Statistics Process Improvement Project PPT?

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MBC638

Data Analysis

*

DEFINE

MEASURE

Process Improvement Project – Cycle Time Reduction

Team Launch

8/23

Define

9/08

Measure

10/16

Analyze

10/24

Control

On-Going

Improve

10/31

Key Dates --->

ANALYZE

IMPROVE

Process owner: Dan

CONTROL

PROJECT TEAM: Dan  Mary  Karen  Linda  Peter

BUSINESS CASE: $54,000 in annual processing costs

It takes 43 days to process a grant application. Only 8% of applications are being processed within 30 days of receipt. The time to process the application has lead to unhappy applicants and staff who are finding more and more of their daily work time being devoted to “grant administration.” The funding levels available to applicants and the number of applications are expected to increase in the near future, which has the potential to compound the problem.

Defects/delays are inherent in the current process. Current SQL is 1.9

The Number of applications received is increasing.

The time to complete a process cycle is also increasing.

Problem: Incomplete and inaccurate applications were identified as the primary factor leading to defects in the process cycle.

Solution: New Application process incorporating drop down menus

New Application Procedure =

Less Mistakes & Quicker Cycle Time

The defect rate reduced from 93% to 32%

Monthly monitor and review procedure is in place. Out of control signal = action plan.

↑ Number of Applications + ↑ Cycle Process Time __Tough Times Ahead

*

DEFINE

MEASURE

Closing the Gap in Incoming Material Analysis

Team Launch

Define

Measure

Analyze

Control

Improve

Key Dates --->

ANALYZE

IMPROVE

Process owner: Bob

CONTROL

Buyer (myself), Vendor, Quality, Accounting, Manufacturing

September 8

October 10

November 10

January 10

September 14

January 15

  • Longer lead time for vendor payment.
  • Additional time reconciling invoices.
  • Increased inventory levels waiting for third party analysis.
  • Animosity in relationship.

25% discrepancies between Receiving & Vendor lead to:

reproducibility

= .0022

Precision-to-total ratio = .4315

Capability ratio = .66

Unacceptable

Measurement

System

  • Define how much discrepancy is defined by the process
  • Create clearer operational definitions
  • Modified Process Map to catch defects
  • Create Standard Operating Procedures
  • Expand improvements to other vendors

Compare analysis on identical samples (DOE)

Maintain lot identity

Standardize sampling and analysis

The “variation” Receiving found

Chart4

0.7215 0.733
0.7289 0.741
0.7298 0.735
0.731 0.715
0.7318 0.72
0.7312 0.711
0.7295 0.726
0.731 0.734
0.7305 0.733
0.728 0.731
0.731 0.728
0.73 0.712
0.7295 0.719
0.73 0.727
0.7315 0.726
0.7285 0.729
0.7318 0.733
0.731 0.727
0.7312 0.714
0.7292 0.725
0.7272 0.727
0.7278 0.729
0.7269 0.735
0.728 0.734
0.7278 0.728
0.727 0.73
0.732 0.734
0.7312 0.734
0.7325 0.731
0.7318 0.733
0.7328 0.741
0.7322 0.737
0.7335 0.736
0.735 0.728
0.7356 0.733
0.7342 0.727
0.7345 0.738
0.7338 0.729
0.7348 0.737
0.7365 0.734
0.739 0.736
0.7382 0.722
0.7375 0.732
0.7362 0.725
0.7358 0.734
0.736 0.741
0.7348 0.734
0.734 0.734
0.733 0.734
0.7335 0.73
0.7322 0.731
0.7328 0.74
0.7325 0.738
0.7329 0.731
0.7261 0.739
0.7315 0.74
0.73 0.736
0.735 0.739
0.731 0.741
0.7312 0.738
0.732 0.732
Beralt
OSI
Beralt - OSI Ore Comparison

Suppliers FY08

Supplier STUs Cumulative % %
Beralt 121.9 23.11% 23.11%
DLA 111.2 44.20% 21.08% 65.21%
Spot 80 59.37% 15.17%
Cantung 72.3 73.08% 13.71%
Dynacor 71.4 86.61% 13.54%
Heemskirk 46.8 95.49% 8.87%
KMT 16.8 98.67% 3.19%
Other 7 100.00% 1.33%
527.4
Pareto

Suppliers FY08

0 0
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&A
Page &P
STUs
Cumulative %
STUs
Tungsten Ore Suppliers FY08

Dynacor

lot Dynacor Analysis OSI Analysis Difference Population Sample of last 20 lots
1 73.50% 74.50% 1.00%
2 75.36% 75.10% -0.26%
3 75.78% 75.20% -0.58% Dynacor
4 75.68% 75.20% -0.48%
5 75.23% 75.20% -0.03% Mean 0.7531547619
6 75.15% 75.60% 0.45% Standard Error 0.0005393807
7 75.39% 75.70% 0.31% Median 0.7535
8 74.69% 75.50% 0.81% Mode 0.7549
9 75.49% 75.60% 0.11% Standard Deviation 0.0034955862
10 75.71% 75.60% -0.11% Sample Variance 0.0000122191
11 75.40% 75.30% -0.10% Kurtosis 17.8674511313
12 75.27% 75.60% 0.33% Skewness -3.6031269153
13 75.34% 75.60% 0.26% Range 0.0228
14 75.34% 75.60% 0.26% Minimum 0.735
15 74.96% 75.10% 0.14% Maximum 0.7578
16 75.01% 75.40% 0.39% Sum 31.6325
17 75.28% 75.50% 0.22% Count 42
18 75.49% 75.40% -0.09%
19 75.31% 75.30% -0.01%
20 75.30% 75.60% 0.30%
21 75.40% 75.00% -0.40% OSI
22 75.08% 75.20% 0.12%
23 75.28% 75.50% 0.22% Mean 0.7530238095
24 75.27% 75.50% 0.23% Standard Error 0.000464148
25 75.49% 75.60% 0.11% Median 0.7535
26 75.46% 75.70% 0.24% Mode 0.756
27 75.20% 75.10% -0.10% Standard Deviation 0.0030080226
28 75.28% 75.30% 0.02% Sample Variance 0.0000090482
29 75.29% 75.50% 0.21% Kurtosis -0.1311559736
30 75.48% 74.80% -0.68% Skewness -0.7805090956
31 75.35% 74.90% -0.45% Range 0.012
32 75.31% 75.60% 0.29% Minimum 0.745
33 75.52% 75.50% -0.02% Maximum 0.757
34 75.57% 74.80% -0.77% Sum 31.627
35 75.43% 75.50% 0.07% Count 42
36 75.33% 74.90% -0.43%
37 75.35% 74.70% -0.65%
38 75.41% 75.30% -0.11%
39 75.49% 74.90% -0.59%
40 75.39% 75.30% -0.09%
41 75.58% 75.40% -0.18%
42 75.61% 75.10% -0.51%
43 -0.01%
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Dynacor

