1.796	2.201	2.718	3.106
12	0.259	0.539	0.873	1.356	1.782	2.179	2.681	3.055
13	0.259	0.538	0.870	1.350	1.771	2.160	2.650	3.012
14	0.258	0.537	0.868	1.345	1.761	2.145	2.624	2.977
15	0.258	0.536	0.866	1.341	1.753	2.131	2.602	2.947
16	0.258	0.535	0.865	1.337	1.746	2.120	2.583	2.921
17	0.257	0.534	0.863	1.333	1.740	2.110	2.567	2.898
18	0.257	0.534	0.862	1.330	1.734	2.101	2.552	2.878
19	0.257	0.533	0.861	1.328	1.729	2.093	2.539	2.861
20	0.257	0.533	0.860	1.325	1.725	2.086	2.528	2.845
21	0.257	0.532	0.859	1.323	1.721	2.080	2.518	2.831
22	0.256	0.532	0.858	1.321	1.717	2.074	2.508	2.819
23	0.256	0.532	0.858	1.319	1.714	2.069	2.500	2.807
24	0.256	0.531	0.857	1.318	1.711	2.064	2.492	2.797
25	0.256	0.531	0.856	1.316	1.708	2.060	2.485	2.787
26	0.256	0.531	0.856	1.315	1.706	2.056	2.479	2.779
27	0.256	0.531	0.855	1.314	1.703	2.052	2.473	2.771
28	0.256	0.530	0.855	1.313	1.701	2.048	2.467	2.763
29	0.256	0.530	0.854	1.311	1.699	2.045	2.462	2.756
30	0.256	0.530	0.854	1.310	1.697	2.042	2.457	2.750
40	0.255	0.529	0.851	1.303	1.684	2.021	2.423	2.704
60	0.254	0.527	0.848	1.296	1.671	2.000	2.390	2.660
120	0.254	0.526	0.845	1.289	1.658	1.980	2.358	2.617
df (degrees of freedom) = number of samples - 1
1 - alpha (for one tail) or 1 - alpha/2 (for two tails)

VILLANOVA UNIVERSITY

F_Distribution_Table

Table of Probabilities for the F Distribution
Alpha =	0.05
D/N	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	20	24	30	40	60	120
1	161.45	199.50	215.71	224.58	230.16	233.99	236.77	238.88	240.54	241.88	242.98	243.91	244.69	245.36	245.95	248.01	249.05	250.10	251.14	252.20	253.25	GO HOME!!
2	18.51	19.00	19.16	19.25	19.30	19.33	19.35	19.37	19.38	19.40	19.40	19.41	19.42	19.42	19.43	19.45	19.45	19.46	19.47	19.48	19.49
3	10.13	9.55	9.28	9.12	9.01	8.94	8.89	8.85	8.81	8.79	8.76	8.74	8.73	8.71	8.70	8.66	8.64	8.62	8.59	8.57	8.55
4	7.71	6.94	6.59	6.39	6.26	6.16	6.09	6.04	6.00	5.96	5.94	5.91	5.89	5.87	5.86	5.80	5.77	5.75	5.72	5.69	5.66
5	6.61	5.79	5.41	5.19	5.05	4.95	4.88	4.82	4.77	4.74	4.70	4.68	4.66	4.64	4.62	4.56	4.53	4.50	4.46	4.43	4.40
6	5.99	5.14	4.76	4.53	4.39	4.28	4.21	4.15	4.10	4.06	4.03	4.00	3.98	3.96	3.94	3.87	3.84	3.81	3.77	3.74	3.70
7	5.59	4.74	4.35	4.12	3.97	3.87	3.79	3.73	3.68	3.64	3.60	3.57	3.55	3.53	3.51	3.44	3.41	3.38	3.34	3.30	3.27
8	5.32	4.46	4.07	3.84	3.69	3.58	3.50	3.44	3.39	3.35	3.31	3.28	3.26	3.24	3.22	3.15	3.12	3.08	3.04	3.01	2.97
9	5.12	4.26	3.86	3.63	3.48	3.37	3.29	3.23	3.18	3.14	3.10	3.07	3.05	3.03	3.01	2.94	2.90	2.86	2.83	2.79	2.75
10	4.96	4.10	3.71	3.48	3.33	3.22	3.14	3.07	3.02	2.98	2.94	2.91	2.89	2.86	2.85	2.77	2.74	2.70	2.66	2.62	2.58
11	4.84	3.98	3.59	3.36	3.20	3.09	3.01	2.95	2.90	2.85	2.82	2.79	2.76	2.74	2.72	2.65	2.61	2.57	2.53	2.49	2.45
12	4.75	3.89	3.49	3.26	3.11	3.00	2.91	2.85	2.80	2.75	2.72	2.69	2.66	2.64	2.62	2.54	2.51	2.47	2.43	2.38	2.34
13	4.67	3.81	3.41	3.18	3.03	2.92	2.83	2.77	2.71	2.67	2.63	2.60	2.58	2.55	2.53	2.46	2.42	2.38	2.34	2.30	2.25
14	4.60	3.74	3.34	3.11	2.96	2.85	2.76	2.70	2.65	2.60	2.57	2.53	2.51	2.48	2.46	2.39	2.35	2.31	2.27	2.22	2.18
15	4.54	3.68	3.29	3.06	2.90	2.79	2.71	2.64	2.59	2.54	2.51	2.48	2.45	2.42	2.40	2.33	2.29	2.25	2.20	2.16	2.11
16	4.49	3.63	3.24	3.01	2.85	2.74	2.66	2.59	2.54	2.49	2.46	2.42	2.40	2.37	2.35	2.28	2.24	2.19	2.15	2.11	2.06
17	4.45	3.59	3.20	2.96	2.81	2.70	2.61	2.55	2.49	2.45	2.41	2.38	2.35	2.33	2.31	2.23	2.19	2.15	2.10	2.06	2.01
18	4.41	3.55	3.16	2.93	2.77	2.66	2.58	2.51	2.46	2.41	2.37	2.34	2.31	2.29	2.27	2.19	2.15	2.11	2.06	2.02	1.97
19	4.38	3.52	3.13	2.90	2.74	2.63	2.54	2.48	2.42	2.38	2.34	2.31	2.28	2.26	2.23	2.16	2.11	2.07	2.03	1.98	1.93
20	4.35	3.49	3.10	2.87	2.71	2.60	2.51	2.45	2.39	2.35	2.31	2.28	2.25	2.22	2.20	2.12	2.08	2.04	1.99	1.95	1.90
21	4.32	3.47	3.07	2.84	2.68	2.57	2.49	2.42	2.37	2.32	2.28	2.25	2.22	2.20	2.18	2.10	2.05	2.01	1.96	1.92	1.87
22	4.30	3.44	3.05	2.82	2.66	2.55	2.46	2.40	2.34	2.30	2.26	2.23	2.20	2.17	2.15	2.07	2.03	1.98	1.94	1.89	1.84
23	4.28	3.42	3.03	2.80	2.64	2.53	2.44	2.37	2.32	2.27	2.24	2.20	2.18	2.15	2.13	2.05	2.01	1.96	1.91	1.86	1.81
24	4.26	3.40	3.01	2.78	2.62	2.51	2.42	2.36	2.30	2.25	2.22	2.18	2.15	2.13	2.11	2.03	1.98	1.94	1.89	1.84	1.79
25	4.24	3.39	2.99	2.76	2.60	2.49	2.40	2.34	2.28	2.24	2.20	2.16	2.14	2.11	2.09	2.01	1.96	1.92	1.87	1.82	1.77
26	4.23	3.37	2.98	2.74	2.59	2.47	2.39	2.32	2.27	2.22	2.18	2.15	2.12	2.09	2.07	1.99	1.95	1.90	1.85	1.80	1.75
27	4.21	3.35	2.96	2.73	2.57	2.46	2.37	2.31	2.25	2.20	2.17	2.13	2.10	2.08	2.06	1.97	1.93	1.88	1.84	1.79	1.73
28	4.20	3.34	2.95	2.71	2.56	2.45	2.36	2.29	2.24	2.19	2.15	2.12	2.09	2.06	2.04	1.96	1.91	1.87	1.82	1.77	1.71
29	4.18	3.33	2.93	2.70	2.55	2.43	2.35	2.28	2.22	2.18	2.14	2.10	2.08	2.05	2.03	1.94	1.90	1.85	1.81	1.75	1.70
30	4.17	3.32	2.92	2.69	2.53	2.42	2.33	2.27	2.21	2.16	2.13	2.09	2.06	2.04	2.01	1.93	1.89	1.84	1.79	1.74	1.68
40	4.08	3.23	2.84	2.61	2.45	2.34	2.25	2.18	2.12	2.08	2.04	2.00	1.97	1.95	1.92	1.84	1.79	1.74	1.69	1.64	1.58
60	4.00	3.15	2.76	2.53	2.37	2.25	2.17	2.10	2.04	1.99	1.95	1.92	1.89	1.86	1.84	1.75	1.70	1.65	1.59	1.53	1.47
120	3.92	3.07	2.68	2.45	2.29	2.18	2.09	2.02	1.96	1.91	1.87	1.83	1.80	1.78	1.75	1.66	1.61	1.55	1.50	1.43	1.35
Right Tailed, D/N = df in denominator = down the rows, df in numerator = across the columns																					Note: Table is for an alpha of 0.05
Table of Probabilities for F Distribution

