Write a 3.5-page to 4.5-page paper that highlights your reflections about relevant operations lessons from the Boeing tour and our course time studying Lean. The paper should address what you observed and learned at Boeing, and tie that to what you read i

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Home>Applied Sciences homework help>Write a 3.5-page to 4.5-page paper that highlights your reflections about relevant operations lessons from the Boeing tour and our course time studying Lean. The paper should address what you observed and learned at Boeing, and tie that to what you read i

Operations and Project Management ELCBUS 340 16 April 2018

1

Today’s Agenda

Class Administration – Littlefield Launch, Team Projects

Quality

Types of Variation

Control Charting

Process Capability Ratio (Cp)

Process Capability Index (Cpk)

Statistical Process Control

Continuous

Discrete

Process Capability Studies

2

50,000 Feet Overview of OPM

Managing Processes

Process Strategy

Process Performance & Quality

Constraint Management

Process Layout

Lean Systems

Process Analysis

Using Operations to Compete

Operations As a

Competitive Weapon

Operations Strategy

Project Management

Managing Value Chains

Supply Chain Strategy

Inventory Management

Location

Forecasting

Sales & Operations Planning

Scheduling

Resource Planning

Process Analysis

3

Service vs. Manufacturing

Small vs. Medium vs. Large Firms

Industry type: hightech, healthcare, aerospace, IT, etc ….

Quality

A term used by customers to describe their general satisfaction with a service or product.

Costs of Quality

Four major categories:

Prevention Costs

Appraisal Costs

Internal Failure Costs

External Failure Costs

Many companies spend significant time, effort, and expense on systems, training, and organizational changes to improve quality and performance of their processes. It is estimated that COQ ranges from 20 to 30 percent of gross sales.

Costs of Quality

Prevention Costs are associated with preventing defects before they happen

Appraisal Costs are incurred when a firm assesses the level of performance of its processes

Internal Failure Costs result from defects that are discovered during the production of a service or product

External Failure Costs arise when a defect is discovered after the customer receives the product or service

Ethical Failure Costs are the societal and monetary costs associated with passing defective services or products to customers

TQM & Six Sigma

What is Total Quality Management?

Total Quality Management (TQM)

Is a quality strategy that focuses on achieving high levels of process performance and quality by stressing three principles:

Customer Satisfaction

Employee Involvement

Continuous Improvement

Customer Satisfaction

Conformance to Specifications

Value

Fitness for Use

Support

Psychological Impressions

Total Quality Management

Principles

Customer satisfaction (internal or external): when customers’ expectations have been met or exceeded.

Conformance to specifications

It is the processes that produced the service or product that are really being judged.

Specifications may relate to consistent quality, on-time delivery, or delivery speed.

Value

How well the service or product serves its intended purpose at a price customers are willing to pay.

Fitness for use: customer may consider the convenience of a service or the mechanical features of a product.

Support: the service or product support may be as important to the customer as the service or product itself.

Psychological impressions: atmosphere, image, or aesthetics

9

Employee Involvement

Cultural Change

Quality at the Source

Teams

Employee Empowerment

Problem-solving teams

Special-purpose teams

Self-managed teams

Total Quality Management

Principles

Employee involvement

Cultural change

Challenge is to define customer for each employee

External customers buy the service or product.

Internal customers are employees in the firm who rely on output of other employees. An assembly line is a chain of internal customer-supplier relationships, with an external customer purchasing the finished goods.

Top management must motivate cultural change.

Everyone is expected to contribute and share the view that quality control is an end to itself

Quality at the source

Teams

Employee involvement is a key tactic for improving processes and quality

Small groups of people

Common purpose.

Set their own performance goals and approaches

Hold themselves accountable for success

Three employee-empowerment approaches to teamwork

Problem-solving teams (also called quality circles)

Special-purpose teams

Self-managing teams, the highest level of worker participation

10

Continuous Improvement

Kaizen

Problem-solving tools

Plan-Do-Study-Act Cycle

Total Quality Management

Principles

Based on the Japanese concept, kaizen

The philosophy of continually seeking ways to improve processes.

Not unique to quality. Applies to process improvement as well.

Getting started

SPC training

Make SPC a normal aspect of daily operations.

Build work teams and employee involvement.

Utilize problem-solving tools within the work teams.

Develop operator ownership in the process.

11

Plan-Do-Study-Act Cycle

Total Quality Management

Principles

Problem-solving process: The Deming Wheel

Plan—select a process needing improvement, document process, analyze data, set improvement goals, discuss alternatives, assess benefits and costs, develop a plan and improvement measures.

Do—implement plan, monitor improvements.

Study—analyze data to evaluate effectiveness of the plan.

Act—document and disseminate improved process as a standard procedure.

12

What is Six Sigma?

Six Sigma

A comprehensive and flexible system for achieving, sustaining, and maximizing business success by minimizing defects and reducing variation in processes.

Six Sigma Project Frameworks

DMAIC

DFSS (Define for Six Sigma)

DMADV

IDOV

DMAIC

5 - 15

Control

An improvement system for existing processes falling below specification and looking for incremental improvement

Define

Measure

Analyze

Improve

DMADV

Verify

An improvement system used to develop new processes or products at Six Sigma quality levels

Define

Measure

Analyze

Design

IDOV

Used for designing a completely new product or business process to meet customer needs and specifications or to achieve Six Sigma quality levels

Identify

Design

Optimize

Verify

The Tools

Six Sigma Tools

[Introduce the Tools]

Standard Work

The best combination of machines and people working together to produce a product or service at a particular point in time.

5S

5S is a workplace organization method used to assure work can be done effectively and efficiently.

SIPOC

SIPOC is a tool that summarizes the inputs, outputs and steps of one or more processes in table form.

RACI

RACI is a method to identify the roles and responsibilities of participants in a cross organizational team.