0.735 0.745
0.7536 0.751
0.7578 0.752
0.7568 0.752
0.7523 0.752
0.7515 0.756
0.7539 0.757
0.7469 0.755
0.7549 0.756
0.7571 0.756
0.754 0.753
0.7527 0.756
0.7534 0.756
0.7534 0.756
0.7496 0.751
0.7501 0.754
0.7528 0.755
0.7549 0.754
0.7531 0.753
0.753 0.756
0.754 0.75
0.7508 0.752
0.7528 0.755
0.7527 0.755
0.7549 0.756
0.7546 0.757
0.752 0.751
0.7528 0.753
0.7529 0.755
0.7548 0.748
0.7535 0.749
0.7531 0.756
0.7552 0.755
0.7557 0.748
0.7543 0.755
0.7533 0.749
0.7535 0.747
0.7541 0.753
0.7549 0.749
0.7539 0.753
0.7558 0.754
0.7561 0.751
Dynacor Analysis
OSI Analysis
%W
W Content by lot

Beralt

Lot Beralt OSI Difference Rec'd date
BS261/191 72.15% 73.30% 1.15% 9-Feb
BS261/192 72.89% 74.10% 1.21% 9-Feb
BS261/193 72.98% 73.50% 0.52% 16-Feb
BS261/194 73.10% 71.50% -1.60% 27-Feb
BS261/195 73.18% 72.00% -1.18% 27-Feb
BS261/196 73.12% 71.10% -2.02% 2-Mar
BS261/197 72.95% 72.60% -0.35% 16-Mar
BS261/198 73.10% 73.40% 0.30% 16-Mar
BS261/199 73.05% 73.30% 0.25% 15-Mar
BS261/200 72.80% 73.10% 0.30% 23-Mar
BS261/201 73.10% 72.80% -0.30% 27-Mar
BS261/202 73.00% 71.20% -1.80% 30-Mar
BS261/203 72.95% 71.90% -1.05% 2-Apr
BS261/204 73.00% 72.70% -0.30% 2-Apr
BS261/205 73.15% 72.60% -0.55% 13-Apr
BS261/206 72.85% 72.90% 0.05% 20-Apr
BS261/207 73.18% 73.30% 0.12% 19-Apr
BS261/208 73.10% 72.70% -0.40% 2-May
BS261/209 73.12% 71.40% -1.72% 17-May
BS261/210 72.92% 72.50% -0.42% 10-May
BS261/211 72.72% 72.70% -0.02% 10-May
BS261/212 72.78% 72.90% 0.12% 16-May
BS261/213 72.69% 73.50% 0.81% 21-May
BS261/214 72.80% 73.40% 0.60% 21-May
BS261/215 72.78% 72.80% 0.02% 29-May
BS261/216 72.70% 73.00% 0.30% 7-Jun lots that were sent to run twice in random order:
BS261/217 73.20% 73.40% 0.20% 12-Jun
BS261/218 73.12% 73.40% 0.28% 13-Jun
BS261/219 73.25% 73.10% -0.15% 19-Jun
BS261/220 73.18% 73.30% 0.12% 19-Jun
BS261/221 73.28% 74.10% 0.82% 27-Jun
BS261/222 73.22% 73.70% 0.48% 28-Jun
BS261/223 73.35% 73.60% 0.25% 9-Jul
BS261/224 73.50% 72.80% -0.70% 9-Jul
BS261/225 73.56% 73.30% -0.26% 23-Jul
BS261/226 73.42% 72.70% -0.72% 23-Jul
BS261/227 73.45% 73.80% 0.35% 26-Jul
BS261/228 73.38% 72.90% -0.48% 2-Aug
BS261/229 73.48% 73.70% 0.22% 2-Aug
BS261/230 73.65% 73.40% -0.25% 14-Aug
BS261/231 73.90% 73.60% -0.30% 15-Aug
BS261/232 73.82% 72.20% -1.62% 16-Aug
BS261/233 73.75% 73.20% -0.55% 16-Aug
BS261/234 73.62% 72.50% -1.12% 22-Aug
BS261/235 73.58% 73.40% -0.18% 22-Aug
BS261/236 73.60% 74.10% 0.50% 24-Sep
BS261/237 73.48% 73.40% -0.08% 3-Oct
BS261/238 73.40% 73.40% 0.00% 2-Oct
BS261/239 73.30% 73.40% 0.10% 15-Oct
BS261/240 73.35% 73.00% -0.35% 15-Oct
BS261/241 73.22% 73.10% -0.12% 17-Oct
BS261/242 73.28% 74.00% 0.72% 23-Oct
BS261/243 73.25% 73.80% 0.55% 22-Oct
BS261/244 73.29% 73.10% -0.19% 7-Nov
BS261/245 72.61% 73.90% 1.29% 19-Nov
BS261/246 73.15% 74.00% 0.85% 19-Nov
BS261/247 73.00% 73.60% 0.60% 20-Nov
BS261/248 73.50% 73.90% 0.40% 20-Nov
BS261/249 73.10% 74.10% 1.00% 3-Dec
BS261/250 73.12% 73.80% 0.68% 4-Dec
BS261/251 73.20% 73.20% 0.00% 30-Nov
-0.06%

Beralt

0 0
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Beralt
OSI
Beralt - OSI Ore Comparison

Process Map
Vendor notifies Towanda of shipment and ETA Vendor provides tungsten content
Ore is weighed sampled and analyzed
Container arrives in Towanda
Ore is not removed from quality hold without vendor approval Ore is transferred to the dept for consumption
Vendor invoices Towanda based on their weight and analysis for tungsten content
Invoice entered into SAP for payment
Vendor invoice is reconciled to Towanda weight and tungsten content
Vendor issues credit or debit memo
Credit or debit memo is entered into SAP

Stratification

Data Stratification Tree
Questions About Process Stratification factors Measurements
X Variables
Can the reconciliation process be eliminated?
How can discrepancies be tracked? Supplier W content
Is the supplier performing the same analysis to determine tungsten content? Osram W content * Discrepancy between W content from supplier,
How much of a discrepancy would constitute a third party analysis? Payment based on W content Third Party W content Osram and third party by lot.
Can the tungsten concentrate be held if a discrepancy evolves? (output y1) Invoice
Would going to strictly third party analysis resolve the pain in the process? Credit/Debit Memo
Could a pre-sample be air shipped to shorten the lead time in determining a discrepancy? Purchase Order
Which analysis is more advantageous to use for future contracts?

*

DEFINE

MEASURE

Process Improvement Project – Graphing Time Reduction

Mike – MBC 638

Team Launch

5/11/08

Define

5/19/08

Measure

5/26/08

Analyze

6/6/08

Control

On-Going

Improve

7/4/08

Key Dates --->

ANALYZE

IMPROVE

BUSINESS CASE: $18,943 Annual Cost Reduction if Implemented in Engineering Department

  • Extensive graphing is required for good data analysis of lab qualification testing

  • 350 Engineer hours in the department are spent on repetitive graphing procedures within Excel. This equates to $52,471/year

  • A 30% reduction in graphing time could result in a $15,741 annual savings.