VILLANOVA UNIVERSITY

Chi_Square_Distribution_Table

Table of Probabilities for the Chi-Squared Distribution
	Alpha Risk
df	0.995	0.990	0.975	0.95	0.9	0.75	0.5	0.25	0.1	0.05	0.25	0.01	0.005	0.001	GO HOME!!
1	0.000039	0.000157	0.000982	0.00393	0.0158	0.102	0.455	1.323	2.706	3.841	1.323	6.635	7.879	10.828
2	0.010	0.020	0.051	0.103	0.211	0.575	1.386	2.773	4.605	5.991	2.773	9.210	10.597	13.816
3	0.072	0.115	0.216	0.352	0.584	1.213	2.366	4.108	6.251	7.815	4.108	11.345	12.838	16.266
4	0.207	0.297	0.484	0.711	1.064	1.923	3.357	5.385	7.779	9.488	5.385	13.277	14.860	18.467
5	0.412	0.554	0.831	1.145	1.610	2.675	4.351	6.626	9.236	11.070	6.626	15.086	16.750	20.515
6	0.676	0.872	1.237	1.635	2.204	3.455	5.348	7.841	10.645	12.592	7.841	16.812	18.548	22.458
7	0.989	1.239	1.690	2.167	2.833	4.255	6.346	9.037	12.017	14.067	9.037	18.475	20.278	24.322
8	1.344	1.646	2.180	2.733	3.490	5.071	7.344	10.219	13.362	15.507	10.219	20.090	21.955	26.124
9	1.735	2.088	2.700	3.325	4.168	5.899	8.343	11.389	14.684	16.919	11.389	21.666	23.589	27.877
10	2.156	2.558	3.247	3.940	4.865	6.737	9.342	12.549	15.987	18.307	12.549	23.209	25.188	29.588
11	2.603	3.053	3.816	4.575	5.578	7.584	10.341	13.701	17.275	19.675	13.701	24.725	26.757	31.264
12	3.074	3.571	4.404	5.226	6.304	8.438	11.340	14.845	18.549	21.026	14.845	26.217	28.300	32.909
13	3.565	4.107	5.009	5.892	7.042	9.299	12.340	15.984	19.812	22.362	15.984	27.688	29.819	34.528
14	4.075	4.660	5.629	6.571	7.790	10.165	13.339	17.117	21.064	23.685	17.117	29.141	31.319	36.123
15	4.601	5.229	6.262	7.261	8.547	11.037	14.339	18.245	22.307	24.996	18.245	30.578	32.801	37.697
16	5.142	5.812	6.908	7.962	9.312	11.912	15.338	19.369	23.542	26.296	19.369	32.000	34.267	39.252
17	5.697	6.408	7.564	8.672	10.085	12.792	16.338	20.489	24.769	27.587	20.489	33.409	35.718	40.790
18	6.265	7.015	8.231	9.390	10.865	13.675	17.338	21.605	25.989	28.869	21.605	34.805	37.156	42.312
19	6.844	7.633	8.907	10.117	11.651	14.562	18.338	22.718	27.204	30.144	22.718	36.191	38.582	43.820
20	7.434	8.260	9.591	10.851	12.443	15.452	19.337	23.828	28.412	31.410	23.828	37.566	39.997	45.315
21	8.034	8.897	10.283	11.591	13.240	16.344	20.337	24.935	29.615	32.671	24.935	38.932	41.401	46.797
22	8.643	9.542	10.982	12.338	14.041	17.240	21.337	26.039	30.813	33.924	26.039	40.289	42.796	48.268
23	9.260	10.196	11.689	13.091	14.848	18.137	22.337	27.141	32.007	35.172	27.141	41.638	44.181	49.728
24	9.886	10.856	12.401	13.848	15.659	19.037	23.337	28.241	33.196	36.415	28.241	42.980	45.559	51.179
25	10.520	11.524	13.120	14.611	16.473	19.939	24.337	29.339	34.382	37.652	29.339	44.314	46.928	52.620
26	11.160	12.198	13.844	15.379	17.292	20.843	25.336	30.435	35.563	38.885	30.435	45.642	48.290	54.052
27	11.808	12.879	14.573	16.151	18.114	21.749	26.336	31.528	36.741	40.113	31.528	46.963	49.645	55.476
28	12.461	13.565	15.308	16.928	18.939	22.657	27.336	32.620	37.916	41.337	32.620	48.278	50.993	56.892
29	13.121	14.256	16.047	17.708	19.768	23.567	28.336	33.711	39.087	42.557	33.711	49.588	52.336	58.301
30	13.787	14.953	16.791	18.493	20.599	24.478	29.336	34.800	40.256	43.773	34.800	50.892	53.672	59.703
40	20.707	22.164	24.433	26.509	29.051	33.660	39.335	45.616	51.805	55.758	45.616	63.691	66.766	73.402
50	27.991	29.707	32.357	34.764	37.689	42.942	49.335	56.334	63.167	67.505	56.334	76.154	79.490	86.661
60	35.534	37.485	40.482	43.188	46.459	52.294	59.335	66.981	74.397	79.082	66.981	88.379	91.952	99.607
70	43.275	45.442	48.758	51.739	55.329	61.698	69.334	77.577	85.527	90.531	77.577	100.425	104.215	112.317
80	51.172	53.540	57.153	60.391	64.278	71.145	79.334	88.130	96.578	101.879	88.130	112.329	116.321	124.839
90	59.196	61.754	65.647	69.126	73.291	80.625	89.334	98.650	107.565	113.145	98.650	124.116	128.299	137.208
100	67.328	70.065	74.222	77.929	82.358	90.133	99.334	109.141	118.498	124.342	109.141	135.807	140.169	149.449
Right Tailed Distribution, df = degrees of freedom = (#Rows - 1) x (#Columns - 1)
Chi Square Table of Probabilities:

VILLANOVA UNIVERSITY

AFFINITY DIAGRAM

DIRECTIONS: CLICK ON CELL A10 FOR INSTRUCTIONS RELATED TO THE "GROUP" BOX. CLICK ON CELL B10 FOR INSTUCTIONS REGARDING THE PLACEMENT OF VOC REGARDLESS OF SOURCE (i.e., Doctor, Nurse, Patient)

GO HOME!!

AFFINITY DIAGRAM
Judy Strzepek: Judy Strzepek: TYPE PROJECT NAME OR BRIEF TITLE

TO ENLARGE BOXES, ADD ROWS USING COLUMN A

GROUP A
tc={93C6192A-A74A-47B9-9584-0A4F667943C4}: [Threaded comment] Your version of Excel allows you to read this threaded comment; however, any edits to it will get removed if the file is opened in a newer version of Excel. Learn more: https://go.microsoft.com/fwlink/?linkid=870924 Comment: TYPE THE CATEGORY FOR THE GROUPING OF VOC . FOR EXAMPLE; DR. APPOINTMENTS ARE TOO LONG

tc={37CE07E6-2E2D-41E1-BC6E-453DF44118AC}: [Threaded comment] Your version of Excel allows you to read this threaded comment; however, any edits to it will get removed if the file is opened in a newer version of Excel. Learn more: https://go.microsoft.com/fwlink/?linkid=870924 Comment: TYPE EACH OF THE VOC COMMENTS REGARDLESS OF SOURCE THAT FIT THIS CATEGORY. KEEP IN MIND, THE INDIVIDUAL COMMENT MAY NOT BE WORDED EXACTLY LIKE THE CATEGORY TITLE BUT THE INTENT AND MEANING FIT THE CATEGORY

GROUP B

GROUP C

GROUP D

GROUP E

PROCESS MAP TEMPLATE

SIX SIGMA PROCESS MAP TEMPLATE

GO HOME!!