5Ys

Statistics

Waste

Worker Realignment

Workplace Reorganization

DIG

CAPA

Affinity

Fishbone

Setup Reduction

Visual Controls

Small Lots

Kanban

A3

1-Piece Flow

SPC

Kaizen

Cycle Time Reduction

TPM

FMEA

DOE

Project Management

Reengineering

Six Sigma Project

Balanced Scorecard

QFD

Hoshin Planning

VOC

18

Six Sigma Certifications

Master Black Belt

Black Belt

Green Belt

Yellow Belt

Certifying Organizations?

Acceptance Sampling

Acceptance Sampling

The application of statistical techniques to determine if a quantity of material from a supplier should be accepted or rejected based on the inspection or test of one or more samples.

Acceptable Quality Level

The quality level desired by the consumer.

Acceptance Sampling

Acceptance Sampling

Firm A uses TQM or Six Sigma to achieve internal process performance

Supplier uses TQM or Six Sigma to achieve internal process performance

Yes

No

Yes

No

Fan motors

Fan blades

Accept blades?

Supplier

Manufactures fan blades

TARGET: Firm A’s specs

Accept motors?

Motor sampling

Blade sampling

Firm A

Manufacturers furnace fan motors

TARGET: Buyer’s specs

Buyer

Manufactures furnaces

Six Sigma Approach

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Process average OK; too much variation

Process variability OK; process off target

Process on target with low variability

Reduce spread

Center process

X

X

X

X

X

X

X

X

X

Statistical Process Control

Statistical Process Control (SPC)

SPC

The application of statistical techniques to determine whether a process is delivering what the customer wants.

Performance Measurements

Variables (Continuous) - Characteristics that can be measured.

Attributes (Discrete) - Characteristics that can be counted.

Statistical Process Control (SPC)

A process that is in statistical control:

Is stable and predictable

Variation will be limited to an expected range

But still may not be capable

A process that is out of statistical control:

Is unstable and unpredictable

Variation will not be limited to the expected range

Variation may be extreme

Types of Variation

Common cause

Variation that is random, unidentifiable and unavoidable

Special cause

Variation that can be identified and eliminated

Effects of Special Cause Variation on the Process Distribution

Control Charts

Time-ordered diagram used to determine whether observed variations are abnormal

Control Charting

A control chart always has a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit.

By comparing current data to these lines, one can make conclusions about whether the process variation is in control or out of control (special cause variation)

Variable data control charts use two charts with attribute data using one chart

[Explain]

Describe the anatomy of a control chart – use the bullets as a guideline for your explanation.

[Draw this on the Board]

[Insert graphic from supplemental PPT, slide 7]

Remember the Galton box?

If you turn the SPC on its end and shook all of the points to the bottom, you would be a Probability Density Function (PDF) that would appear to be a normal distribution.

[Next Slide]

Control charting process

29

Types of Control Charts

Variable Data Control Charts

X-bar Chart – Measures whether the process is generating output consistent with a target value.

R Chart – Measures the variability of the process.

S Chart – Measures the Standard Deviation of the process.

Attribute Data Control Charts

p-chart – Measures the proportion of defective services of products in a process.

c-chart – Measures the proportion of defects in one service or product.

Continuous Control Charts Charts R Charts S Charts

[Explain]

Describe the anatomy of a control chart – use the bullets as a guideline for your explanation.

[Draw this on the Board]

[Insert graphic from supplemental PPT, slide 7]

Remember the Galton box?

If you turn the SPC on its end and shook all of the points to the bottom, you would be a Probability Density Function (PDF) that would appear to be a normal distribution.

[Next Slide]

Control charting process

31

- Chart

Data are collected in a face-and-plunge operation done on a lathe. The dimension being measured is the groove inside diameter (ID), which has a tolerance of 7.125 ± 0.010. Four parts are measured every hour. These values have been entered in the table below.

Chart Control Limits

=

=

Where:

= the central line of the chart

= a constant to provide three-sigma limits for the sample mean

Calculating Control Chart Factors

Chart Control Limits

=

=

Plot data over time

Centerline =

Upper and Lower Control Limits

LCL

UCL

=

=

Where:

= average of several R values and the central line of the R control chart

, = constants that provide three standard deviation limits for the given sample size

R-Chart

Control Limits

Calculating Control Chart Factors

R-Chart

Control Limits

=

= 2.282(0.0037) = 0.008443

=

= 0(0.0037) = 0

Plot the Range of each subgroup overtime, the calculated value is the centerline.

R-Chart

Variation and out of control data points

Common Cause Variation

Out-of-control point (Special Cause)

Time plot of sequential process measurements

Sample Number 1 2 3 4 5
1 0.5014 0.5022 0.5009 0.5027 0.5045
2 0.5021 0.5041 0.5024 0.5020 0.5062
3 0.5018 0.5026 0.5035 0.5023 0.5054
4 0.5008 0.5034 0.5024 0.5015 0.5047
5 0.5041 0.5056 0.5034 0.5047 0.5043    
0.50204 0.50358 0.50252 0.50264 0.50502 0.50316
R 0.0033 0.0034 0.0026 0.0032 0.0019 0.00288

Example

The management of West Allis Industries is concerned about the production of a special metal screw used by several of the company’s largest customers. The diameter of the screw is critical to the customers. Data from five samples appear in the accompanying table. The sample size is 5. Is the process in statistical control?

=

0.5032 + 0.577(0.0029) = 0.5048

=

0.5032 – 0.577(0.0029) = 0.5015

Example

Compute the mean for each sample and the control limits.

Process average is NOT in statistical control.

Example

05- 46

Compute the range for each sample and the control limits

= = 2.114(0.0029) = 0.0061

= = 0(0.0029) = 0

Example

Process variability is in statistical control.