$

=

Sigma Quality Level

Increased from 1.72

to 3.26

$18,943 annual cost reduction!

$

Eliminated wasteful, repetitive steps that can be automated with Excel Macros

Pareto showed that 80% of graphs consisted of 8 variables or less

95% confidence interval that true graphing time is 57 +/- 5.16 seconds

Hypothesis test indicates 88% confidence that new process meets the goal of at least a 30% improvement in graphing time

Identified Critical Inputs and Outputs to Measure

Measurement Systems Analysis using X-bar, R Charts and Precision-To-Total Ratio

R Charts in control.

Xbar Charts show ability to

measure differences

PTR = 0.22

Control

  • Maintain Revision Control on original spreadsheet macros
  • Provide to Engineering Department
  • Survey engineers for usage in 3 months

Chart1

35 59.1 66.244 51.956
59.5 59.1 66.244 51.956
93 59.1 66.244 51.956
46.5 59.1 66.244 51.956
61.5 59.1 66.244 51.956
xbar
Xbar2
UCL
LCL
Run #
Xbar
Day 1/Operator 1 - Xbar Chart

DataStratification

Data Stratification Tree
Questions about Process Output Stratification Factors Measurements
X Output
Is y affected by the number of data points recorded in a test? X1 = Total Data points collected Number of data points collected
Is y affected by the total number of columns graphed? Y = Graphing Time = f (X) Number of different variables measured
Is y affected by the person creating the graphs? Name of engineer
Is y affected by the quality of the graph required? Title, labels, presentation ready
Is y affected by additional graphs required for comparison? Number of graphs
Is y affected by the total number of columns of data available? Total number of available variables

Costs

Cost Reduction
Current Improved
Tests/month/engineer 60 60
Tests/year/engineer 11100 11100
Engineers 4 4
Total tests/year 44400 44400
$/hour 150 150
Graphs/test 1 1
Graphs/year 22200 22200
Time per graph (sec) 57 36
Time spent graphing/year (hr) 350 224
Annual Cost Reduction $ 52,471 $ 33,529
% Percent Annual Cost Reduction 36%
$ 15,741.41

Initial Data Collection

Run Number of Data Points Collected Total Number of Different Variables Included in Graphs Total number of available variables Name of Operator Title, Labels, Presentation Number of Graphs Time (sec) Time per Graph (sec) Number of data points collected
1 308 4 129 MB Yes 1 51 51 Column1 Number of different variables measured
2 31 4 160 MB Yes 1 58 58.0 Name of engineer
3 820 8 160 MB Yes 2 158 79.0 Mean 56.7258064516 Title, labels, presentation ready
4 31 1 155 MB Yes 1 43 43.0 Standard Error 2.6336276364 Number of graphs
5 820 7 160 MB Yes 1 95 95.0 Median 53 Total number of available variables
6 760 7 160 MB Yes 1 83 83.0 Mode 51
7 61 24 155 MB Yes 1 53 53.0 Standard Deviation 14.663418099
8 362 4 162 MB Yes 1 56 56.0 Sample Variance 215.0158303465
9 362 6 162 MB Yes 2 109 54.5 Kurtosis 0.5911961314
10 482 16 131 MB Yes 2 140 70.0 Skewness 1.0232211831
11 308 8 129 MB Yes 3 174 58.0 Range 57
12 743 3 160 MB Yes 1 70 70.0 Minimum 38
13 30 2 164 MB Yes 1 54 54.0 Maximum 95
14 30 29 164 MB Yes 1 69 69.0 Sum 1758.5
15 30 8 125 MB Yes 1 43 43.0 Count 31
16 31 6 159 MB Yes 3 119 39.7 Confidence Level(95.0%) 5.3785796423
17 30 3 164 MB Yes 1 52 52.0 n= 31
18 30 4 168 MB Yes 1 67 67.0 x bar (sec) = 56.7 39.7080645161
19 173 6 156 MB Yes 2 118 59.0 s = 14.7
20 30 4 168 MB Yes 1 44 44.0 1- alpha = 0.95
21 31 6 129 MB Yes 2 112 56.0 alpha = 0.05
22 143 2 30 MB Yes 1 48 48.0 alpha/2 = 0.025
23 31 12 123 MB Yes 2 105 52.5
24 31 13 123 MB Yes 2 79 39.5 U= 61.89
25 362 8 162 MB Yes 2 87 43.5 L= 51.56
26 30 8 168 MB Yes 1 51 51.0 95% Confidence Interval for the true average graphing time
27 451 4 218 MB Yes 1 88 88.0 51.56 <= Population Mean <= 61.89
28 121 6 218 MB Yes 3 156 52.0 57 +/- 5.16 seconds
29 31 6 218 MB Yes 2 105 52.5
30 175 4 218 MB Yes 2 76 38.0
31 141 13 218 MB Yes 3 118 39.3 Find SQL
SQL Baseline
Population Mean = 56.7
Std Deviation = 14.7
The sample size I chose for my initial baseline estimate of the population statistics was based on time constraints and the Central Limit Theorem. For almost all populations, the sampling distribution of the mean can be approximated closely by a normal d X2 (Upper Spec Limit) 60
Z2 = 0.223
P(X>60) = 0.412
P(X is out of spec) = 0.412
DPM = 411655
SQL = 1.72
Number of Variables 1 to 4 5 to 7 8 to 10 11 to 13 >13
Total 12.0 8.0 5.0 3.0 3.0
% 38.7% 25.8% 16.1% 9.7% 9.7%
Cumul Freq 38.7% 64.5% 80.6% 90.3% 100.0%

Initial Data Collection

0 0
0 0
0 0
0 0
0 0
cumulative Frequency
Number Variables
Cumulative Frequency
Pareto Diagram of Number of Variables Graphed