PROCESS

ANALYSIS COMPLETED BY

DEPARTMENT(S)

DATE COMPLETED

K E Y

COPY AND PASTE BLANK ICONS BELOW

LEARN MORE ABOUT SMARTSHEET FOR PROJECT MANAGEMENT

STEP

START / END

INPUT / OUTPUT

DOCUMENT

FLOWCHART LINK

CONNECTORS

https://goo.gl/wZizs0

Tree Diagram Template

TREE DIAGRAM TEMPLATE				GO HOME!!
	OBJECTIVE /		PRIMARY MEANS /		SECONDARY MEANS /	TERTIARY MEANS /	FOURTH LEVEL /
	VISION		LONG-TERM		SHORT-TERM	MEASURES	TARGETS
		LEARN MORE ABOUT SMARTSHEET FOR PROJECT MANAGEMENT

DATA

https://goo.gl/PpiO3g

CORRELATION COEFFICIENT

FOR CORRELATION COEFFICIENT USE"PEARSON" FUNCTION IN THE "

GO HOME!!

For PEARSON formula: FORMULAS> MORE FUNCTIONS > PEARSON

FOR HELP: USE "HELP" ACROSS THE EXCEL TOOL BAR. TYPE "CORRELATION COEFICIENT" > SELECT PEARSON

Description

Returns the Pearson product moment correlation coefficient, r, a dimensionless index that ranges from -1.0 to 1.0 inclusive and reflects the extent of a linear relationship between two data sets.

PEARSON(array1, array2) : Array 1 requires a set of Independent Values; Array2 requires a set of Dependent Values

Source: Khan Academy

The correlation coefficient r measures the direction and strength of a linear relationship.

Here are some facts about r:

•It always has a value between -1and 1.

•Strong positive linear relationships have values of r closer to 1.

•Strong negative linear relationships have values of r closer to -1.

•Weaker relationships have values of r closer to 0.

https://www.khanacademy.org/math/probability/scatterplots-a1/creating-interpreting-scatterplots/v/correlation-coefficient-intuition-examples