Example

=

=

Where:

= average of several Stdev values and the central line of the S control chart

, = constants that provide three standard deviation limits for the given sample size

S-Chart

Control Limits

S - Chart

Subgroup Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Obs 6 Obs 7 Obs 8 Obs 9 Obs 10
1 46.8204 58.8572 67.7175 51.3078 53.3025 51.3258 59.0268 49.9933 47.086 60.4783
2 53.9847 47.4005 59.1598 57.2251 57.3207 50.4045 54.8046 55.7574 58.8662 59.2083
3 52.4315 63.2146 61.4096 59.342 57.4605 53.7083 57.0489 58.4325 48.5544 61.4105
4 50.9712 53.4314 52.9449 66.827 43.9849 67.8154 57.4312 44.3194 60.5493 59.6383
5 62.0421 57.1784 60.1955 56.4687 64.9641 52.9195 48.6739 56.3773 60.3216 58.9171
6 53.1269 58.374 63.7938 50.8965 52.4253 52.696 64.2078 65.9364 55.8426 54.478
7 55.0507 53.8931 51.8424 68.7073 50.173 58.0991 59.3456 57.9232 69.2396 60.2033
8 54.3315 52.3679 65.2346 62.6795 61.5929 54.0084 61.4465 58.4423 55.7608 54.1888
9 59.9584 59.1762 51.5629 63.0753 59.4856 63.2215 50.8982 62.4343 49.4303 48.9902
10 54.0402 56.3253 53.3773 54.7368 59.8292 54.6631 62.2161 61.5533 66.2283 63.0929
11 57.2273 65.8816 67.9839 51.7812 63.3054 56.5156 54.5318 54.4049 54.6459 52.6297
12 51.5133 61.0216 61.2776 62.1072 56.1983 54.805 59.083 58.8301 51.2939 54.9033
13 41.6784 46.7246 90.9593 57.7698 57.6619 53.9903 47.1248 50.2183 52.0052 57.2942
14 52.8303 42.4179 58.0054 60.1385 59.9954 60.5936 49.6827 68.2645 53.5693 60.6435
15 58.1128 53.4343 49.8567 53.3065 48.6588 53.4726 61.1457 61.6733 54.4246 51.8054
16 59.4674 66.2816 71.1186 63.6602 65.4012 53.2372 55.0633 46.6954 57.0477 61.8819
17 63.6288 47.3453 45.6509 40.2198 51.7382 51.0804 56.4197 57.7979 65.3047 66.539
18 59.5853 50.9825 56.2445 103.441 52.6224 63.7297 43.3771 58.7982 59.8339 57.9202
19 57.8042 49.2275 56.9069 55.4057 60.342 62.0972 57.2 38.6509 61.459 59.144
20 53.2788 62.1238 48.7058 58.0984 52.3153 56.8277 53.3615 64.6894 56.0133 56.9455
21 61.0891 52.2114 55.0061 50.2427 55.6495 53.7419 63.6856 56.5452 55.6084 67.2915
22 47.6385 62.0744 71.2102 64.6661 58.1218 56.8151 62.913 53.8949 64.6937 53.5819
23 46.1471 57.2321 60.0446 59.5476 54.4676 48.8446 57.6602 58.5467 65.4449 50.6271
24 53.1199 52.4063 53.1227 52.1897 56.6952 53.0823 61.1469 50.5565 56.9315 60.0423
25 55.3156 60.7648 55.0855 56.2381 60.3981 61.7266 69.0841 51.4446 58.1248 50.136  
54.44778 55.61393 59.53668 59.20314 56.56439 55.97686 57.06316 56.08721 57.5312 57.67965 56.9704
Stdev 5.286458 6.28949 9.49476 11.10656 5.147585 4.750668 5.9335 6.835565 5.76572 4.830527 6.544084

Calculating Control Chart Factors

Chart Control Limits when using large sample sizes (S Chart)

=

=

S-Chart

Control Limits

=

= 1.436(6.5441) = 9.3973

=

= 0.564(6.5441) = 3.6909

54.447775999999983 55.613932000000005 59.53667999999999 59.203140000000012 56.564391999999991 55.976856000000005 57.063160000000011 56.087208000000011 57.531196000000001 57.679648

56.970398800000012 56.970398800000012 56.970398800000012 56.970398800000012 56.97039880000001 2 56.970398800000012 56.970398800000012 56.970398800000012 56.970398800000012 56.970398800000012

53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074

60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951

X-Bar: Stacked Data (Y)

5.2864584810532644 6.2894901987177159 9.4947599494406294 11.106561756232184 5.1475848615248676 4.7506682219522194 5.9335003652986451 6.8355648020676014 5.7657197453628175 4.8305269359839684

6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903

3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296

9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.392214642942251 5 9.3922146429422515

S: Stacked Data (Y)

Control Chart Evaluation

Control Chart Rules

Rule Name Out of Control Condition Chart Type
Variables Attributes
Beyond Limits One or more points beyond the control limits X X
Zone C 9 or more consecutive points on one side of the average (in Zone C or beyond) X X
Trend 7 consecutive points trending up or trending down X X
Over-control 14 consecutive points alternating up and down X X
Zone A 2 out of 3 consecutive points in Zone A or beyond X  
Zone B 4 out of 5 consecutive points in Zone B or beyond X  
Stratification 15 consecutive points in Zone C X  
Mixture 8 consecutive points with no points in Zone C X  

Discrete Control Charts c-charts np-charts

56

Control Charts for Attributes Data c-chart

c-charts count the number of defects per unit of service encounter

The underlying distribution is the Poisson distribution

The mean of the distribution is and the standard deviation is .

c-chart example

The Woodland Paper Company produces paper for the newspaper industry. As a final step in the process, the paper passes through a machine that measures various product quality characteristics. When the paper production process is in control, it averages 20 defects per roll.

a. Set up a control chart for the number of defects per roll. For this example, use two-sigma control limits.

b. Five rolls had the following number of defects: 16, 21, 17, 22, and 24, respectively. The sixth roll, using pulp from a different supplier, had 5 defects. Is the paper production process in control?

a. The average number of defects per roll is 20. Therefore:

c-chart example

Example 5.4

The process is out of control due to Sample 6.

c-chart example

However, sample 6 is from a new supplier and results in a better product.