Process Improved Data

Run Number of Data Points Collected Total Number of Different Variables Included in Graphs Total number of available variables Name of Operator Title, Labels, Presentation Number of Graphs Time (sec) Time per Graph (sec)
Determine Sample Size That would be required 1 308 4 129 MB Yes 1 33 33
2 31 4 160 MB Yes 1 25 25.0
Before process improvement 3 820 8 160 MB Yes 2 54 27.0
U / L = 86.48 +/- 13.05 4 31 1 155 MB Yes 1 14 14.0
After process Improvement 5 820 7 160 MB Yes 1 54 54.0
Desire 95% confidence interval that produces an interval half width of only 5 seconds 6 760 7 160 MB Yes 1 53 53.0
7* 61 24 155 MB Yes 1 53 53.0
Z = 95% 8 362 4 162 MB Yes 1 29 29.0
1- alpha = 0.95 9 362 6 162 MB Yes 2 62 31.0
1- alpha/2 = 0.975 10* 482 16 131 MB Yes 2 140 70.0
Confidence = Z(.975) = 1.96 11 308 8 129 MB Yes 3 79 26.3
Est Pop Std Deviation = 13.48 12 743 3 160 MB Yes 1 35 35.0
n = 28 13 30 2 164 MB Yes 1 25 25.0
14* 30 29 164 MB Yes 1 69 69.0
15 30 8 125 MB Yes 1 40 40.0
Column1 16 31 6 159 MB Yes 3 71 23.7
17 30 3 164 MB Yes 1 34 34.0
Mean 36.247311828 18 30 4 168 MB Yes 1 45 45.0
Standard Error 2.4214650296 19 173 6 156 MB Yes 2 56 28.0
Median 33 20 30 4 168 MB Yes 1 36 36.0
Mode 25 21 31 6 129 MB Yes 2 59 29.5
Standard Deviation 13.4821466974 22 143 2 30 MB Yes 1 22 22.0
Sample Variance 181.7682795699 23* 31 12 123 MB Yes 2 105 52.5
Kurtosis 0.6312076295 24* 31 13 123 MB Yes 2 79 39.5
Skewness 1.003498986 25 362 8 162 MB Yes 2 69 34.5
Range 56 26 30 8 168 MB Yes 1 47 47.0
Minimum 14 27 451 4 218 MB Yes 1 29 29.0
Maximum 70 28 121 6 218 MB Yes 3 76 25.3
Sum 1123.6666666667 29 31 6 218 MB Yes 2 61 30.5
Count 31 30 175 4 218 MB Yes 2 47 23.5
Confidence Level(95.0%) 4.9452862403 31* 141 13 218 MB Yes 3 118 39.3
n= 31 * Graphs calling for # variables > 8 used previous recorded time. Process fix works on up to 8 variables
x bar = 36.2
s = 13.5
1- alpha = 0.95
alpha = 0.05
alpha/2 = 0.025
U= 40.99
L= 31.50
95% Confidence Interval for the true average graphing time
31.5 <= Population Mean <= 40.99
36 +/- 4.7 sec
`
SQL Improved Process
Population Mean = 36.2
Std Deviation = 13.5
X2 (Upper Spec Limit) 60
Z2 = 1.762
P(X>60) = 0.039
P(X is out of spec) = 0.039
DPM = 39052
SQL = 3.26

Hypothesis Testing

The goal of the project is to reduce the time it takes to create graphs by 30%. This means we want to reduce the estimated population mean from 57 seconds to 40 seconds. This forms the bases of a One-Sided, One-Sample Hypothesis test of the mean.
H0: mu >= 40
H1: mu < 40
Acceptable Level of Risk= 10%
alpha = 0.10
n = 31
New Process Mean = 36.2
New Process Variance = 181.8
Zo = -1.549759392
P = 2* Z() 0.12 0.2423986059
Confidence = 87.9%
Since [P =b24] < [alpha = .10] reject Ho and conclude H1) with (1-b24)*100% confidence. We can be X % confident that the new process has reduced the time it takes to create graphs by 50%.

Measurement System Analysis

1. Establish operational Definitions
An operational definition is a clear concise, unambiguous definition of what time start and stop means.
Start - Time starts when the operator clicks on the spreadsheet to open it.
Stop - Time stops when the closes the file indicating that all graphs are complete.
Completed Graph: A Completed graph includes a title and labeled x and y axis.
2. Kappa technique to assess Measurement system within the operator
Choose 10 different graphs. Do each graph twice.
Use Kappa technique to assess measurement system capability Column1 Day 1
Day 1 Day 2 # graphs variables Xbar line UCL LCL R bar line R- UCL
Run # M1 M2 xbar R M1 M2 xbar R Mean 57.1 1 59.1 66.2 52.0 3.8 12.4
1 36.0 34.0 35.0 2.0 34.0 33.0 33.5 1.0 1 2 Standard Error 4.6111421122 2 59.1 66.2 52.0 3.8 12.4
2 59.0 60.0 59.5 1.0 56.0 58.0 57.0 2.0 2 4 Median 58 3 59.1 66.2 52.0 3.8 12.4
3 96.0 90.0 93.0 6.0 87.0 93.0 90.0 6.0 3 8 Mode 58 4 59.1 66.2 52.0 3.8 12.4
4 48.0 45.0 46.5 3.0 37.0 35.0 36.0 2.0 1 4 Standard Deviation 20.6216544336 5 59.1 66.2 52.0 3.8 12.4
5 58.0 65.0 61.5 7.0 60.0 58.0 59.0 2.0 2 6 Sample Variance 425.2526315789
Xbar2 = 59.1 Xbar2 = 55.1 Kurtosis -0.5588580019
Rbar = 3.8 Rbar = 2.6 Skewness 0.657122154 Day 2
Range 63 Xbar line UCL LCL R bar line R -UCL
Xbar UCL 66.2 Xbar UCL 60.0 Minimum 33 1 55.1 60.0 50.2 2.6 8.5
Xbar LCL 52.0 Xbar LCL 50.2 Maximum 2 55.1 60.0 50.2 2.6 8.5
R UCL 12.426 R UCL 8.502 Sum 1142 3 55.1 60.0 50.2 2.6 8.5
R LCL 0 R LCL 0 Count 20 4 55.1 60.0 50.2 2.6 8.5
Confidence Level(95.0%) 9.6512343576 5 55.1 60.0 50.2 2.6 8.5
Average of Average Ranges = 3.20 0.22 > 0.10, measurement system not capable? Need to explore why.
Repeatability Std Deviation= 2.83
Reproducibility Std Deviation= 3.54
Measurement Variance= 20.55
Measurement Std Dev = 4.53
Total Variance (All 20 Meas.)= 425.25
Total Standard Deviation = 20.62
Precision to Total Ratio = Measurement Std Dev / Total Std Dev = 0.22
A Rule of thumb used to determine if the measurement system is capable is to see if the precision to total ratio is less than 10%. In this case, 0.27 is greater than .10, so the measurement system is a little out of control. Sigma reproducibility is the
R charts are in control both days, but on Day 1 I exhibited more repeatability variability as evidenced by an average range of 5.2 vs a range of 2.8 on Day 2. Possible reasons might be that on day 2 I had made the graphs before and was more familiar wher

Measurement System Analysis
xbar
Xbar2
UCL
LCL
Run #
Xbar
Day 1/Operator 1 - Xbar Chart
R
Rbar
UCL
Run #
R
Day 1/Operator 1 - R Chart
xbar
Xbar2
UCL
LCL
Run #
Xbar
Day 2/Operator2 - Xbar Chart
R
R bar
R- UCL
Run #
R
Day 2/Operator 2 - R Chart
UCL=66.2
LCL=52.0
xbar2=59.1
UCL=60.0
LCL=50.2
xbar2=55.1
UCL=12.4
Rbar=3.8
UCL=8.5
Rbar=2.6

Data Stratification Tree

Questions About Process

Stratification factors

X Variables

Measurements

Handicap Index

Ball (Titleist, Nike)

Putter (Titleist, Callaway)

Tempo (Normal, Slow)

(ULTIMATE

Output Y

1

)

Does Tempo impact my performance?

