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Process Improvementand
Process Capability
© Christian Terwiesch 2003
The Concept of Yields
90% 80% 90% 100% 90%
Line Yield: 0.9 x 0.8 x 0.9 x 1 x 0.9
Yield of Resource= rate Flow
resource the atcorrectly processed units of rate Flow
Yield of Process= rate Flow
correctly processed units of rate Flow
Rework / Elimination of Flow Units
Step 1 Test 1 Step 2 Test 2 Step 3 Test 3
Rework
Step 1 Test 1 Step 2 Test 2 Step 3 Test 3
Step 1 Test 1 Step 2 Test 2 Step 3 Test 3
Rework: Defects can be corrected Same or other resource Leads to variability Examples: - Readmission to ICU - Toyota case
Loss of Flow units: Defects can NOT be corrected Leads to variability To get X units, we have to start X/y units Examples: - Interviewing - Semiconductor fab
The Concept of Consistency:Who is the Better Target Shooter?
Not just the mean is important, but also the variance
Need to look at the distribution function
The Impact of Variation on Quality: The Xootr Case
Variation is (again) the root cause of all evil
Two Types of Causes for Variation
Common Cause Variation (low level)
Common Cause Variation (high level)
Assignable Cause Variation
• Need to measure and reduce common cause variation• Identify assignable cause variation as soon as possible
Statistical Process Control: Control Charts
Time
ProcessParameter
Upper Control Limit (UCL)
Lower Control Limit (LCL)
Center Line
• Track process parameter over time - mean - percentage defects
• Distinguish between - common cause variation (within control limits) - assignable cause variation (outside control limits)
• Measure process performance: how much common cause variation is in the process while the process is “in control”?
Parameters for Creating X-bar Charts
Number of Observations in Subgroup
(n)
Factor for X-bar Chart
(A2)
Factor for Lower
control Limit in R chart
(D3)
Factor for Upper
control limit in R chart
(D4)
Factor to estimate Standard
deviation, (d2)
2 1.88 0 3.27 1.128 3 1.02 0 2.57 1.693 4 0.73 0 2.28 2.059 5 0.58 0 2.11 2.326 6 0.48 0 2.00 2.534 7 0.42 0.08 1.92 2.704 8 0.37 0.14 1.86 2.847 9 0.34 0.18 1.82 2.970
10 0.31 0.22 1.78 3.078
The X-bar Chart: Application to Call Center
n
xxxX n
...21
},...,min{
},...,max{
21
21
n
n
xxx
xxxR
Period x1 x2 x3 x4 x5 Mean Range
1 1.7 1.7 3.7 3.6 2.8 2.7 2 2 2.7 2.3 1.8 3 2.1 2.38 1.2 3 2.1 2.7 4.5 3.5 2.9 3.14 2.4 4 1.2 3.1 7.5 6.1 3 4.18 6.3 5 4.4 2 3.3 4.5 1.4 3.12 3.1 6 2.8 3.6 4.5 5.2 2.1 3.64 3.1 7 3.9 2.8 3.5 3.5 3.1 3.36 1.1 8 16.5 3.6 2.1 4.2 3.3 5.94 14.4 9 2.6 2.1 3 3.5 2.1 2.66 1.4
10 1.9 4.3 1.8 2.9 2.1 2.6 2.5 11 3.9 3 1.7 2.1 5.1 3.16 3.4 12 3.5 8.4 4.3 1.8 5.4 4.68 6.6 13 29.9 1.9 7 6.5 2.8 9.62 28 14 1.9 2.7 9 3.7 7.9 5.04 7.1 15 1.5 2.4 5.1 2.5 10.9 4.48 9.4 16 3.6 4.3 2.1 5.2 1.3 3.3 3.9 17 3.5 1.7 5.1 1.8 3.2 3.06 3.4 18 2.8 5.8 3.1 8 4.3 4.8 5.2 19 2.1 3.2 2.2 2 1 2.1 2.2 20 3.7 1.7 3.8 1.2 3.6 2.8 2.6 21 2.1 2 17.1 3 3.3 5.5 15.1 22 3 2.6 1.4 1.7 1.8 2.1 1.6 23 12.8 2.4 2.4 3 3.3 4.78 10.4 24 2.3 1.6 1.8 5 1.5 2.44 3.5 25 3.8 1.1 2.5 4.5 3.6 3.1 3.4 26 2.3 1.8 1.7 11.2 4.9 4.38 9.5 27 2 6.7 1.8 6.3 1.6 3.68 5.1
Average
3.81
5.85
• Collect samples over time
• Compute the mean:
• Compute the range:
as a proxy for the variance
• Average across all periods - average mean - average range
• Normally distributed
Control Charts: The X-bar Chart
• Define control limits
• Constants are taken from a table
• Identify assignable causes: - point over UCL - point below LCL - many (6) points on one side of center
• In this case: - problems in period 13 - new operator was assigned
0
2
4
6
8
10
12
1 3 5 7 9 11 13 15 17 19 21 23 25 27
UCL=X +A2 ×R=3.81+0.58*5.85=7.19
LCL=X -A2 ×R=3.81-0.58*5.85=0.41
CSR 1 CSR 2 CSR 3 CSR 4 CSR 5 mean 2.95 3.23 7.63 3.08 4.26 st-dev 0.96 2.36 7.33 1.87 4.41
The Statistical Meaning of Six Sigma
Process capability measure
• Estimate standard deviation:• Look at standard deviation relative to specification limits• Don’t confuse control limits with specification limits: a process can be out of control, yet be incapable
= R / d 2
3
Upper Specification Limit (USL)
LowerSpecificationLimit (LSL)
X-3A X-2A X-1AX X+1A
X+2 X+3A
X-6BX X+6B
Process A(with st. dev A)
Process B(with st. dev B)
6
LSLUSLC p
x Cp P{defect} ppm
1 0.33 0.317 317,000
2 0.67 0.0455 45,500
3 1.00 0.0027 2,700
4 1.33 0.0001 63
5 1.67 0.0000006 0,6
6 2.00 2x10-9 0,00
Attribute Based Control Charts: The p-chart
pUCL= + 3
pLCL= - 3
SizeSample
pp )1( =
• Estimate average defect percentage
• Estimate Standard Deviation
• Define control limits
• DAV case: - calibration period (capability analysis) - conformance analysis
1 300 18 0.0602 300 15 0.0503 300 18 0.0604 300 6 0.0205 300 20 0.0676 300 16 0.0537 300 16 0.0538 300 19 0.0639 300 20 0.067