16 21 17 22 24 5

20 20 20 20 20 20

11.06 11.06 11.06 11.06 11.06 11.06

28.94 28.94 28.94 28.94 28.94 28.94

C - Defects

np-chart

np-charts are used to control the proportion defective

Sampling involves yes/no decisions so the underlying distribution is the binomial distribution

np-chart

np-chart example

A Test was conducted to determine the presence of the Rh factor in 13 samples of donated blood. The results of the test are given in the table on the next slide.

Using three-sigma control limits, is the accuracy of the blood testing process in statistical control?

np-chart example

Example 5.3

189

1614

= = 0.1171

p =

Total defectives

Total number of observations

Calculate the sample proportion defective and plot each sample proportion defective on the chart.

np-chart example

np-chart example

np-chart example

The process is in statistical control.

Control Chart Evaluation

Control Chart Rules

Rule Name Out of Control Condition Chart Type
Variables Attributes
Beyond Limits One or more points beyond the control limits X X
Zone C 9 or more consecutive points on one side of the average (in Zone C or beyond) X X
Trend 7 consecutive points trending up or trending down X X
Over-control 14 consecutive points alternating up and down X X
Zone A 2 out of 3 consecutive points in Zone A or beyond X  
Zone B 4 out of 5 consecutive points in Zone B or beyond X  
Stratification 15 consecutive points in Zone C X  
Mixture 8 consecutive points with no points in Zone C X  

Continuous

Discrete

n = 1 n = 2 to 9 n = 10+

I-MR

chart

Xbar-R chart

Xbar-S chart

Defects

Defectives

Yes No

c chart

u chart

Yes No

np chart

p chart

Type of Data

Subgroup Size

Defectives or Defects

Constant Sample Size

Constant Sample Size

Basic Control Charting Decision Tree

Process Capability – The ability of the process to meet the design specification for a service or product

Process Capability

Process Capability

20

25

30

Minutes

Upper

specification

Lower

specification

Nominal

value

(a) Process is capable

Process distribution

20

25

30

Minutes

Upper

specification

Lower

specification

Nominal

value

(b) Process is not capable

Process distribution

Process Capability

Process Capability

Lower

specification

Mean

Upper

specification

Nominal value

Six sigma

Four sigma

Two sigma

Process Capability

Process Capability Ratio

A test to see if the process variability is capable of producing output within a product’s specifications.

Cp =

Upper specification – Lower specification

6σ

Process Capability Ratio

Example 5.5

The intensive care unit lab process has an average turnaround time of 26.2 minutes and a standard deviation of 1.53 minutes.

The nominal value for this service is 25 minutes ± 5 minutes.

Is the lab process capable of four sigma-level performance?

Upper specification = 30 minutes

Lower specification = 20 minutes

Average service = 26.2 minutes

 = 1.53 minutes

Process Capability Ratio

Example 5.5

Process did not meet 4-sigma level of 1.33

Process Capability Ratio

Process Capability Index

Measures how well a process is centered and whether the variability is acceptable

Cpk = Minimum of ,

x – Lower specification

3σ

Upper specification – x

3σ

where

σ = standard deviation of the process distribution

Process Capability Index

Example 5.5

The intensive care unit lab process has an average turnaround time of 26.2 minutes and a standard deviation of 1.53 minutes.

The nominal value for this service is 25 minutes ± 5 minutes.

Is the lab process capable of four sigma-level performance?

Upper specification = 30 minutes

Lower specification = 20 minutes

Average service = 26.2 minutes

 = 1.53 minutes

Process Capability Index

Example 5.5

Cpk = Minimum of 26.2 – 20 , 30 – 26.2

3 ( 1.53) 3( 1.53)

Cpk = Minimum of ,

 

 

Process does not meets 4-sigma level of 1.33

Cpk = Minimum of 1.35, 0.83

Cpk = 0.83

Process Capability Index

Example 5.5

New Data is collected:

Upper specification = 30 minutes

Lower specification = 20 minutes

Average service = 26.1 minutes

 = 1.20 minutes

Process meets 4-sigma level of 1.33 for variability

Process Capability Ratio

Example 5.5

Cpk = Minimum of 26.1 – 20 , 30 – 26.1

3 ( 1.20) 3 ( 1.20)

Cpk = 0.59

Process does not meets 4-sigma level of 1.33

Process Capability Index

Cpk = Minimum of ,

x – Lower specification

3σ

Upper specification – x

3σ

Cpk = Minimum of 0.59 1.08

Example 5.5

Process Capability Failure Rates

10.04

17.58

25.11

5.40

10.40

15.40

20.40

25.40

30.40

05101520

Chart3

1 1 1 1
2 2 2 2
3 3 3 3
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12 12 12 12
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17 17 17 17
18 18 18 18
19 19 19 19
Y
LCL
Avg
UCL
10.04
17.58
25.11
17
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
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10.0434860744
17.5789470673
25.1144080602
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10.0434860744
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25.1144080602
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10.0434860744
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25.1144080602
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10.0434860744
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10.0434860744
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10.0434860744
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10.0434860744
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25.1144080602

Sheet1

8 15
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Y
LCL
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2.18
7.05
11.93
7
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903
9
2.1767448534
7.0526313782
11.928517903
7
2.1767448534
7.0526313782
11.928517903
10
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903
7
2.1767448534
7.0526313782
11.928517903
6
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903
9
2.1767448534
7.0526313782
11.928517903
5
2.1767448534
7.0526313782
11.928517903
6
2.1767448534
7.0526313782
11.928517903
7
2.1767448534
7.0526313782
11.928517903
5
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903
6
2.1767448534
7.0526313782
11.928517903
4
2.1767448534
7.0526313782
11.928517903
6
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903

Sheet2

1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
10 10 10 10
11 11 11 11
12 12 12 12
13 13 13 13
14 14 14 14
15 15 15 15
16 16 16 16
17 17 17 17
18 18 18 18
19 19 19 19
Y
LCL
Avg
UCL
10.04
17.58
25.11
17
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
18
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
16
10.0434860744
17.5789470673
25.1144080602
15
10.0434860744
17.5789470673
25.1144080602
18
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
21
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
6
10.0434860744
17.5789470673
25.1144080602
15
10.0434860744
17.5789470673
25.1144080602
17
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
18
10.0434860744
17.5789470673
25.1144080602
17
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602