Does equipment impact my performance on

putting green and consequently my USGA

handicap index?

Stance (Open like Jack N., Normal)

FiskarRuler

Does my stance affect the putting result?

•# of feet to hole

What % of my putts are within 2 feet?

Does music (sounds) impact

performance on the putting green?

Does the distance from the hole matter?

Will randomization show different results?

Is there variability in the measurement?

What is the average distance from the hole from

10, 20 and 40 feet?

Measuring Tape

•# of inches from hole after putt

•Measure variation with music, tempo,

stance from each distance

•% of putts within 2 feet

•repeatability

•reproducibility

•average distance from 10 feet

•Average distance from 20 feet

•Average distance from 40 feet

Putter and ball combination?

Music (On, None)

•Average change in inches further from hole

Is there a financial impact on the result?

Handicap Index as Measure

•Compare USGA index before and after

Inches from Hole

(Output Y

2

)

Percentage

Within 2 feet

(from 20 feet

And further)

Percentage

Of putts made

(from 10 feet and

Closer)

(Output Y

3

)

(Output Y

4

)

HOW DO I IMPROVE MY GOLF GAME

AND LOWER MY HANDICAP?

Questions about ProcessOutputStratification FactorsMeasurements

X

Is y affected by the number of

data points recorded in a test?

X1 = Total Data points collectedNumber of data points collected

Is y affected by the total number

of columns graphed?

X

2

= Variables included in graphNumber of different variables measured

Is y affected by the person

creating the graphs?

X

3

= OperatorName of engineer

Is y affected by the quality of the

graph required?

X

4

= Graph qualityTitle, labels, presentation ready

Is y affected by additional graphs

required for comparison?

X

5

= Number of graphsNumber of graphs

Is y affected by the total number

of columns of data available?

X

6

= Total number of available variablesTotal number of available variables

Data Stratification Tree

Y = Graphing Time = f (X)

Y = f(X

1

,X

2

,X

3

,X

4

,X

5

,X

6

)

Questions about ProcessOutputStratification FactorsMeasurements

X

Is y affected by the number of

data points recorded in a test?

X1 = Total Data points

collected

Number of data points

collected

Is y affected by the total number

of columns graphed?

X

2

= Variables included in

graph

Number of different

variables measured

Is y affected by the person

creating the graphs?

X

3

= OperatorName of engineer

Is y affected by the quality of the

graph required?

X

4

= Graph quality

Title, labels,

presentation ready

Is y affected by additional graphs

required for comparison?

X

5

= Number of graphsNumber of graphs

Is y affected by the total number

of columns of data available?

X

6

= Total number of

available variables

Total number of

available variables

Data Stratification Tree

Y =

Graphing

Time =

f (X)

Y = f(X

1

,X

2

,X

3

,X

4

,X

5

,X

6

)

Chart2

2 3.8 12.426
1 3.8 12.426
6 3.8 12.426
3 3.8 12.426
7 3.8 12.426
R
Rbar
UCL
Run #
R
Day 1/Operator 1 - R Chart

DataStratification

Data Stratification Tree
Questions about Process Output Stratification Factors Measurements
X Output
Is y affected by the number of data points recorded in a test? X1 = Total Data points collected Number of data points collected
Is y affected by the total number of columns graphed? Y = Graphing Time = f (X) Number of different variables measured
Is y affected by the person creating the graphs? Name of engineer
Is y affected by the quality of the graph required? Title, labels, presentation ready
Is y affected by additional graphs required for comparison? Number of graphs
Is y affected by the total number of columns of data available? Total number of available variables

Costs

Cost Reduction
Current Improved
Tests/month/engineer 60 60
Tests/year/engineer 11100 11100
Engineers 4 4
Total tests/year 44400 44400
$/hour 150 150
Graphs/test 1 1
Graphs/year 22200 22200
Time per graph (sec) 57 36
Time spent graphing/year (hr) 350 224
Annual Cost Reduction $ 52,471 $ 33,529
% Percent Annual Cost Reduction 36%
$ 15,741.41

Initial Data Collection

Run Number of Data Points Collected Total Number of Different Variables Included in Graphs Total number of available variables Name of Operator Title, Labels, Presentation Number of Graphs Time (sec) Time per Graph (sec) Number of data points collected
1 308 4 129 MB Yes 1 51 51 Column1 Number of different variables measured
2 31 4 160 MB Yes 1 58 58.0 Name of engineer
3 820 8 160 MB Yes 2 158 79.0 Mean 56.7258064516 Title, labels, presentation ready
4 31 1 155 MB Yes 1 43 43.0 Standard Error 2.6336276364 Number of graphs
5 820 7 160 MB Yes 1 95 95.0 Median 53 Total number of available variables
6 760 7 160 MB Yes 1 83 83.0 Mode 51
7 61 24 155 MB Yes 1 53 53.0 Standard Deviation 14.663418099
8 362 4 162 MB Yes 1 56 56.0 Sample Variance 215.0158303465
9 362 6 162 MB Yes 2 109 54.5 Kurtosis 0.5911961314
10 482 16 131 MB Yes 2 140 70.0 Skewness 1.0232211831
11 308 8 129 MB Yes 3 174 58.0 Range 57
12 743 3 160 MB Yes 1 70 70.0 Minimum 38
13 30 2 164 MB Yes 1 54 54.0 Maximum 95
14 30 29 164 MB Yes 1 69 69.0 Sum 1758.5
15 30 8 125 MB Yes 1 43 43.0 Count 31
16 31 6 159 MB Yes 3 119 39.7 Confidence Level(95.0%) 5.3785796423
17 30 3 164 MB Yes 1 52 52.0 n= 31
18 30 4 168 MB Yes 1 67 67.0 x bar (sec) = 56.7 39.7080645161
19 173 6 156 MB Yes 2 118 59.0 s = 14.7
20 30 4 168 MB Yes 1 44 44.0 1- alpha = 0.95
21 31 6 129 MB Yes 2 112 56.0 alpha = 0.05
22 143 2 30 MB Yes 1 48 48.0 alpha/2 = 0.025
23 31 12 123 MB Yes 2 105 52.5
24 31 13 123 MB Yes 2 79 39.5 U= 61.89
25 362 8 162 MB Yes 2 87 43.5 L= 51.56
26 30 8 168 MB Yes 1 51 51.0 95% Confidence Interval for the true average graphing time
27 451 4 218 MB Yes 1 88 88.0 51.56 <= Population Mean <= 61.89
28 121 6 218 MB Yes 3 156 52.0 57 +/- 5.16 seconds
29 31 6 218 MB Yes 2 105 52.5
30 175 4 218 MB Yes 2 76 38.0
31 141 13 218 MB Yes 3 118 39.3 Find SQL
SQL Baseline
Population Mean = 56.7
Std Deviation = 14.7
The sample size I chose for my initial baseline estimate of the population statistics was based on time constraints and the Central Limit Theorem. For almost all populations, the sampling distribution of the mean can be approximated closely by a normal d X2 (Upper Spec Limit) 60
Z2 = 0.223
P(X>60) = 0.412
P(X is out of spec) = 0.412
DPM = 411655
SQL = 1.72
Number of Variables 1 to 4 5 to 7 8 to 10 11 to 13 >13
Total 12.0 8.0 5.0 3.0 3.0
% 38.7% 25.8% 16.1% 9.7% 9.7%
Cumul Freq 38.7% 64.5% 80.6% 90.3% 100.0%