Tool to Use

Tool	What does it do?	Why use?	When use?	Data Type	P < .05 indicates	Picture	GO HOME!!
1-Sample t-Test	Compares mean to target	The 1-sample t-test is useful in identifying a significant difference between a sample mean and a specified value when the difference is not readily apparent from graphical tools. Using the 1-sample t-test to compare data gathered before process improvements and after is a way to prove that the mean has actually shifted.	The 1-sample t-test is used with continuous data any time you need to compare a sample mean to a specified value. This is useful when you need to make judgments about a process based on a sample output from that process.	Continuous X & Y	Not equal	1
1-Way ANOVA	ANOVA tests to see if the difference between the means of each level is significantly more than the variation within each level. 1-way ANOVA is used when two or more means (a single factor with three or more levels) must be compared with each other.	One-way ANOVA is useful for identifying a statistically significant difference between means of three or more levels of a factor.	Use 1-way ANOVA when you need to compare three or more means (a single factor with three or more levels) and determine how much of the total observed variation can be explained by the factor.	Continuous Y, Discrete Xs	At least one group of data is different than at least one other group.	0
2-Sample t-Test	A statistical test used to detect differences between means of two populations.	The 2-sample t-test is useful for identifying a significant difference between means of two levels (subgroups) of a factor. It is also extremely useful for identifying important Xs for a project Y.	When you have two samples of continuous data, and you need to know if they both come from the same population or if they represent two different populations	Continuous X & Y	There is a difference in the means	0
ANOVA GLM	ANOVA General Linear Model (GLM) is a statistical tool used to test for differences in means. ANOVA tests to see if the difference between the means of each level is significantly more than the variation within each level. ANOVA GLM is used to test the effect of two or more factors with multiple levels, alone and in combination, on a dependent variable.	The General Linear Model allows you to learn one form of ANOVA that can be used for all tests of mean differences involving two or more factors or levels. Because ANOVA GLM is useful for identifying the effect of two or more factors (independent variables) on a dependent variable, it is also extremely useful for identifying important Xs for a project Y. ANOVA GLM also yields a percent contribution that quantifies the variation in the response (dependent variable) due to the individual factors and combinations of factors.	You can use ANOVA GLM any time you need to identify a statistically significant difference in the mean of the dependent variable due to two or more factors with multiple levels, alone and in combination. ANOVA GLM also can be used to quantify the amount of variation in the response that can be attributed to a specific factor in a designed experiment.	Continuous Y & all X's	At least one group of data is different than at least one other group.	0
Benchmarking	Benchmarking is an improvement tool whereby a company: Measures its performance or process against other companies' best in class practices, Determines how those companies achieved their performance levels, Uses the information to improve its own performance.	Benchmarking is an important tool in the improvement of your process for several reasons. First, it allows you to compare your relative position for this product or service against industry leaders or other companies outside your industry who perform similar functions. Second, it helps you identify potential Xs by comparing your process to the benchmarked process. Third, it may encourage innovative or direct applications of solutions from other businesses to your product or process. And finally, benchmarking can help to build acceptance for your project's results when they are compared to benchmark data obtained from industry leaders.	Benchmarking can be done at any point in the Six Sigma process when you need to develop a new process or improve an existing one	all	N/A	1
Best Subsets	Tells you the best X to use when you're comparing multiple X's in regression assessment.	Best Subsets is an efficient way to select a group of "best subsets" for further analysis by selecting the smallest subset that fulfills certain statistical criteria. The subset model may actually estimate the regression coefficients and predict future responses with smaller variance than the full model using all predictors	Typically used before or after a multiple-regression analysis. Particularly useful in determining which X combination yields the best R-sq value.	Continuous X & Y	N/A	0
Binary Logistic Regression	Binary logistic regression is useful in two important applications: analyzing the differences among discrete Xs and modeling the relationship between a discrete binary Y and discrete and/or continuous Xs.	Binary logistic regression is useful in two applications: analyzing the differences among discrete Xs and modeling the relationship between a discrete binary Y and discrete and/or continuous Xs. Binary logistic regression can be used to model the relationship between a discrete binary Y and discrete and/or continuous Xs. The predicted values will be probabilities p(d) of an event such as success or failure-not an event count. The predicted values will be bounded between zero and one (because they are probabilities).	Generally speaking, logistic regression is used when the Ys are discrete and the Xs are continuous	Defectives Y / Continuous & Discrete X	The goodness-of-fit tests, with p-values ranging from 0.312 to 0.724, indicate that there is insufficient evidence for the model not fitting the data adequately. If the p-value is less than your accepted a level, the test would indicate sufficient evidence for a conclusion of an inadequate fit.	0
Box Plot	A box plot is a basic graphing tool that displays the centering, spread, and distribution of a continuous data set. In simplified terms, it is made up of a box and whiskers (and occasional outliers) that correspond to each fourth, or quartile, of the data set. The box represents the second and third quartiles of data. The line that bisects the box is the median of the entire data set-50% of the data points fall below this line and 50% fall above it. The first and fourth quartiles are represented by "whiskers," or lines that extend from both ends of the box.	a box plot can help you visualize the centering, spread, and distribution of your data quickly. It is especially useful to view more than one box plot simultaneously to compare the performance of several processes such as the price quote cycle between offices or the accuracy of component placement across several production lines. A box plot can help identify candidates for the causes behind your list of potential Xs. It also is useful in tracking process improvement by comparing successive plots generated over time	You can use a box plot throughout an improvement project, although it is most useful in the Analyze phase. In the Measure phase you can use a box plot to begin to understand the nature of a problem. In the Analyze phase a box plot can help you identify potential Xs that should be investigated further. It also can help eliminate potential Xs. In the Improve phase you can use a box plot to validate potential improvements	Continuous X & Y	N/A	1
Box-Cox Transformation	used to find the mathematical function needed to translate a continuous but nonnormal distribution into a normal distribution. After you have entered your data, Minitab tells you what mathematical function can be applied to each of your data points to bring your data closer to a normal distribution.	Many tools require that data be normally distributed to produce accurate results. If the data set is not normal, this may reduce significantly the confidence in the results obtained.	If your data is not normally distributed, you may encounter problems in Calculating Z values with continuous data. You could calculate an inaccurate representation of your process capability. In constructing control charts.... Your process may appear more or less in control than it really is. In Hypothesis testing... As your data becomes less normal, the results of your tests may not be valid.	Continuous X & Y	N/A	1
Brainstorming	Brainstorming is a tool that allows for open and creative thinking. It encourages all team members to participate and to build on each other's creativity	Brainstorming is helpful because it allows your team to generate many ideas on a topic creatively and efficiently without criticism or judgment.	Brainstorming can be used any time you and your team need to creatively generate numerous ideas on any topic. You will use brainstorming many times throughout your project whenever you feel it is appropriate. You also may incorporate brainstorming into other tools, such as QFD, tree diagrams, process mapping, or FMEA.	all	N/A	0
c Chart	a graphical tool that allows you to view the actual number of defects in each subgroup. Unlike continuous data control charts, discrete data control charts can monitor many product quality characteristics simultaneously. For example, you could use a c chart to monitor many types of defects in a call center process (like hang ups, incorrect information given, disconnections) on a single chart when the subgroup size is constant.	The c chart is a tool that will help you determine if your process is in control by determining whether special causes are present. The presence of special cause variation indicates that factors are influencing the output of your process. Eliminating the influence of these factors will improve the performance of your process and bring your process into control	Control phase to verify that your process remains in control after the sources of special cause variation have been removed. The c chart is used for processes that generate discrete data. The c chart monitors the number of defects per sample taken from a process. You should record between 5 and 10 readings, and the sample size must be constant. The c chart can be used in both low- and high- volume environments	Continuous X, Attribute Y	N/A	0
CAP Includes/Excludes	A group exercise used to establish scope and facilitate discussion. Effort focuses on delineating project boundaries.	Encourages group participation. Increases individual involvement and understanding of team efforts. Prevents errant team efforts in later project stages (waste). Helps to orient new team members.	Define	all	N/A	0
CAP Stakeholder Analysis	Confirms management or stakeholder acceptance and prioritization of Project and team efforts.	Helps to eliminate low priority projects. Insure management support and compatibility with business goals.	Defone	all	N/A	0
Capability Analysis	Capability analysis is a MinitabTM tool that visually compares actual process performance to the performance standards. The capability analysis output includes an illustration of the data and several performance statistics. The plot is a histogram with the performance standards for the process expressed as upper and lower specification limits (USL and LSL). A normal distribution curve is calculated from the process mean and standard deviation; this curve is overlaid on the histogram. Beneath this graphic is a table listing several key process parameters such as mean, standard deviation, capability indexes, and parts per million (ppm) above and below the specification limits.	When describing a process, it is important to identify sources of variation as well as process segments that do not meet performance standards. Capability analysis is a useful tool because it illustrates the centering and spread of your data in relation to the performance standards and provides a statistical summary of process performance. Capability analysis will help you describe the problem and evaluate the proposed solution in statistical terms.	Capability analysis is used with continuous data whenever you need to compare actual process performance to the performance standards. You can use this tool in the Measure phase to describe process performance in statistical terms. In the Improve phase, you can use capability analysis when you optimize and confirm your proposed solution. In the Control phase, capability analysis will help you compare the actual improvement of your process to the performance standards.	Continuous X & Y	N/A	1
Cause and Effect Diagram	A cause and effect diagram is a visual tool that logically organizes possible causes for a specific problem or effect by graphically displaying them in increasing detail. It is sometimes called a fishbone diagram because of its fishbone shape. This shape allows the team to see how each cause relates to the effect. It then allows you to determine a classification related to the impact and ease of addressing each cause	A cause and effect diagram allows your team to explore, identify, and display all of the possible causes related to a specific problem. The diagram can increase in detail as necessary to identify the true root cause of the problem. Proper use of the tool helps the team organize thinking so that all the possible causes of the problem, not just those from one person's viewpoint, are captured. Therefore, the cause and effect diagram reflects the perspective of the team as a whole and helps foster consensus in the results because each team member can view all the inputs	You can use the cause and effect diagram whenever you need to break an effect down into its root causes. It is especially useful in the Measure, Analyze, and Improve phases of the DMAIC process	all	N/A	0
Chi Square--Test of Independence	The chi square-test of independence is a test of association (nonindependence) between discrete variables. It is also referred to as the test of association. It is based on a mathematical comparison of the number of observed counts against the expected number of counts to determine if there is a difference in output counts based on the input category. Example: The number of units failing inspection on the first shift is greater than the number of units failing inspection on the second shift. Example: There are fewer defects on the revised application form than there were on the previous application form	The chi square-test of independence is useful for identifying a significant difference between count data for two or more levels of a discrete variable Many statistical problem statements and performance improvement goals are written in terms of reducing DPMO/DPU. The chi square-test of independence applied to before and after data is a way to prove that the DPMO/DPU have actually been reduced.	When you have discrete Y and X data (nominal data in a table-of-total-counts format, shown in fig. 1) and need to know if the Y output counts differ for two or more subgroup categories (Xs), use the chi square test. If you have raw data (untotaled), you need to form the contingency table. Use Stat > Tables > Cross Tabulation and check the Chisquare analysis box.	discrete (category or count)	At least one group is statistically different.	0