Sheet3

QCCharts XYZZ
Sheet1 Chart 1 Sheet1 Chart 2
Obs Y LCL Avg UCL Obs Y LCL Avg UCL
1 7.00 2.18 7.05 11.93 1 17.00 10.04 17.58 25.11
2 8.00 2.18 7.05 11.93 2 20.00 10.04 17.58 25.11
3 9.00 2.18 7.05 11.93 3 18.00 10.04 17.58 25.11
4 7.00 2.18 7.05 11.93 4 19.00 10.04 17.58 25.11
5 10.00 2.18 7.05 11.93 5 16.00 10.04 17.58 25.11
6 8.00 2.18 7.05 11.93 6 15.00 10.04 17.58 25.11
7 7.00 2.18 7.05 11.93 7 18.00 10.04 17.58 25.11
8 6.00 2.18 7.05 11.93 8 19.00 10.04 17.58 25.11
9 8.00 2.18 7.05 11.93 9 20.00 10.04 17.58 25.11
10 9.00 2.18 7.05 11.93 10 21.00 10.04 17.58 25.11
11 5.00 2.18 7.05 11.93 11 19.00 10.04 17.58 25.11
12 6.00 2.18 7.05 11.93 12 6.00 10.04 17.58 25.11
13 7.00 2.18 7.05 11.93 13 15.00 10.04 17.58 25.11
14 5.00 2.18 7.05 11.93 14 17.00 10.04 17.58 25.11
15 8.00 2.18 7.05 11.93 15 19.00 10.04 17.58 25.11
16 6.00 2.18 7.05 11.93 16 20.00 10.04 17.58 25.11
17 4.00 2.18 7.05 11.93 17 18.00 10.04 17.58 25.11
18 6.00 2.18 7.05 11.93 18 17.00 10.04 17.58 25.11
19 8.00 2.18 7.05 11.93 19 20.00 10.04 17.58 25.11

DateNumber of DefectivesSample Sizep

08-Sep121150.104348

09-Sep141250.11200

10-Sep181110.162162

11-Sep131330.097744

12-Sep171200.141667

13-Sep151180.127119

14-Sep151370.109489

15-Sep161080.148148

16-Sep111100.10000

17-Sep141240.11290

18-Sep131280.101563

19-Sep141440.097222

20-Sep171410.120567

0.118072

݌ҧൌ

Control Chart Diagram

xbar-R

Sample 7am 8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm
1 7.127 7.125 7.123 7.127 7.128 7.125 7.126 7.126 7.127 7.128
2 7.123 7.126 7.129 7.127 7.125 7.125 7.123 7.126 7.129 7.123
3 7.123 7.121 7.129 7.124 7.126 7.127 7.123 7.127 7.128 7.122
4 7.126 7.122 7.124 7.125 7.127 7.128 7.125 7.128 7.129 7.124
Average 7.12475 7.1235 7.12625 7.12575 7.1265 7.12625 7.12425 7.12675 7.12825 7.12425 7.12565
Range (R) 0.004 0.005 0.006 0.003 0.003 0.003 0.003 0.002 0.002 0.006 0.0037
7.1283473
7.1229527
0.0084434
0

Data are collected in a face-and-plunge operation done on a lathe. The dimensions being measured is the grouve inside diameter (ID), which has a tolerance of 7.125 ± 0.010. Four parts are measured every hour. These values have been entered in the table below.

xbar-S

Subgroup Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Obs 6 Obs 7 Obs 8 Obs 9 Obs 10
1 46.8204 58.8572 67.7175 51.3078 53.3025 51.3258 59.0268 49.9933 47.086 60.4783
2 53.9847 47.4005 59.1598 57.2251 57.3207 50.4045 54.8046 55.7574 58.8662 59.2083
3 52.4315 63.2146 61.4096 59.342 57.4605 53.7083 57.0489 58.4325 48.5544 61.4105
4 50.9712 53.4314 52.9449 66.827 43.9849 67.8154 57.4312 44.3194 60.5493 59.6383
5 62.0421 57.1784 60.1955 56.4687 64.9641 52.9195 48.6739 56.3773 60.3216 58.9171
6 53.1269 58.374 63.7938 50.8965 52.4253 52.696 64.2078 65.9364 55.8426 54.478
7 55.0507 53.8931 51.8424 68.7073 50.173 58.0991 59.3456 57.9232 69.2396 60.2033
8 54.3315 52.3679 65.2346 62.6795 61.5929 54.0084 61.4465 58.4423 55.7608 54.1888
9 59.9584 59.1762 51.5629 63.0753 59.4856 63.2215 50.8982 62.4343 49.4303 48.9902
10 54.0402 56.3253 53.3773 54.7368 59.8292 54.6631 62.2161 61.5533 66.2283 63.0929
11 57.2273 65.8816 67.9839 51.7812 63.3054 56.5156 54.5318 54.4049 54.6459 52.6297
12 51.5133 61.0216 61.2776 62.1072 56.1983 54.805 59.083 58.8301 51.2939 54.9033
13 41.6784 46.7246 90.9593 57.7698 57.6619 53.9903 47.1248 50.2183 52.0052 57.2942
14 52.8303 42.4179 58.0054 60.1385 59.9954 60.5936 49.6827 68.2645 53.5693 60.6435
15 58.1128 53.4343 49.8567 53.3065 48.6588 53.4726 61.1457 61.6733 54.4246 51.8054
16 59.4674 66.2816 71.1186 63.6602 65.4012 53.2372 55.0633 46.6954 57.0477 61.8819
17 63.6288 47.3453 45.6509 40.2198 51.7382 51.0804 56.4197 57.7979 65.3047 66.539
18 59.5853 50.9825 56.2445 103.441 52.6224 63.7297 43.3771 58.7982 59.8339 57.9202
19 57.8042 49.2275 56.9069 55.4057 60.342 62.0972 57.2 38.6509 61.459 59.144
20 53.2788 62.1238 48.7058 58.0984 52.3153 56.8277 53.3615 64.6894 56.0133 56.9455
21 61.0891 52.2114 55.0061 50.2427 55.6495 53.7419 63.6856 56.5452 55.6084 67.2915
22 47.6385 62.0744 71.2102 64.6661 58.1218 56.8151 62.913 53.8949 64.6937 53.5819
23 46.1471 57.2321 60.0446 59.5476 54.4676 48.8446 57.6602 58.5467 65.4449 50.6271
24 53.1199 52.4063 53.1227 52.1897 56.6952 53.0823 61.1469 50.5565 56.9315 60.0423
25 55.3156 60.7648 55.0855 56.2381 60.3981 61.7266 69.0841 51.4446 58.1248 50.136
54.447776 55.613932 59.53668 59.20314 56.564392 55.976856 57.06316 56.087208 57.531196 57.679648 56.9703988
5.2864584811 6.2894901987 9.4947599494 11.1065617562 5.1475848615 4.750668222 5.9335003653 6.8355648021 5.7657197454 4.830526936 6.5440835318
60.9361134202
53.0046841798
9.3907598681
3.6974071954