Initial Data Collection

0 0
0 0
0 0
0 0
0 0
cumulative Frequency
Number Variables
Cumulative Frequency
Pareto Diagram of Number of Variables Graphed

Process Improved Data

Run Number of Data Points Collected Total Number of Different Variables Included in Graphs Total number of available variables Name of Operator Title, Labels, Presentation Number of Graphs Time (sec) Time per Graph (sec)
Determine Sample Size That would be required 1 308 4 129 MB Yes 1 33 33
2 31 4 160 MB Yes 1 25 25.0
Before process improvement 3 820 8 160 MB Yes 2 54 27.0
U / L = 86.48 +/- 13.05 4 31 1 155 MB Yes 1 14 14.0
After process Improvement 5 820 7 160 MB Yes 1 54 54.0
Desire 95% confidence interval that produces an interval half width of only 5 seconds 6 760 7 160 MB Yes 1 53 53.0
7* 61 24 155 MB Yes 1 53 53.0
Z = 95% 8 362 4 162 MB Yes 1 29 29.0
1- alpha = 0.95 9 362 6 162 MB Yes 2 62 31.0
1- alpha/2 = 0.975 10* 482 16 131 MB Yes 2 140 70.0
Confidence = Z(.975) = 1.96 11 308 8 129 MB Yes 3 79 26.3
Est Pop Std Deviation = 13.48 12 743 3 160 MB Yes 1 35 35.0
n = 28 13 30 2 164 MB Yes 1 25 25.0
14* 30 29 164 MB Yes 1 69 69.0
15 30 8 125 MB Yes 1 40 40.0
Column1 16 31 6 159 MB Yes 3 71 23.7
17 30 3 164 MB Yes 1 34 34.0
Mean 36.247311828 18 30 4 168 MB Yes 1 45 45.0
Standard Error 2.4214650296 19 173 6 156 MB Yes 2 56 28.0
Median 33 20 30 4 168 MB Yes 1 36 36.0
Mode 25 21 31 6 129 MB Yes 2 59 29.5
Standard Deviation 13.4821466974 22 143 2 30 MB Yes 1 22 22.0
Sample Variance 181.7682795699 23* 31 12 123 MB Yes 2 105 52.5
Kurtosis 0.6312076295 24* 31 13 123 MB Yes 2 79 39.5
Skewness 1.003498986 25 362 8 162 MB Yes 2 69 34.5
Range 56 26 30 8 168 MB Yes 1 47 47.0
Minimum 14 27 451 4 218 MB Yes 1 29 29.0
Maximum 70 28 121 6 218 MB Yes 3 76 25.3
Sum 1123.6666666667 29 31 6 218 MB Yes 2 61 30.5
Count 31 30 175 4 218 MB Yes 2 47 23.5
Confidence Level(95.0%) 4.9452862403 31* 141 13 218 MB Yes 3 118 39.3
n= 31 * Graphs calling for # variables > 8 used previous recorded time. Process fix works on up to 8 variables
x bar = 36.2
s = 13.5
1- alpha = 0.95
alpha = 0.05
alpha/2 = 0.025
U= 40.99
L= 31.50
95% Confidence Interval for the true average graphing time
31.5 <= Population Mean <= 40.99
36 +/- 4.7 sec
`
SQL Improved Process
Population Mean = 36.2
Std Deviation = 13.5
X2 (Upper Spec Limit) 60
Z2 = 1.762
P(X>60) = 0.039
P(X is out of spec) = 0.039
DPM = 39052
SQL = 3.26

Hypothesis Testing

The goal of the project is to reduce the time it takes to create graphs by 30%. This means we want to reduce the estimated population mean from 57 seconds to 40 seconds. This forms the bases of a One-Sided, One-Sample Hypothesis test of the mean.
H0: mu >= 40
H1: mu < 40
Acceptable Level of Risk= 10%
alpha = 0.10
n = 31
New Process Mean = 36.2
New Process Variance = 181.8
Zo = -1.549759392
P = 2* Z() 0.12 0.2423986059
Confidence = 87.9%
Since [P =b24] < [alpha = .10] reject Ho and conclude H1) with (1-b24)*100% confidence. We can be X % confident that the new process has reduced the time it takes to create graphs by 50%.

Measurement System Analysis

1. Establish operational Definitions
An operational definition is a clear concise, unambiguous definition of what time start and stop means.
Start - Time starts when the operator clicks on the spreadsheet to open it.
Stop - Time stops when the closes the file indicating that all graphs are complete.
Completed Graph: A Completed graph includes a title and labeled x and y axis.
2. Kappa technique to assess Measurement system within the operator
Choose 10 different graphs. Do each graph twice.
Use Kappa technique to assess measurement system capability Column1 Day 1
Day 1 Day 2 # graphs variables Xbar line UCL LCL R bar line R- UCL
Run # M1 M2 xbar R M1 M2 xbar R Mean 57.1 1 59.1 66.2 52.0 3.8 12.4
1 36.0 34.0 35.0 2.0 34.0 33.0 33.5 1.0 1 2 Standard Error 4.6111421122 2 59.1 66.2 52.0 3.8 12.4
2 59.0 60.0 59.5 1.0 56.0 58.0 57.0 2.0 2 4 Median 58 3 59.1 66.2 52.0 3.8 12.4
3 96.0 90.0 93.0 6.0 87.0 93.0 90.0 6.0 3 8 Mode 58 4 59.1 66.2 52.0 3.8 12.4
4 48.0 45.0 46.5 3.0 37.0 35.0 36.0 2.0 1 4 Standard Deviation 20.6216544336 5 59.1 66.2 52.0 3.8 12.4
5 58.0 65.0 61.5 7.0 60.0 58.0 59.0 2.0 2 6 Sample Variance 425.2526315789
Xbar2 = 59.1 Xbar2 = 55.1 Kurtosis -0.5588580019
Rbar = 3.8 Rbar = 2.6 Skewness 0.657122154 Day 2
Range 63 Xbar line UCL LCL R bar line R -UCL
Xbar UCL 66.2 Xbar UCL 60.0 Minimum 33 1 55.1 60.0 50.2 2.6 8.5
Xbar LCL 52.0 Xbar LCL 50.2 Maximum 2 55.1 60.0 50.2 2.6 8.5
R UCL 12.426 R UCL 8.502 Sum 1142 3 55.1 60.0 50.2 2.6 8.5
R LCL 0 R LCL 0 Count 20 4 55.1 60.0 50.2 2.6 8.5
Confidence Level(95.0%) 9.6512343576 5 55.1 60.0 50.2 2.6 8.5
Average of Average Ranges = 3.20 0.22 > 0.10, measurement system not capable? Need to explore why.
Repeatability Std Deviation= 2.83
Reproducibility Std Deviation= 3.54
Measurement Variance= 20.55
Measurement Std Dev = 4.53
Total Variance (All 20 Meas.)= 425.25
Total Standard Deviation = 20.62
Precision to Total Ratio = Measurement Std Dev / Total Std Dev = 0.22
A Rule of thumb used to determine if the measurement system is capable is to see if the precision to total ratio is less than 10%. In this case, 0.27 is greater than .10, so the measurement system is a little out of control. Sigma reproducibility is the
R charts are in control both days, but on Day 1 I exhibited more repeatability variability as evidenced by an average range of 5.2 vs a range of 2.8 on Day 2. Possible reasons might be that on day 2 I had made the graphs before and was more familiar wher