Control Charts	Control charts are time-ordered graphical displays of data that plot process variation over time. Control charts are the major tools used to monitor processes to ensure they remain stable. Control charts are characterized by A centerline, which represents the process average, or the middle point about which plotted measures are expected to vary randomly. Upper and lower control limits, which define the area three standard deviations on either side of the centerline. Control limits reflect the expected range of variation for that process. Control charts determine whether a process is in control or out of control. A process is said to be in control when only common causes of variation are present. This is represented on the control chart by data points fluctuating randomly within the control limits. Data points outside the control limits and those displaying nonrandom patterns indicate special cause variation. When special cause variation is present, the process is said to be out of control. Control charts identify when special cause is acting on the process but do not identify what the special cause is. There are two categories of control charts, characterized by type of data you are working with: continuous data control charts and discrete data control charts.	Control charts serve as a tool for the ongoing control of a process and provide a common language for discussing process performance. They help you understand variation and use that knowledge to control and improve your process. In addition, control charts function as a monitoring system that alerts you to the need to respond to special cause variation so you can put in place an immediate remedy to contain any damage.	In the Measure phase, use control charts to understand the performance of your process as it exists before process improvements. In the Analyze phase, control charts serve as a troubleshooting guide that can help you identify sources of variation (Xs). In the Control phase, use control charts to : 1. Make sure the vital few Xs remain in control to sustain the solution - 2. Show process performance after full-scale implementation of your solution. You can compare the control chart created in the Control phase with that from the Measure phase to show process improvement -3. Verify that the process remains in control after the sources of special cause variation have been removed	all	N/A	0
Data Collection Plan		Failing to establish a data collection plan can be an expensive mistake in a project. Without a plan, data collection may be haphazard, resulting in insufficient, unnecessary, or inaccurate information. This is often called "bad" data. A data collection plan provides a basic strategy for collecting accurate data efficiently	Any time data is needed, you should draft a data collection plan before beginning to collect it.	all	N/A	0
Design Analysis Spreadsheet	The design analysis spreadsheet is an MS-Excel™ workbook that has been designed to perform partial derivative analysis and root sum of squares analysis. The design analysis spreadsheet provides a quick way to predict the mean and standard deviation of an output measure (Y), given the means and standard deviations of the inputs (Xs). This will help you develop a statistical model of your product or process, which in turn will help you improve that product or process. The partial derivative of Y with respect to X is called the sensitivity of Y with respect to X or the sensitivity coefficient of X. For this reason, partial derivative analysis is sometimes called sensitivity analysis.	The design analysis spreadsheet can help you improve, revise, and optimize your design. It can also:Improve a product or process by identifying the Xs which have the most impact on the response.Identify the factors whose variability has the highest influence on the response and target their improvement by adjusting tolerances.Identify the factors that have low influence and can be allowed to vary over a wider range.Be used with the Solver optimization routine for complex functions (Y equations) with many constraints. Note that you must unprotect the worksheet before using Solver.Be used with process simulation to visualize the response given a set of constrained	Partial derivative analysis is widely used in product design, manufacturing, process improvement, and commercial services during the concept design, capability assessment, and creation of the detailed design.When the Xs are known to be highly non-normal (and especially if the Xs have skewed distributions), Monte Carlo analysis may be a better choice than partial derivative analysis.Unlike root sum of squares (RSS) analysis, partial derivative analysis can be used with nonlinear transfer functions.Use partial derivative analysis when you want to predict the mean and standard deviation of a system response (Y), given the means and standard deviations of the inputs (Xs), when the transfer function Y=f(X1, X2, ., Xn) is known. However, the inputs (Xs) must be independent of one another (i.e., not correlated).	Continuous X & Y	N/A	0
Design of Experiment (DOE)	Design of experiment (DOE) is a tool that allows you to obtain information about how factors (Xs), alone and in combination, affect a process and its output (Y). Traditional experiments generate data by changing one factor at a time, usually by trial and error. This approach often requires a great many runs and cannot capture the effect of combined factors on the output. By allowing you to test more than one factor at a time-as well as different settings for each factor-DOE is able to identify all factors and combinations of factors that affect the process Y.	DOE uses an efficient, cost-effective, and methodical approach to collecting and analyzing data related to a process output and the factors that affect it. By testing more than one factor at a time, DOE is able to identify all factors and combinations of factors that affect the process Y	In general, use DOE when you want toIdentify and quantify the impact of the vital few Xs on your process outputDescribe the relationship between Xs and a Y with a mathematical modelDetermine the best configuration	Continuous Y & all X's	N/A	0
Design Scorecards	Design scorecards are a means for gathering data, predicting final quality, analyzing drivers of poor quality, and modifying design elements before a product is built. This makes proactive corrective action possible, rather than initiating reactive quality efforts during pre-production. Design scorecards are an MS-Excel™ workbook that has been designed to automatically calculate Z values for a product based on user-provided inputs of for all the sub-processes and parts that make up the product. Design scorecards have six basic components: 1 Top-level scorecard-used to report the rolled-up ZST prediction 2. Performance worksheet-used to estimate defects caused by lack of design margin 3. Process worksheet-used to estimate defects in process as a result of the design configuration 4.Parts worksheet-used to estimate defects due to incoming materialsSoftware worksheet-used to estimate defects in software 5. Software worksheet-used to estimate defects in software 6. Reliability worksheet-used to estimate defects due to reliability		Design scorecards can be used anytime that a product or process is being designed or modified and it is necessary to predict defect levels before implementing a process. They can be used in either the DMADV or DMAIC processes.	all	N/A	0
Discrete Data Analysis Method	The Discrete Data Analysis (DDA) method is a tool used to assess the variation in a measurement system due to reproducibility, repeatability, and/or accuracy. This tool applies to discrete data only.	The DDA method is an important tool because it provides a method to independently assess the most common types of measurement variation-repeatability, reproducibility, and/or accuracy. Completing the DDA method will help you to determine whether the variation from repeatability, reproducibility, and/or accuracy in your measurement system is an acceptably small portion of the total observed variation.	Use the DDA method after the project data collection plan is formulated or modified and before the project data collection plan is finalized and data is collected. Choose the DDA method when you have discrete data and you want to determine if the measurement variation due to repeatability, reproducibility, and/or accuracy is an acceptably small portion of the total observed variation	discrete (category or count)	N/A	0
Discrete Event Simulation (Process ModelTM)	Discrete event simulation is conducted for processes that are dictated by events at distinct points in time; each occurrence of an event impacts the current state of the process. Examples of discrete events are arrivals of phone calls at a call center. Timing in a discrete event model increases incrementally based on the arrival and departure of the inputs or resources	ProcessModelTM is a process modeling and analysis tool that accelerates the process improvement effort. It combines a simple flowcharting function with a simulation process to produce a quick and easy tool for documenting, analyzing, and improving business processes.	Discrete event simulation is used in the Analyze phase of a DMAIC project to understand the behavior of important process variables. In the Improve phase of a DMAIC project, discrete event simulation is used to predict the performance of an existing process under different conditions and to test new process ideas or alternatives in an isolated environment. Use ProcessModelTM when you reach step 4, Implement, of the 10-step simulation process.	Continuous Y, Discrete Xs	N/A	0
Dot Plot	Quick graphical comparison of two or more processes' variation or spread	Quick graphical comparison of two or more processes' variation or spread	Comparing two or more processes' variation or spread	Continuous Y, Discrete Xs	N/A
Failure Mode and Effects Analysis	A means / method to Identify ways a process can fail, estimate th risks of those failures, evaluate a control plan, prioritize actions related to the process		Complex or new processes. Customers are involved.	all	N/A	0
Gage R & R--ANOVA Method	Gage R&R-ANOVA method is a tool used to assess the variation in a measurement system due to reproducibility and/or repeatability. An advantage of this tool is that it can separate the individual effects of repeatability and reproducibility and then break down reproducibility into the components "operator" and "operator by part." This tool applies to continuous data only.	Gage R&R-ANOVA method is an important tool because it provides a method to independently assess the most common types of measurement variation - repeatability and reproducibility. This tool will help you to determine whether the variation from repeatability and/or reproducibility in your measurement system is an acceptably small portion of the total observed variation.	Measure -Use Gage R&R-ANOVA method after the project data collection plan is formulated or modified and before the project data collection plan is finalized and data is collected. Choose the ANOVA method when you have continuous data and you want to determine if the measurement variation due to repeatability and/or reproducibility is an acceptably small portion of the total observed variation.	Continuous X & Y		0
Gage R & R--Short Method	Gage R&R-Short Method is a tool used to assess the variation in a measurement system due to the combined effect of reproducibility and repeatability. An advantage of this tool is that it requires only two operators and five samples to complete the analysis. A disadvantage of this tool is that the individual effects of repeatability and reproducibility cannot be separated. This tool applies to continuous data only	Gage R&R-Short Method is an important tool because it provides a quick method of assessing the most common types of measurement variation using only five parts and two operators. Completing the Gage R&R-Short Method will help you determine whether the combined variation from repeatability and reproducibility in your measurement system is an acceptably small portion of the total observed variation.	Use Gage R&R-Short Method after the project data collection plan is formulated or modified and before the project data collection plan is finalized and data is collected. Choose the Gage R&R-Short Method when you have continuous data and you believe the total measurement variation due to repeatability and reproducibility is an acceptably small portion of the total observed variation, but you need to confirm this belief. For example, you may want to verify that no changes occurred since a previous Gage R&R study. Gage R&R-Short Method can also be used in cases where sample size is limited.	Continuous X & Y		0
GRPI		GRPI is an excellent tool for organizing newly formed teams. It is valuable in helping a group of individuals work as an effective team-one of the key ingredients to success in a DMAIC project	GRPI is an excellent team-building tool and, as such, should be initiated at one of the first team meetings. In the DMAIC process, this generally happens in the Define phase, where you create your charter and form your team. Continue to update your GRPI checklist throughout the DMAIC process as your project unfolds and as your team develops	all	N/A	0
Histogram	A histogram is a basic graphing tool that displays the relative frequency or occurrence of data values-or which data values occur most and least frequently. A histogram illustrates the shape, centering, and spread of data distribution and indicates whether there are any outliers. The frequency of occurrence is displayed on the y-axis, where the height of each bar indicates the number of occurrences for that interval (or class) of data, such as 1 to 3 days, 4 to 6 days, and so on. Classes of data are displayed on the x-axis. The grouping of data into classes is the distinguishing feature of a histogram	it is important to identify and control all sources of variation. Histograms allow you to visualize large quantities of data that would otherwise be difficult to interpret. They give you a way to quickly assess the distribution of your data and the variation that exists in your process. The shape of a histogram offers clues that can lead you to possible Xs. For example, when a histogram has two distinct peaks, or is bimodal, you would look for a cause for the difference in peaks.	Histograms can be used throughout an improvement project. In the Measure phase, you can use histograms to begin to understand the statistical nature of the problem. In the Analyze phase, histograms can help you identify potential Xs that should be investigated further. They can also help eliminate potential Xs. In the Improve phase, you can use histograms to characterize and confirm your solution. In the Control phase, histograms give you a visual reference to help track and maintain your improvements.	Continuous Y & all X's	N/A	1