I-mR

Reading Individual Data Element
1 290
2 288 2
3 285 3
4 290 5
5 291 1
6 287 4
7 284 3
8 290 6
9 290 0
10 288 2
288.3 2.8888888889
295.9844444444
280.6155555556
9.438
0

c-chart

Date Number of Defects Sample Size
15-May 19 150
16-May 12 150
17-May 13 150
18-May 12 150
19-May 18 150
20-May 19 150
21-May 17 150
22-May 20 150
23-May 22 150
24-May 18 150
25-May 19 150
26-May 17 150
27-May 11 150
217
16.6923076923
28.9491738999
4.4354414847

Panes of glass are inspected for defects such as bubbles, scratches, chips, inclusions, waves and dips. The results of the inspection are given in the table below.

u-chart

Date Number of Defects Sample Size
4-Jul 4 125 0.1048159691 -0.0112558233
5-Jul 8 111 0.1083672378 -0.014807092
6-Jul 3 133 0.103043461 -0.0094833152
7-Jul 7 120 0.1060127114 -0.0124525656
8-Jul 5 118 0.1065125738 -0.0130
9-Jul 5 137 0.1022160132 -0.0086558674
10-Jul 6 108 0.1092167561 -0.0156566103
11-Jul 10 110 0.1086465461 -0.0150864003
12-Jul 4 124 0.1050495149 -0.0114893691
13-Jul 3 128 0.1041318286 -0.0105716827
14-Jul 4 144 0.1008518267 -0.0072916809
15-Jul 7 138 0.1020147931 -0.0084546473
16-Jul 11 150 0.0997593554 -0.0061992096
sum 77 1646
0.0467800729

Panes of glass are inspected for defects such as bubbles, scratches, chips, inclusions, waves, and dips. The results of the inspection are given in the table below.

np-chart

Date number of defectives sample size
8-Sep 9 1000 0.009
9-Sep 12 1000 0.012
10-Sep 13 1000 0.013
11-Sep 12 1000 0.012
12-Sep 11 1000 0.011
13-Sep 9 1000 0.009
14-Sep 7 1000 0.007
15-Sep 0 1000 0
16-Sep 12 1000 0.012
17-Sep 8 1000 0.008
18-Sep 9 1000 0.009
19-Sep 7 1000 0.007
20-Sep 11 1000 0.011
0.0092307692
9.2307692308
18.3032583695
0.1582800921

Packages containing 1000 lightbulbs are randomly selected, and all 1000 bulbs are light-tested. The results of the tests are given in the below table.

p-chart

Date Number of Defectives Sample Size p LCL UCL
8-Sep 12 115 0.1043478261 0.02780 0.2083455413
9-Sep 14 125 0.11200 0.0314840857 0.2046593271
10-Sep 18 111 0.1621621622 0.0261857113 0.2099577015
11-Sep 13 133 0.0977443609 0.0341286086 0.2020148041
12-Sep 17 120 0.1416666667 0.02970 0.2064448267
13-Sep 15 118 0.1271186441 0.0289528081 0.2071906046
14-Sep 15 137 0.1094890511 0.0353631332 0.2007802796
15-Sep 16 108 0.1481481481 0.0249182584 0.2112251544
16-Sep 11 110 0.10000 0.0257689926 0.2103744202
17-Sep 14 124 0.11290 0.0311356432 0.2050077696
18-Sep 13 128 0.1015625 0.03250 0.2036386122
19-Sep 14 144 0.0972222222 0.03740 0.1987449588
20-Sep 17 141 0.1205673759 0.036544745 0.19960
0.1180717064

A test was conducted to determine the presence of the Rh factor in 13 samples of donated blood. The results of the test are given in the below table.

Constants

Sample Size = n
2 1.880 2.659 1.128 0 3.267 0 3.267 2.660
3 1.023 1.954 1.693 0 2.574 0 2.568 1.772
4 0.729 1.628 2.059 0 2.282 0 2.266 1.457
5 0.577 1.427 2.326 0 2.114 0 2.089 1.290
6 0.483 1.287 2.534 0 2.004 0.030 1.970 1.184
7 0.419 1.182 2.704 0.076 1.924 0.118 1.882 1.109
8 0.373 1.099 2.847 0.136 1.864 0.185 1.815 1.054
9 0.337 1.032 2.970 0.184 1.816 0.239 1.761 1.010
10 0.308 0.975 3.078 0.223 1.777 0.284 1.716 0.975
11 0.285 0.927 3.173 0.256 1.744 0.321 1.679 0.945
12 0.266 0.886 3.258 0.283 1.717 0.354 1.646 0.921
13 0.249 0.850 3.336 0.307 1.693 0.382 1.618 0.899
14 0.235 0.817 3.407 0.328 1.672 0.406 1.594 0.881
15 0.223 0.789 3.472 0.347 1.653 0.428 1.572 0.864
16 0.212 0.763 3.532 0.363 1.637 0.448 1.552 0.849
17 0.203 0.739 3.588 0.378 1.622 0.466 1.534 0.836
18 0.194 0.718 3.640 0.391 1.608 0.482 1.518 0.824
19 0.187 0.698 3.689 0.403 1.597 0.497 1.503 0.813
20 0.180 0.680 3.735 0.415 1.585 0.510 1.490 0.803
21 0.173 0.663 3.778 0.425 1.575 0.523 1.477 0.794
22 0.167 0.647 3.819 0.434 1.566 0.534 1.466 0.786
23 0.162 0.633 3.858 0.443 1.557 0.545 1.455 0.778
24 0.157 0.619 3.895 0.451 1.548 0.555 1.445 0.770
25 0.153 0.606 3.931 0.459 1.541 0.565 1.435 0.763