Measurement System Analysis
xbar
Xbar2
UCL
LCL
Run #
Xbar
Day 1/Operator 1 - Xbar Chart
R
Rbar
UCL
Run #
R
Day 1/Operator 1 - R Chart
xbar
Xbar2
UCL
LCL
Run #
Xbar
Day 2/Operator2 - Xbar Chart
R
R bar
R- UCL
Run #
R
Day 2/Operator 2 - R Chart
UCL=66.2
LCL=52.0
xbar2=59.1
UCL=60.0
LCL=50.2
xbar2=55.1
UCL=12.4
Rbar=3.8
UCL=8.5
Rbar=2.6

Data Stratification Tree

Questions About Process

Stratification factors

X Variables

Measurements

Handicap Index

Ball (Titleist, Nike)

Putter (Titleist, Callaway)

Tempo (Normal, Slow)

(ULTIMATE

Output Y

1

)

Does Tempo impact my performance?

Does equipment impact my performance on

putting green and consequently my USGA

handicap index?

Stance (Open like Jack N., Normal)

FiskarRuler

Does my stance affect the putting result?

•# of feet to hole

What % of my putts are within 2 feet?

Does music (sounds) impact

performance on the putting green?

Does the distance from the hole matter?

Will randomization show different results?

Is there variability in the measurement?

What is the average distance from the hole from

10, 20 and 40 feet?

Measuring Tape

•# of inches from hole after putt

•Measure variation with music, tempo,

stance from each distance

•% of putts within 2 feet

•repeatability

•reproducibility

•average distance from 10 feet

•Average distance from 20 feet

•Average distance from 40 feet

Putter and ball combination?

Music (On, None)

•Average change in inches further from hole

Is there a financial impact on the result?

Handicap Index as Measure

•Compare USGA index before and after

Inches from Hole

(Output Y

2

)

Percentage

Within 2 feet

(from 20 feet

And further)

Percentage

Of putts made

(from 10 feet and

Closer)

(Output Y

3

)

(Output Y

4

)

HOW DO I IMPROVE MY GOLF GAME

AND LOWER MY HANDICAP?

Questions about ProcessOutputStratification FactorsMeasurements

X

Is y affected by the number of

data points recorded in a test?

X1 = Total Data points collectedNumber of data points collected

Is y affected by the total number

of columns graphed?

X

2

= Variables included in graphNumber of different variables measured

Is y affected by the person

creating the graphs?

X

3

= OperatorName of engineer

Is y affected by the quality of the

graph required?

X

4

= Graph qualityTitle, labels, presentation ready

Is y affected by additional graphs

required for comparison?

X

5

= Number of graphsNumber of graphs

Is y affected by the total number

of columns of data available?

X

6

= Total number of available variablesTotal number of available variables

Data Stratification Tree

Y = Graphing Time = f (X)

Y = f(X

1

,X

2

,X

3

,X

4

,X

5

,X

6

)

Questions about ProcessOutputStratification FactorsMeasurements

X

Is y affected by the number of

data points recorded in a test?

X1 = Total Data points

collected

Number of data points

collected

Is y affected by the total number

of columns graphed?

X

2

= Variables included in

graph

Number of different

variables measured

Is y affected by the person

creating the graphs?

X

3

= OperatorName of engineer

Is y affected by the quality of the

graph required?

X

4

= Graph quality

Title, labels,

presentation ready

Is y affected by additional graphs

required for comparison?

X

5

= Number of graphsNumber of graphs

Is y affected by the total number

of columns of data available?

X

6

= Total number of

available variables

Total number of

available variables

Data Stratification Tree

Y =

Graphing

Time =

f (X)

Y = f(X

1

,X

2

,X

3

,X

4

,X

5

,X

6

)

*

DEFINE

MEASURE

Team Launch:

Define:

Measure:

Analyze:

Control:

Improve:

Key Dates

ANALYZE

IMPROVE

Process owner: Landon

CONTROL

September 10

September 17

September 24

October 29

November 19

Landon, Engineering Project Managers, Finance Office, Stakeholders

September 6

Problem Statement

Cycle time for a signature sheet averaged 11.25 days with each project manger spending about 11.25 hours for each purchase over $100,000.

Business Impact

The average wage a project manager earns is $35/hr, therefore it costs $393.75 per project in just gathering signatures! At 144 projects a year this process costs $56,700 annually.

  • Finance Office will not accept old version of signature sheet.
  • Purchases tracked in SharePoint
  • Appraisal rated on compliance

High man-hours

High cycle time

Too many steps!

Need to take PM out of all these steps

  • Cycle time reduced to 2.88 days!
  • Man-hours reduced to 0.20 hours!
  • Cost savings $55,692 annually!
  • SQL raised from 2.3 to 3.6 and rising!

SQL = 2.3

Hypothesis Test

Ho: mu ≥ 11.25 hr Ha: mu < 11.25 hr

P-value ≈ 0

Electronic Signature Sheet

*

DEFINE – 5/15/11

MEASURE - 6/1/11

Finding the Skinny on Thin Film Sensor Reject Rates

Control

Improve

ANALYZE - 7/1/11

IMPROVE - 8/1/11

1) Problem Statement:

Production reject rate of thin film sensors increases after process change.

3) Business Impact:

Reducing/eliminating frequency rejects will prevent reworking of part, extra inventory and labor from 100% testing which could potentially save

The r2 shows that the amount of raw material used from Vendor A explains 46.6 % of the change in reject rate.

8) Probable Cause 2 – Evaporation Fixture Geometry

7) Probable Cause 1 - Raw Material Supply

The sensors are held in a fixture positioned over a evaporation source that coats them with metal. I performed a test run to measure baseline performance. The data revealed that the metallic coating has too much variation in thickness w/ a mean of 2235 Å, but the range should be 500 Å. This could be caused by the position of the source, size of mask or angle of the holding fixture.

2) Work on largest category of defect for MAXIUM IMPACT

Before

After

4) Out-of-Control:

Process is highly variable to begin w/ but much worse after change.