Homogeneity of Variance	Homogeneity of variance is a test used to determine if the variances of two or more samples are different, or not homogeneous. The homogeneity of variance test is a comparison of the variances (sigma, or standard deviations) of two or more distributions.	While large differences in variance between a small number of samples are detectable with graphical tools, the homogeneity of variance test is a quick way to reliably detect small differences in variance between large numbers of samples.	There are two main reasons for using the homogeneity of variance test:1. A basic assumption of many statistical tests is that the variances of the different samples are equal. Some statistical procedures, such as 2-sample t-test, gain additional test power if the variances of the two samples can be considered equal.2. Many statistical problem statements and performance improvement goals are written in terms of "reducing the variance." Homogeneity of variance tests can be performed on before and after data, as a way to prove that the variance has been reduced.	Continuous Y, Discrete Xs	(Use Levene's Test) At least one group of data is different than at least one other group	1
I-MR Chart	The I-MR chart is a tool to help you determine if your process is in control by seeing if special causes are present.	The presence of special cause variation indicates that factors are influencing the output of your process. Eliminating the influence of these factors will improve the performance of your process and bring your process into control	The Measure phase to separate common causes of variation from special causesThe Analyze and Improve phases to ensure process stability before completing a hypothesis testThe Control phase to verify that the process remains in control after the sources of special cause variation have been removed	Continuous X & Y	N/A	1
Kano Analysis	Kano analysis is a customer research method for classifying customer needs into four categories; it relies on a questionnaire filled out by or with the customer. It helps you understand the relationship between the fulfillment or nonfulfillment of a need and the satisfaction or dissatisfaction experienced by the customer. The four categories are 1. delighters, 2. Must Be elements, 3. One - dimensionals, & 4. Indeifferent elements. There are two additional categories into which customer responses to the Kano survey can fall: they are reverse elements and questionable result. --The categories in Kano analysis represent a point in time, and needs are constantly evolving. Often what is a delighter today can become simply a must-be over time.	Kano analysis provides a systematic, data-based method for gaining deeper understanding of customer needs by classifying them	Use Kano analysis after a list of potential needs that have to be satisfied is generated (through, for example, interviews, focus groups, or observations). Kano analysis is useful when you need to collect data on customer needs and prioritize them to focus your efforts.	all	N/A	0
Kruskal-Wallis Test	Compare two or more means with unknown distributions			non-parametric (measurement or count)	At least one mean is different	0
Matrix Plot	Tool used for high-level look at relationships between several parameters. Matrix plots are often a first step at determining which X's contribute most to your Y.	Matrix plots can save time by allowing you to drill-down into data and determine which parameters best relate to your Y.	You should use matrix plots early in your analyze phase.	Continuous Y & all X's	N/A
Mistake Proofing	Mistake-proofing devices prevent defects by preventing errors or by predicting when errors could occur.	Mistake proofing is an important tool because it allows you to take a proactive approach to eliminating errors at their source before they become defects.	You should use mistake proofing in the Measure phase when you are developing your data collection plan, in the Improve phase when you are developing your proposed solution, and in the Control phase when developing the control plan.Mistake proofing is appropriate when there are :1. Process steps where human intervention is required2. Repetitive tasks where physical manipulation of objects is required3. Steps where errors are known to occur4. Opportunities for predictable errors to occur	all	N/A	0
Monte Carlo Analysis	Monte Carlo analysis is a decision-making and problem-solving tool used to evaluate a large number of possible scenarios of a process. Each scenario represents one possible set of values for each of the variables of the process and the calculation of those variables using the transfer function to produce an outcome Y. By repeating this method many times, you can develop a distribution for the overall process performance. Monte Carlo can be used in such broad areas as finance, commercial quality, engineering design, manufacturing, and process design and improvement. Monte Carlo can be used with any type of distribution; its value comes from the increased knowledge we gain in terms of variation of the output	Performing a Monte Carlo analysis is one way to understand the variation that naturally exists in your process. One of the ways to reduce defects is to decrease the output variation. Monte Carlo focuses on understanding what variations exist in the input Xs in order to reduce the variation in output Y.		Continuous Y & all X's	N/A	0
Multi-Generational Product/Process Planning	Multigenerational product/process planning (MGPP) is a procedure that helps you create, upgrade, leverage, and maintain a product or process in a way that can reduce production costs and increase market share. A key element of MGPP is its ability to help you follow up product/process introduction with improved, derivative versions of the original product.	Most products or processes, once introduced, tend to remain unchanged for many years. Yet, competitors, technology, and the marketplace-as personified by the ever more demanding consumer-change constantly. Therefore, it makes good business sense to incorporate into product/process design a method for anticipating and taking advantage of these changes.	You should follow an MGPP in conjunction with your business's overall marketing strategy. The market process applied to MGPP usually takes place over three or more generations. These generations cover the first three to five years of product/process development and introduction.	all	N/A	0
Multiple Regression	method that enables you to determine the relationship between a continuous process output (Y) and several factors (Xs).	Multiple regression will help you to understand the relationship between the process output (Y) and several factors (Xs) that may affect the Y. Understanding this relationship allows you to1. Identify important Xs2. Identify the amount of variation explained by the model3. Reduce the number of Xs prior to design of experiment (DOE )4. Predict Y based on combinations of X values5. Identify possible nonlinear relationships such as a quadratic (X12) or an interaction (X1X2)The output of a multiple regression analysis may demonstrate the need for designed experiments that establish a cause and effect relationship or identify ways to further improve the process.	You can use multiple regression during the Analyze phase to help identify important Xs and during the Improve phase to define the optimized solution. Multiple regression can be used with both continuous and discrete Xs. If you have only discrete Xs, use ANOVA-GLM. Typically you would use multiple regression on existing data. If you need to collect new data, it may be more efficient to use a DOE.	Continuous X & Y	A correlation is detected	0
Multi-Vari Chart	A multi-vari chart is a tool that graphically displays patterns of variation. It is used to identify possible Xs or families of variation, such as variation within a subgroup, between subgroups, or over time	A multi-vari chart enables you to see the effect multiple variables have on a Y. It also helps you see variation within subgroups, between subgroups, and over time. By looking at the patterns of variation, you can identify or eliminate possible Xs		Continuous Y & all X's	N/A	0
Normal Probability Plot	Allows you to determine the normality of your data.	To determine the normality of data. To see if multiple X's exist in your data.		cont (measurement)	Data does not follow a normal distribution	1
Normality Test	A normality test is a statistical process used to determine if a sample, or any group of data, fits a standard normal distribution. A normality test can be done mathematically or graphically.	Many statistical tests (tests of means and tests of variances) assume that the data being tested is normally distributed. A normality test is used to determine if that assumption is valid.	There are two occasions when you should use a normality test: 1. When you are first trying to characterize raw data, normality testing is used in conjunction with graphical tools such as histograms and box plots. 2. When you are analyzing your data, and you need to calculate basic statistics such as Z values or employ statistical tests that assume normality, such as t-test and ANOVA.	cont (measurement)	not normal	0
np Chart	a graphical tool that allows you to view the actual number of defectives and detect the presence of special causes.	The np chart is a tool that will help you determine if your process is in control by seeing if special causes are present. The presence of special cause variation indicates that factors are influencing the output of your process. Eliminating the influence of these factors will improve the performance of your process and bring your process into control.	You will use an np chart in the Control phase to verify that the process remains in control after the sources of special cause variation have been removed. The np chart is used for processes that generate discrete data. The np chart is used to graph the actual number of defectives in a sample. The sample size for the np chart is constant, with between 5 and 10 defectives per sample on the average.	Defectives Y / Continuous & Discrete X	N/A	1
Out-of-the-Box Thinking	Out-of-the-box thinking is an approach to creativity based on overcoming the subconscious patterns of thinking that we all develop.	Many businesses are successful for a brief time due to a single innovation, while continued success is dependent upon continued innovation	Root cause analysis and new product / process development	all	N/A	0
p Chart	a graphical tool that allows you to view the proportion of defectives and detect the presence of special causes. The p chart is used to understand the ratio of nonconforming units to the total number of units in a sample.	The p chart is a tool that will help you determine if your process is in control by determining whether special causes are present. The presence of special cause variation indicates that factors are influencing the output of your process. Eliminating the influence of these factors will improve the performance of your process and bring your process into control	You will use a p chart in the Control phase to verify that the process remains in control after the sources of special cause variation have been removed. The p chart is used for processes that generate discrete data. The sample size for the p chart can vary but usually consists of 100 or more	Defectives Y / Continuous & Discrete X	N/A	1
Pareto Chart	A Pareto chart is a graphing tool that prioritizes a list of variables or factors based on impact or frequency of occurrence. This chart is based on the Pareto principle, which states that typically 80% of the defects in a process or product are caused by only 20% of the possible causes	. It is easy to interpret, which makes it a convenient communication tool for use by individuals not familiar with the project. The Pareto chart will not detect small differences between categories; more advanced statistical tools are required in such cases.	In the Define phase to stratify Voice of the Customer data...In the Measure phase to stratify data collected on the project Y…..In the Analyze phase to assess the relative impact or frequency of different factors, or Xs	all	N/A	0
Process Mapping	Process mapping is a tool that provides structure for defining a process in a simplified, visual manner by displaying the steps, events, and operations (in chronological order) that make up a process	As you examine your process in greater detail, your map will evolve from the process you "think" exists to what "actually" exists. Your process map will evolve again to reflect what "should" exist-the process after improvements are made.	In the Define phase, you create a high-level process map to get an overview of the steps, events, and operations that make up the process. This will help you understand the process and verify the scope you defined in your charter. It is particularly important that your high-level map reflects the process as it actually is, since it serves as the basis for more detailed maps.In the Measure and Analyze phases, you create a detailed process map to help you identify problems in the process. Your improvement project will focus on addressing these problems.In the Improve phase, you can use process mapping to develop solutions by creating maps of how the process "should be."	all	N/A	0
Pugh Matrix	the tool used to facilitate a disciplined, team-based process for concept selection and generation. Several concepts are evaluated according to their strengths and weaknesses against a reference concept called the datum. The datum is the best current concept at each iteration of the matrix. The Pugh matrix encourages comparison of several different concepts against a base concept, creating stronger concepts and eliminating weaker ones until an optimal concept finally is reached	provides an objective process for reviewing, assessing, and enhancing design concepts the team has generated with reference to the project's CTQs. Because it employs agreed-upon criteria for assessing each concept, it becomes difficult for one team member to promote his or her own concept for irrational reasons.	The Pugh matrix is the recommended method for selecting the most promising concepts in the Analyze phase of the DMADV process. It is used when the team already has developed several alternative concepts that potentially can meet the CTQs developed during the Measure phase and must choose the one or two concepts that will best meet the performance requirements for further development in the Design phase	all	N/A	0