DateNumber of DefectivesSample SizeLCLUCL

08-Sep121150.027150.207052

09-Sep141250.030820.203379

10-Sep181110.025540.208658

11-Sep131330.033460.200743

12-Sep171200.029040.205158

13-Sep151180.028300.205901

14-Sep151370.034690.199513

15-Sep161080.024280.209921

16-Sep111100.025130.209073

17-Sep141240.030470.203726

18-Sep131280.031840.202361

19-Sep141440.036720.197485

20-Sep171410.035860.198336

0.11710037

݌ҧൌ

Control Chart Diagram

xbar-R

Sample 7am 8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm
1 7.127 7.125 7.123 7.127 7.128 7.125 7.126 7.126 7.127 7.128
2 7.123 7.126 7.129 7.127 7.125 7.125 7.123 7.126 7.129 7.123
3 7.123 7.121 7.129 7.124 7.126 7.127 7.123 7.127 7.128 7.122
4 7.126 7.122 7.124 7.125 7.127 7.128 7.125 7.128 7.129 7.124
Average 7.12475 7.1235 7.12625 7.12575 7.1265 7.12625 7.12425 7.12675 7.12825 7.12425 7.12565
Range (R) 0.004 0.005 0.006 0.003 0.003 0.003 0.003 0.002 0.002 0.006 0.0037
7.1283473
7.1229527
0.0084434
0

Data are collected in a face-and-plunge operation done on a lathe. The dimensions being measured is the grouve inside diameter (ID), which has a tolerance of 7.125 ± 0.010. Four parts are measured every hour. These values have been entered in the table below.

xbar-S

Subgroup Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Obs 6 Obs 7 Obs 8 Obs 9 Obs 10
1 46.8204 58.8572 67.7175 51.3078 53.3025 51.3258 59.0268 49.9933 47.086 60.4783
2 53.9847 47.4005 59.1598 57.2251 57.3207 50.4045 54.8046 55.7574 58.8662 59.2083
3 52.4315 63.2146 61.4096 59.342 57.4605 53.7083 57.0489 58.4325 48.5544 61.4105
4 50.9712 53.4314 52.9449 66.827 43.9849 67.8154 57.4312 44.3194 60.5493 59.6383
5 62.0421 57.1784 60.1955 56.4687 64.9641 52.9195 48.6739 56.3773 60.3216 58.9171
6 53.1269 58.374 63.7938 50.8965 52.4253 52.696 64.2078 65.9364 55.8426 54.478
7 55.0507 53.8931 51.8424 68.7073 50.173 58.0991 59.3456 57.9232 69.2396 60.2033
8 54.3315 52.3679 65.2346 62.6795 61.5929 54.0084 61.4465 58.4423 55.7608 54.1888
9 59.9584 59.1762 51.5629 63.0753 59.4856 63.2215 50.8982 62.4343 49.4303 48.9902
10 54.0402 56.3253 53.3773 54.7368 59.8292 54.6631 62.2161 61.5533 66.2283 63.0929
11 57.2273 65.8816 67.9839 51.7812 63.3054 56.5156 54.5318 54.4049 54.6459 52.6297
12 51.5133 61.0216 61.2776 62.1072 56.1983 54.805 59.083 58.8301 51.2939 54.9033
13 41.6784 46.7246 90.9593 57.7698 57.6619 53.9903 47.1248 50.2183 52.0052 57.2942
14 52.8303 42.4179 58.0054 60.1385 59.9954 60.5936 49.6827 68.2645 53.5693 60.6435
15 58.1128 53.4343 49.8567 53.3065 48.6588 53.4726 61.1457 61.6733 54.4246 51.8054
16 59.4674 66.2816 71.1186 63.6602 65.4012 53.2372 55.0633 46.6954 57.0477 61.8819
17 63.6288 47.3453 45.6509 40.2198 51.7382 51.0804 56.4197 57.7979 65.3047 66.539
18 59.5853 50.9825 56.2445 103.441 52.6224 63.7297 43.3771 58.7982 59.8339 57.9202
19 57.8042 49.2275 56.9069 55.4057 60.342 62.0972 57.2 38.6509 61.459 59.144
20 53.2788 62.1238 48.7058 58.0984 52.3153 56.8277 53.3615 64.6894 56.0133 56.9455
21 61.0891 52.2114 55.0061 50.2427 55.6495 53.7419 63.6856 56.5452 55.6084 67.2915
22 47.6385 62.0744 71.2102 64.6661 58.1218 56.8151 62.913 53.8949 64.6937 53.5819
23 46.1471 57.2321 60.0446 59.5476 54.4676 48.8446 57.6602 58.5467 65.4449 50.6271
24 53.1199 52.4063 53.1227 52.1897 56.6952 53.0823 61.1469 50.5565 56.9315 60.0423
25 55.3156 60.7648 55.0855 56.2381 60.3981 61.7266 69.0841 51.4446 58.1248 50.136
54.447776 55.613932 59.53668 59.20314 56.564392 55.976856 57.06316 56.087208 57.531196 57.679648 56.9703988
5.2864584811 6.2894901987 9.4947599494 11.1065617562 5.1475848615 4.750668222 5.9335003653 6.8355648021 5.7657197454 4.830526936 6.5440835318
60.9361134202
53.0046841798
9.3907598681
3.6974071954