DPMO of 31,934,Ouch!

5) Change of Focus

The change did cause an increase in variability, but the process is not very good to start w/ a DPMO of 19,263! Finding the root cause of the inherent process variability should solve the new issue.

6) Identify Primary Inputs (Y)

Separated wheat from chaff

A second run was done to test if a centered evaporation source would decrease thickness variability (Ha). A

one-tail test was performed & the P value was high,

thus it did not significantly improve the process. This points to the mask size & fixture as the root cause of

the variation.

Z=

Z = -1.19 P = 1-Z = 1-1.19 =0.86 =86%

=

Ho: Test 1 thickness variability ≤ Test 2

  • Receipt of material from Vendor A

was halted. A comparison of their measurements vs. ours found a 7.6 KHz difference!

They recalibrated their instruments & next shipment was markedly improved with a mean very close to the center of our specification range of 6.055 as shown on this histogram.

9) Solution to Probable Cause 1

10) Solution to Probable Cause 2

I’m working with engineering to

develop a new fixture that will

improve the geometry.

Scatter plot reveals that using raw materials from Vendor A has a strong positive correlation of 0.7 with the reject rate.

Constructing a control chart of measurements taken by QC of frequency illustrates that the vendors process is out of control.

10) Changes to be Made:

  • QC technician does acceptance testing of raw materials w/ zero tolerance.
  • Vendor supplies Certificate of Analysis w/ test statistics.
  • Control chart created for raw materials.
  • New fixture for more uniform thickness to prevent any frequency rejects.

Control – 8/8/11

Box Plot

Pareto Chart

C&E Matrix

Control Chart

Scatter Plot

Hypothesis Test

Histogram

Rick, Steve & Production Staff

Cause & Effect Matrix
Scoring:1=low, 3 = med, 5=high, Importance to Customer (sensors w/ correct frequency) = 1
Process Inputs (X) Effect Rating Probability Score
Vendor frequency sorting quality Allow accurate calculation of thickness 5 High, makes adjustments when providing thickness data to techs 25
Fixture Geometry Even coating thickness 5 High, location determines the thickness of the coating. 25

30

31

32

*

*

*

*

*

Invoice Cost Increase

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

$16,000

Jun-07Jul-07Aug-07

Invoice Cost

Invoice (X)

Mean

UNPL

LNPL

Page Views Increase

8,000,000

9,000,000

10,000,000

11,000,000

12,000,000

13,000,000

14,000,000

15,000,000

16,000,000

17,000,000

18,000,000

May-07Jun-07Jul-07

Pageviews

Mean

UNPL

LNPL

Invoice Cost After Improvement

$9,500

$9,700

$9,900

$10,100

$10,300

$10,500

$10,700

$10,900

$11,100

$11,300

$11,500

Aug-07

Sep-07

Oct-07

Number of Complete Applications

5

7

888

7

9

1111

12

1313

14

0

5

10

15

Jul, 2006

Sept

Nov

Jan

Mar

May

Jul, 2007

Date

Number

Series1

Linear (Series1)

Time to Complete Proccess Cycle

28

33

38

43

48

53

58

Jul-06AugSeptOct NovDecJanFebMarchAprilMayJuneJul-07

Date/Time/Period

Time (Days)

Data 1

Median

Goal

Total Application Errors by Type

132

21

14

9

75.0%

86.9%

94.9%

0

20

40

60

80

100

120

140

160

Incomplete/Incorrect ApplicationsStalled Approvals In The Log-in

Phase,

Stalled Approval At The

Managerial Level

Reworks

Type

Defects

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

Base Group

62.06UCL

42.50CL

22.94LCL

16

21

26

31

36

41

46

51

56

61

66

16111621263136414651566166717681869196101106111116121126

Units

Cycle Time- Days

New "Improved" Process

UCL 44.59

CL 28.56

LCL 12.53

7

12

17

22

27

32

37

42

47

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Units

Cycle Time

Beralt - OSI Ore Comparison

69.50%

70.00%

70.50%

71.00%

71.50%

72.00%

72.50%

73.00%

73.50%

74.00%

74.50%

BS261/191

BS261/195

BS261/199

BS261/203

BS261/207

BS261/211

BS261/215

BS261/219

BS261/223

BS261/227

BS261/231

BS261/235

BS261/239

BS261/243

BS261/247

BS261/251

Beralt

OSI

Tungsten Ore Suppliers FY08

0

20

40

60

80

100

120

140

Beralt

DLA

Spot

CantungDynacor

Heemskirk

KMT

Other

STUs

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

STUs

Cumulative %

Questions about Process

Output

Stratification Factors

Measurements

X

Is y affected by the number of

data points recorded in a test?

X1 = Total Data points

collected

Number of data points

collected

Is y affected by the total number

of columns graphed?

X

2

= Variables included in

graph

Number of different

variables measured

Is y affected by the person

creating the graphs?

X

3

= Operator

Name of engineer

Is y affected by the quality of the

graph required?

X

4

= Graph quality

Title, labels,

presentation ready

Is y affected by additional graphs

required for comparison?

X

5

= Number of graphs

Number of graphs

Is y affected by the total number

of columns of data available?

X

6

= Total number of

available variables

Total number of

available variables

Data Stratification Tree

Y =

Graphing

Time =

f (X)

Y = f(X

1

,X

2

,X

3

,X

4

,X

5

,X

6

)

Day 1/Operator 1 - Xbar Chart

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

0123456

Run #

Xbar

Day 1/Operator 1 - R Chart

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0123456

Run #

R

Pareto Diagram of Number of Variables Graphed

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

1 to 4

5 to 7

8 to 10

11 to 13

>13

Number Variables

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

Cumulative Frequency

Current

Improved

Time per graph (sec)

57

36

Time spent

graphing/year (hr)

350

224

Annual Cost Reduction

52,471

$

33,529

$

% Percent Annual Cost

Reduction

Cost Reduction

36%

Population Mean =

56.7

Std Deviation =

14.7

X2 (Upper Spec Limit)

60

Z2 =

0.223

P(X>60) =

0.412

P(X is out of spec) =

0.412

DPM =

411655

SQL =

1.72

SQL Baseline

Population Mean =

36.2

Std Deviation =

13.5

X2 (Upper Spec Limit)

60

Z2 =

1.762

P(X>60) =

0.039

P(X is out of spec) =

0.039

DPM =

39052

SQL =

3.26

SQL Improved Process

H0: mu >=

40

H1: mu <

40

Acceptable Level of Risk=

10%

alpha =

0.10

n =

31

New Process Mean =

36.2

New Process Variance =

181.8

Zo =

-1.55

P = 2* Z()

0.12

Confidence =

87.9%

n=

31

x bar (sec) =

56.7

s =

14.7

1- alpha =

0.95

alpha =

0.05

alpha/2 =

0.025

U=

61.89

L=

51.56

95% Confidence Interval for the true average graphing time

51.56 <= Population Mean <= 61.89

57 +/- 5.16 seconds

7

.

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