Quality Function Deployment	a methodology that provides a flowdown process for CTQs from the highest to the lowest level. The flowdown process begins with the results of the customer needs mapping (VOC) as input. From that point we cascade through a series of four Houses of Quality to arrive at the internal controllable factors. QFD is a prioritization tool used to show the relative importance of factors rather than as a transfer function.	QFD drives a cross-functional discussion to define what is important. It provides a vehicle for asking how products/services will be measured and what are the critical variables to control processes.The QFD process highlights trade-offs between conflicting properties and forces the team to consider each trade off in light of the customer's requirements for the product/service.Also, it points out areas for improvement by giving special attention to the most important customer wants and systematically flowing them down through the QFD process.	QFD produces the greatest results in situations where1. Customer requirements have not been clearly defined 2. There must be trade-offs between the elements of the business 3. There are significant investments in resources required	all	N/A	0
Reqression	see Multiple Regression			Continuous X & Y	A correlation is detected	0
Risk Assessment	The risk-management process is a methodology used to identify risks,analyze risks,plan, communicate, and implement abatement actions, andtrack resolution of abatement actions.	Any time you make a change in a process, there is potential for unforeseen failure or unintended consequences. Performing a risk assessment allows you to identify potential risks associated with planned process changes and develop abatement actions to minimize the probability of their occurrence. The risk-assessment process also determines the ownership and completion date for each abatement action.	In DMAIC, risk assessment is used in the Improve phase before you make changes in the process (before running a DOE, piloting, or testing solutions) and in the Control phase to develop the control plan. In DMADV, risk assessment is used in all phases of design, especially in the Analyze and Verify phases where you analyze and verify your concept design.	all	N/A	0
Root Sum of Squares	Root sum of squares (RSS) is a statistical tolerance analysis method used to estimate the variation of a system output Y from variations in each of the system's inputs Xs.	RSS analysis is a quick method for estimating the variation in system output given the variation in system component inputs, provided the system behavior can be modeled using a linear transfer function with unit (± 1) coefficients. RSS can quickly tell you the probability that the output (Y) will be outside its upper or lower specification limits. Based on this information, you can decide whether some or all of your inputs need to be modified to meet the specifications on system output, and/or if the specifications on system output need to be changed.	Use RSS when you need to quantify the variation in the output given the variation in inputs. However, the following conditions must be met in order to perform RSS analysis: 1. The inputs (Xs) are independent. 2. The transfer function is linear with coefficients of +1 and/or - 1. 3. In addition, you will need to know (or have estimates of) the means and standard deviations of each X.	Continuous X & Y	N/A	0
Run Chart	A run chart is a graphical tool that allows you to view the variation of your process over time. The patterns in the run chart can help identify the presence of special cause variation.	The patterns in the run chart allow you to see if special causes are influencing your process. This will help you to identify Xs affecting your process run chart.	used in many phases of the DMAIC process. Consider using a run chart to 1. Look for possible time-related Xs in the Measure phase 2. Ensure process stability before completing a hypothesis test 3. Look at variation within a subgroup; compare subgroup to subgroup variation	cont (measurement)	N/A	1
Sample Size Calculator	The sample size calculator simplifies the use of the sample size formula and provides you with a statistical basis for determining the required sample size for given levels of a and b risks	The calculation helps link allowable risk with cost. If your sample size is statistically sound, you can have more confidence in your data and greater assurance that resources spent on data collection efforts and/or planned improvements will not be wasted		all	N/A	1
Scatter Plot	a basic graphic tool that illustrates the relationship between two variables.The variables may be a process output (Y) and a factor affecting it (X), two factors affecting a Y (two Xs), or two related process outputs (two Ys).	Useful in determining whether trends exist between two or more sets of data.	Scatter plots are used with continuous and discrete data and are especially useful in the Measure, Analyze, and Improve phases of DMAIC projects.	all	N/A	0
Simple Linear Regression	Simple linear regression is a method that enables you to determine the relationship between a continuous process output (Y) and one factor (X). The relationship is typically expressed in terms of a mathematical equation, such as Y = b + mX, where Y is the process output, b is a constant, m is a coefficient, and X is the process input or factor	Simple linear regression will help you to understand the relationship between the process output (Y) and any factor that may affect it (X). Understanding this relationship will allow you to predict the Y, given a value of X. This is especially useful when the Y variable of interest is difficult or expensive to measure	You can use simple linear regression during the Analyze phase to help identify important Xs and during the Improve phase to define the settings needed to achieve the desired output.	Continuous X & Y	indicate that there is sufficient evidence that the coefficients are not zero for likely Type I error rates (a levels)... SEE MINITAB	0
Simulation	Simulation is a powerful analysis tool used to experiment with a detailed process model to determine how the process output Y will respond to changes in its structure, inputs, or surroundings Xs. Simulation model is a computer model that describes relationships and interactions among inputs and process activities. It is used to evaluate process output under a range of different conditions. Different process situations need different types of simulation models. Discrete event simulation is conducted for processes that are dictated by events at distinct points in time; each occurrence of an event impacts the current state of the process. ProcessModel is GE Company's standard software tool for running discrete event models.Continuous simulation is used for processes whose variables or parameters do not experience distinct start and end points. CrystalBall is GE's standard software tool for running continuous models	Simulation can help you: 1. Identify interactions and specific problems in an existing or proposed process 2. Develop a realistic model for a process 3. Predict the behavior of the process under different conditions 4. Optimize process performance	Simulation is used in the Analyze phase of a DMAIC project to understand the behavior of important process variables. In the Improve phase of a DMAIC project, simulation is used to predict the performance of an existing process under different conditions and to test new process ideas or alternatives in an isolated environment	all	N/A	0
Six Sigma Process Report	A Six Sigma process report is a MinitabÔ tool that provides a baseline for measuring improvement of your product or process	It helps you compare the performance of your process or product to the performance standard and determine if technology or control is the problem	A Six Sigma process report, used with continuous data, helps you determine process capability for your project Y. Process capability is calculated after you have gathered your data and have determined your performance standards	Continuous Y & all X's	N/A	0
Six Sigma Product Report	calculates DPMO and process short term capability	It helps you compare the performance of your process or product to the performance standard and determine if technology or control is the problem	used with discrete data, helps you determine process capability for your project Y. You would calculate Process capability after you have gathered your data and determined your performance standards.	Continuous Y, Discrete Xs	N/A	0
Stepwise Regression	Regression tool that filters out unwanted X's based on specified criteria.			Continuous X & Y	N/A	0
Tree Diagram	A tree diagram is a tool that is used to break any concept (such as a goal, idea, objective, issue, or CTQ) into subcomponents, or lower levels of detail.	Useful in organizing information into logical categories. See "When use?" section for more detail	A tree diagram is helpful when you want to 1. Relate a CTQ to subprocess elements (Project CTQs) 2. Determine the project Y (Project Y) 3. Select the appropriate Xs (Prioritized List of All Xs) 4. Determine task-level detail for a solution to be implemented (Optimized Solution)	all	N/A	0
u Chart	A u chart, shown in figure 1, is a graphical tool that allows you to view the number of defects per unit sampled and detect the presence of special causes	The u chart is a tool that will help you determine if your process is in control by determining whether special causes are present. The presence of special cause variation indicates that factors are influencing the output of your process. Eliminating the influence of these factors will improve the performance of your process and bring your process into control	You will use a u chart in the Control phase to verify that the process remains in control after the sources of special cause variation have been removed. The u chart is used for processes that generate discrete data. The u chart monitors the number of defects per unit taken from a process. You should record between 20 and 30 readings, and the sample size may be variable.		N/A	1
Voice of the Customer	The following tools are commonly used to collect VOC data: Dashboard ,Focus group, Interview, Scorecard, and Survey.. Tools used to develop specific CTQs and associated priorities.	Each VOC tool provides the team with an organized method for gathering information from customers. Without the use of structured tools, the data collected may be incomplete or biased. Key groups may be inadvertently omitted from the process, information may not be gathered to the required level of detail, or the VOC data collection effort may be biased because of your viewpoint.	You can use VOC tools at the start of a project to determine what key issues are important to the customers, understand why they are important, and subsequently gather detailed information about each issue. VOC tools can also be used whenever you need additional customer input such as ideas and suggestions for improvement or feedback on new solutions	all	N/A	0
Worst Case Analysis	A worst case analysis is a nonstatistical tolerance analysis tool used to identify whether combinations of inputs (Xs) at their upper and lower specification limits always produce an acceptable output measure (Y).	Worst case analysis tells you the minimum and maximum limits within which your total product or process will vary. You can then compare these limits with the required specification limits to see if they are acceptable. By testing these limits in advance, you can modify any incorrect tolerance settings before actually beginning production of the product or process.	You should use worst case analysis : To analyze safety-critical Ys, and when no process data is available and only the tolerances on Xs are known. Worst case analysis should be used sparingly because it does not take into account the probabilistic nature (that is, the likelihood of variance from the specified values) of the inputs.	all	N/A	0
Xbar-R Chart	The Xbar-R chart is a tool to help you decide if your process is in control by determining whether special causes are present.	The presence of special cause variation indicates that factors are influencing the output of your process. Eliminating the influence of these factors will improve the performance of your process and bring your process into control	Xbar-R charts can be used in many phases of the DMAIC process when you have continuous data broken into subgroups. Consider using an Xbar-R chart· in the Measure phase to separate common causes of variation from special causes,· in the Analyze and Improve phases to ensure process stability before completing a hypothesis test, or· in the Control phase to verify that the process remains in control after the sources of special cause variation have been removed.	Continuous X & Y	N/A	1
Xbar-S Chart	An Xbar-S chart, or mean and standard deviation chart, is a graphical tool that allows you to view the variation in your process over time. An Xbar-S chart lets you perform statistical tests that signal when a process may be going out of control. A process that is out of control has been affected by special causes as well as common causes. The chart can also show you where to look for sources of special cause variation. The X portion of the chart contains the mean of the subgroups distributed over time. The S portion of the chart represents the standard deviation of data points in a subgroup	The Xbar-S chart is a tool to help you determine if your process is in control by seeing if special causes are present. The presence of special cause variation indicates that factors are influencing the output of your process. Eliminating the influence of these factors will improve the performance of your process and bring it into control	An Xbar-S chart can be used in many phases of the DMAIC process when you have continuous data. Consider using an Xbar-S chart……in the Measure phase to separate common causes of variation from special causes, in the Analyze and Improve phases to ensure process stability before completing a hypothesis test, or in the Control phase to verify that the process remains in control after the sources of special cause variation have been removed. NOTE - Use Xbar-R if the sample size is small.	Continuous X & Y	N/A	1