I-mR

Reading Individual Data Element
1 290
2 288 2
3 285 3
4 290 5
5 291 1
6 287 4
7 284 3
8 290 6
9 290 0
10 288 2
288.3 2.8888888889
295.9844444444
280.6155555556
9.438
0

c-chart

Date Number of Defects Sample Size
15-May 19 150
16-May 12 150
17-May 13 150
18-May 12 150
19-May 18 150
20-May 19 150
21-May 17 150
22-May 20 150
23-May 22 150
24-May 18 150
25-May 19 150
26-May 17 150
27-May 11 150
217
16.6923076923
28.9491738999
4.4354414847

Panes of glass are inspected for defects such as bubbles, scratches, chips, inclusions, waves and dips. The results of the inspection are given in the table below.

u-chart

Date Number of Defects Sample Size
4-Jul 4 125 0.1048159691 -0.0112558233
5-Jul 8 111 0.1083672378 -0.014807092
6-Jul 3 133 0.103043461 -0.0094833152
7-Jul 7 120 0.1060127114 -0.0124525656
8-Jul 5 118 0.1065125738 -0.0130
9-Jul 5 137 0.1022160132 -0.0086558674
10-Jul 6 108 0.1092167561 -0.0156566103
11-Jul 10 110 0.1086465461 -0.0150864003
12-Jul 4 124 0.1050495149 -0.0114893691
13-Jul 3 128 0.1041318286 -0.0105716827
14-Jul 4 144 0.1008518267 -0.0072916809
15-Jul 7 138 0.1020147931 -0.0084546473
16-Jul 11 150 0.0997593554 -0.0061992096
sum 77 1646
0.0467800729

Panes of glass are inspected for defects such as bubbles, scratches, chips, inclusions, waves, and dips. The results of the inspection are given in the table below.

np-chart

Date number of defectives sample size
8-Sep 9 1000 0.009
9-Sep 12 1000 0.012
10-Sep 13 1000 0.013
11-Sep 12 1000 0.012
12-Sep 11 1000 0.011
13-Sep 9 1000 0.009
14-Sep 7 1000 0.007
15-Sep 0 1000 0
16-Sep 12 1000 0.012
17-Sep 8 1000 0.008
18-Sep 9 1000 0.009
19-Sep 7 1000 0.007
20-Sep 11 1000 0.011
0.0092307692
9.2307692308
18.3032583695
0.1582800921

Packages containing 1000 lightbulbs are randomly selected, and all 1000 bulbs are light-tested. The results of the tests are given in the below table.

p-chart

Date Number of Defectives Sample Size LCL UCL
8-Sep 12 115 0.02715 0.2070516084
9-Sep 14 125 0.03082 0.203378567
10-Sep 18 111 0.02554 0.2086580074
11-Sep 13 133 0.03346 0.2007434944
12-Sep 17 120 0.02904 0.205157686
13-Sep 15 118 0.02830 0.2059007989
14-Sep 15 137 0.03469 0.1995133815
15-Sep 16 108 0.02428 0.209920931
16-Sep 11 110 0.02513 0.2090732369
17-Sep 14 124 0.03047 0.2037257644
18-Sep 13 128 0.03184 0.2023614997
19-Sep 14 144 0.03672 0.1974853341
20-Sep 17 141 0.03586 0.1983359923
0.1171003717

A test was conducted to determine the presence of the Rh factor in 13 samples of donated blood. The results of the test are given in the below table.

Constants

Sample Size = n
2 1.880 2.659 1.128 0 3.267 0 3.267 2.660
3 1.023 1.954 1.693 0 2.574 0 2.568 1.772
4 0.729 1.628 2.059 0 2.282 0 2.266 1.457
5 0.577 1.427 2.326 0 2.114 0 2.089 1.290
6 0.483 1.287 2.534 0 2.004 0.030 1.970 1.184
7 0.419 1.182 2.704 0.076 1.924 0.118 1.882 1.109
8 0.373 1.099 2.847 0.136 1.864 0.185 1.815 1.054
9 0.337 1.032 2.970 0.184 1.816 0.239 1.761 1.010
10 0.308 0.975 3.078 0.223 1.777 0.284 1.716 0.975
11 0.285 0.927 3.173 0.256 1.744 0.321 1.679 0.945
12 0.266 0.886 3.258 0.283 1.717 0.354 1.646 0.921
13 0.249 0.850 3.336 0.307 1.693 0.382 1.618 0.899
14 0.235 0.817 3.407 0.328 1.672 0.406 1.594 0.881
15 0.223 0.789 3.472 0.347 1.653 0.428 1.572 0.864
16 0.212 0.763 3.532 0.363 1.637 0.448 1.552 0.849
17 0.203 0.739 3.588 0.378 1.622 0.466 1.534 0.836
18 0.194 0.718 3.640 0.391 1.608 0.482 1.518 0.824
19 0.187 0.698 3.689 0.403 1.597 0.497 1.503 0.813
20 0.180 0.680 3.735 0.415 1.585 0.510 1.490 0.803
21 0.173 0.663 3.778 0.425 1.575 0.523 1.477 0.794
22 0.167 0.647 3.819 0.434 1.566 0.534 1.466 0.786
23 0.162 0.633 3.858 0.443 1.557 0.545 1.455 0.778
24 0.157 0.619 3.895 0.451 1.548 0.555 1.445 0.770
25 0.153 0.606 3.931 0.459 1.541 0.565 1.435 0.763

𝐶

𝑝

𝑣𝑎𝑙𝑢𝑒 𝑍 𝑣𝑎𝑙𝑢𝑒 𝑝𝑝𝑚

0.33 1.00 317,311

0.67 2.00 45,500

1.00 3.00 2,700

1.10 3.30 967

1.20 3.60 318

1.30 3.90 96

1.33 4.00 63

1.40 4.20 27

1.50 4.50 6.8

1.60 4.80 1.6

1.67 5.00 0.57

1.80 5.40 0.067

2.00 6.00 0.002