10 300 16 0.05311 300 10 0.03312 300 14 0.04713 300 21 0.07014 300 13 0.04315 300 13 0.04316 300 13 0.04317 300 17 0.05718 300 17 0.05719 300 21 0.07020 300 18 0.06021 300 16 0.05322 300 14 0.04723 300 33 0.11024 300 46 0.15325 300 10 0.03326 300 12 0.04027 300 13 0.04328 300 18 0.06029 300 19 0.06330 300 14 0.047
p =0.052
=0.013
=0.091=0.014
Period n defects p
Attribute Based Control Charts: The p-chart
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.180
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Statistical Process Control
CapabilityAnalysis
ConformanceAnalysis
Investigate forAssignable Cause
EliminateAssignable Cause
Capability analysis • What is the currently "inherent" capability of my process when it is "in control"?
Conformance analysis• SPC charts identify when control has likely been lost and assignable cause variation has occurred
Investigate for assignable cause• Find “Root Cause(s)” of Potential Loss of Statistical Control
Eliminate or replicate assignable cause• Need Corrective Action To Move Forward
How do you get to a Six Sigma Process? Step 1: Do Things Consistently (ISO 9000)
1. Management Responsibility2. Quality System3. Contract review4. Design control5. Document control6. Purchasing / Supplier evaluation7. Handling of customer supplied material8. Products must be traceable9. Process control10. Inspection and testing
11. Inspection, Measuring, Test Equipment12. Records of inspections and tests13. Control of nonconforming products14. Corrective action15. Handling, storage, packaging, delivery16. Quality records17. Internal quality audits18. Training19. Servicing20. Statistical techniques
Examples: “The design process shall be planned”, “production processes shall be defined and planned”
Minimum acceptable value
Maximum acceptable value
Target value
Quality
Good
Bad
Performance Metric
Target value
QualityLoss
Performance Metric, x
Loss = C(x-T)2
Step 2: Reduce Variability in the ProcessThe Idea of Taguchi: Even Small Deviations are Quality Losses
It is not enough to look at “Good” vs “Bad” Outcomes
Only looking at good vs bad wastes opportunities for learning; especially as failures become rare (closer to six sigma) you need to learn from the “near misses”
Catapult: Land “in the box” opposed to “perfect on target”
• Double-checking (see Toshiba)• Fool-proofing, Poka yoke (see Toyota)• Process recipe (see Brownie)
Step 3: Accommodate Residual Variability Through Robust Design
Pictures from www.qmt.co.uk
F2F1
Chewiness of Brownie=F1(Bake Time) + F2(Oven Temperature)
Bake Time Oven Temperature
25 min. 30 min. 350 F 375 F
Design A
Design B
Jesica Santillam, 17, has waited three years for donor organs to become available. (Photo: AP)
The Case of Jesica Santillam
Line of Causes leading to the mismatch• Jaggers did not take home the list of blood types• Coordinator initially misspelled Jesica’s name• Once UNOS identified Jesica, no further check on blood type• Little confidence in information system / data quality• Pediatric nurse did not double check• Harvest-surgeon did not know blood type
The Case of Jesica Santillam (ctd)
As a result of this tragic event, it is clear to us at Duke that we need to have more robust processes internally and a better understanding of the responsibilities of all partners involved in the organ procurement process," said William Fulkerson, M.D., CEO of Duke University Hospital.
“We didn’t have enough checks”, Ralph Snyderman, Duke University Hospital
Not the first death in organ transplantation because of blood type mismatch
Why Having a Process is so Important:Two Examples of Rare-Event Failures
Case 1: Process does not matter in most cases• Airport security• Safety elements (e.g. seat-belts)
Case 2: Process has built-in rework loops• Double-checking• Jesica’s case
1 problem every 10,000 units
99% correct
“Bad” outcome only happens with probability (1-0.99)3
Good
Bad
99% 99%
99%
1%
1% 1%
Learning should be driven by process deviations, not by defects
“Bad” outcome only happens Every 10 Mio units
Step 1: Define and map processes - Jaegger had probably forgotten the list with blood groups 20 times before - Persons involved in the process did not double-check, everybody checked sometimes - Learning is triggered following deaths / process deviations are ignored
Step 2: Reduce variability - quality of data (initially misspelled the name)
Step 3: Robust Design - color coding between patient card / box holding the organ - information system with no manual work-around
The Three Steps in the Case of Jesica
To End with a Less Sad Perspective:Predicting Distance can be Important…
© www.jochen-schweizer.de
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