Minitab

Tool	Use When	Example	Minitab Format	Data Format	Y	Xs	p < 0.05 indicates	GO HOME!!
ANOVA	Determine if the average of a group of data is different than the average of other (multiple) groups of data	Compare multiple fixtures to determine if one or more performs differently	Stat ANOVA Oneway	Response data must be stacked in one column and the individual points must be tagged (numerically) in another column.	Variable	Attribute	At least one group of data is different than at least one other group.
Box & Whisker Plot	Compare median and variation between groups of data. Also identifies outliers.	Compare turbine blade weights using different scales.	Graph Boxplot	Response data must be stacked in one column and the individual points must be tagged (numerically) in another column.	Variable	Attribute	N/A
Cause & Effect Diagram/ Fishbone	Brainstorming possible sources of variation for a particular effect	Potential sources of variation in gage r&r	Stat Quality Tools Cause and Effect	Input ideas in proper column heading for main branches of fishbone. Type effect in pulldown window.	All	All	N/A
Chi-Square	Determine if one set of defectives data is different than other sets of defectives data.	Compare DPUs between GE90 and CF6	Stat Tables Chi-square Test	Input two columns; one column containing the number of non-defective, and the other containing the number of defective.	Discrete	Discrete	At least one group is statistically different.
Dot Plot	Quick graphical comparison of two or more processes' variation or spread	Compare length of service of GE90 technicians to CF6 technicians	Graph Character Graphs Dotplot	Input multiple columns of data of equal length	Variable	Attribute	N/A
General Linear Models	Determine if difference in categorical data between groups is real when taking into account other variable x's	Determine if height and weight are significant variables between two groups when looking at pay	Stat ANOVA General Linear Model	Response data must be stacked in one column and the individual points must be tagged (numerically) in another column. Other variables must be stacked in separate columns.	Variable	Attribute/ Variable	At least one group of data is different than at least one other group.
Histogram	View the distribution of data (spread, mean, mode, outliers, etc.)	View the distribution of Y	Graph Histogram or Stat Quality Tools Process Capability	Input one column of data	Variable	Attribute	N/A
Homogeneity of Variance	Determine if the variation in one group of data is different than the variation in other (multiple) groups of data	Compare the variation between teams	Stat ANOVA Homogeneity of Variance	Response data must be stacked in one column and the individual points must be tagged (numerically) in another column.	Variable	Attribute	(Use Levene's Test) At least one group of data is different than at least one other group
Kruskal-Wallis Test	Determine if the means of non-normal data are different	Compare the means of cycle time for different delivery methods	Stat Nonparametrics Kruskal-Wallis	Response data must be stacked in one column and the individual points must be tagged (numerically) in another column.	Variable	Attribute	At least one mean is different
Multi Vari Analysis (See also Run Chart / Time Series Plot)	Helps identify most important types or families of variation	Compare within piece, piece to piece or time to time making of airfoils leading edge thickness	Graph Interval Plot	Response data must be stacked in one column and the individual points must be tagged (numerically) in another column in time order.	Variable	Attribute	N/A
Notched Box Plot	Compare median of a given confidence interval and variation between groups of data	Compare different hole drilling patterns to see if the median and spread of the diameters are the same	Graph Character Graphs Boxplot	Response data must be stacked in one column and the individual points must be tagged (numerically) in another column.	Variable	Attribute	N/A
One-sample t-test	Determine if average of a group of data is statistically equal to a specific target	Manufacturer claims the average number of cookies in a 1 lb. package is 250. You sample 10 packages and find that the average is 235. Use this test to disprove the manufacturer's claim.	Stat Basic Statistics 1 Sample t	Input one column of data	Variable	N/A	Not equal
Pareto	Compare how frequently different causes occur	Determine which defect occurs the most often for a particular engine program	Stat Quality Tools Pareto Chart	Input two columns of equal length	Variable	Attribute	N/A
Process Mapping	Create visual aide of each step in the process being evaluated	Map engine horizontal area with all rework loops and inspection points	N/A	Use rectangles for process steps and diamonds for decision points	N/A	N/A	N/A
Regression	Determine if a group of data incrementally changes with another group	Determine if a runout changes with temperature	Stat Regression Regression	Input two columns of equal length	Variable	Variable	A correlation is detected
Run Chart/Time Series Plot	Look for trends, outliers, oscillations, etc.	View runout values over time	Stat Quality Tools Run Chart or Graph Time Series Plot	Input one column of data. Must also input a subgroup size (1 will show all points)	Variable	N/A	N/A
Scatter Plot	Look for correlations between groups of variable data	Determine if rotor blade length varies with home position	Graph Plot or Graph Marginal Plot or Graph Matrix Plot (multiples)	Input two or more groups of data of equal length	Variable	Variable	N/A
Two-sample t-test	Determine if the average of one group of data is greater than (or less than) the average of another group of data	Determine if the average radius produced by one grinder is different than the average radius produced by another grinder	Stat Basic Statistics 2 Sample t	Input two columns of equal length	Variable	Variable	There is a difference in the means