Transcript Slide 1
Process Improvement and Process Capability
© Christian Terwiesch 2003
The Concept of Yields
Yield of Resource=
Flow rate of units processed correctly at the resource Flow rate
Yield of Process=
Flow rate of units processed correctly Flow rate 90% 80% 90% Line Yield: 0.9 x 0.8 x 0.9 x 1 x 0.9
100% 90%
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
Rework:
Defects can be corrected Same or other resource Leads to variability Examples: - Readmission to ICU - Toyota case Step 1 Test 1 Step 2 Test 2 Step 3 Test 3
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
Process Parameter
Upper Control Limit (UCL) Center Line Lower Control Limit (LCL)
Time
• 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)
2 3 4 5 6 7 8 9 10
Factor for X bar Chart (A
2
)
1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31
Factor for Lower control Limit in R chart (D
3
)
0 0 0 0 0 0.08 0.14 0.18 0.22
Factor for Upper control limit in R chart (D
4
)
3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78
Factor to estimate Standard deviation, (d
2
)
1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078
The X-bar Chart: Application to Call Center
Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 x 1 1.7 2.7 2.1 1.2 4.4 2.8 3.9 16.5 2.6 1.9 3.9 3.5 29.9 1.9 1.5 3.6 3.5 2.8 2.1 3.7 2.1 3 12.8 2.3 3.8 2.3 2 x 2 1.7 2.3 2.7 3.1 2 3.6 2.8 3.6 2.1 4.3 3 8.4 1.9 2.7 2.4 4.3 1.7 5.8 3.2 1.7 2 2.6 2.4 1.6 1.1 1.8 6.7 x 3 3.7 1.8 4.5 7.5 3.3 4.5 3.5 2.1 3 1.8 1.7 4.3 7 9 5.1 2.1 5.1 3.1 2.2 3.8 17.1 1.4 2.4 1.8 2.5 1.7 1.8 x 4 3.6 3 3.5 6.1 4.5 5.2 3.5 4.2 3.5 2.9 2.1 1.8 6.5 3.7 2.5 5.2 1.8 8 2 1.2 3 1.7 3 5 4.5 11.2 6.3 x 5 2.8 2.1 2.9 3 1.4 2.1 3.1 3.3 2.1 2.1 5.1 5.4 2.8 7.9 10.9 1.3 3.2 4.3 1 3.6 3.3 1.8 3.3 1.5 3.6 4.9 1.6 Average Mean 2.7 2.38 3.14 4.18 3.12 3.64 3.36 5.94 2.66 2.6 3.16 4.68 9.62 5.04 4.48 3.3 3.06 4.8 2.1 2.8 5.5 2.1 4.78 2.44 3.1 4.38 3.68
3.81
Range 2 1.2 2.4 6.3 3.1 3.1 1.1 14.4 1.4 2.5 3.4 6.6 28 7.1 9.4 3.9 3.4 5.2 2.2 2.6 15.1 1.6 10.4 3.5 3.4 9.5 5.1
5.85
• Collect samples over time • Compute the mean:
X
x
1
x
2 ...
n
• Compute the range:
R
max{
x
1 , min{
x
1 ,
x
2
x
2 ,...
x n
} • Normally distributed
x n
,...
x n
} as a proxy for the variance • Average across all periods - average mean - average range
12
Control Charts: The X-bar Chart
• Define control limits UCL=
X
+A 2 ×
R
=3.81+0.58*5.85=7.19 LCL=
X
-A 2 ×
R
=3.81-0.58*5.85=0.41 • Constants are taken from a table 10 8 6 4 • Identify assignable causes: - point over UCL - point below LCL - many (6) points on one side of center 2 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 • In this case: - problems in period 13 - new operator was assigned mean st-dev
CSR 1
2.95 0.96
CSR 2
3.23 2.36
CSR 3
7.63 7.33
CSR 4
3.08 1.87
CSR 5
4.26 4.41
The Statistical Meaning of Six Sigma
Lower Specification Limit (LSL)
Process A (with st. dev s A ) Process B (with st. dev s B )
Upper Specification Limit (USL)
X-3 s A X-2 s A X-1 s A X X+1 s A X+2 s
3
s X+3 s A
Process capability measure
C p
USL
6 s ˆ
LSL
x s 1 s 2 s 3 s 4 s 5 s 6 s C p 0.33
0.67
1.00
1.33
1.67
2.00
P{defect} 0.317
0.0455
0.0027
0.0001
0.0000006
2x10 -9 X-6 s B X X+6 s B • Estimate standard deviation: s =
R
/
d 2
• 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 ppm 317,000 45,500 2,700 63 0,6 0,00
Attribute Based Control Charts: The p-chart
Period n defects p
300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 24 25 26 27 28 29 30 1 8 9 10 11 12 2 3 4 5 6 7 19 20 21 22 23 13 14 15 16 17 18 0.060
0.050
0.060
0.020
0.067
0.053
0.053
0.063
0.067
0.053
0.033
0.047
0.070
0.043
0.043
0.043
0.057
0.057
0.070
0.060
0.053
0.047
0.110
0.153
0.033
0.040
0.043
0.060
0.063
0.047
46 10 12 13 18 19 14 18 19 20 16 10 14 15 18 6 20 16 16 21 18 16 14 33 21 13 13 13 17 17 • Estimate average defect percentage s ˆ =
p
=0.052
• Estimate Standard Deviation
p
( 1
p
)
Sample Size
• Define control limits
p p
s ˆ s ˆ =0.013
=0.091
=0.014
• DAV case: - calibration period (capability analysis) - conformance analysis
Attribute Based Control Charts: The p-chart 0.180
0.160
0.140
0.120
0.100
0.080
0.060
0.040
0.020
0.000
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Statistical Process Control
Capability Analysis Conformance Analysis Eliminate Assignable Cause Investigate for Assignable 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 Responsibility 2. Quality System 3. Contract review 4. Design control 5. Document control 6. Purchasing / Supplier evaluation 7. Handling of customer supplied material 8. Products must be traceable 9. Process control 10. Inspection and testing 11. Inspection, Measuring, Test Equipment 12. Records of inspections and tests 13. Control of nonconforming products 14. Corrective action 15. Handling, storage, packaging, delivery 16. Quality records 17. Internal quality audits 18. Training 19. Servicing 20. Statistical techniques
Examples: “The design process shall be planned”, “production processes shall be defined and planned”
Step 2: Reduce Variability in the Process The Idea of Taguchi: Even Small Deviations are Quality Losses
Quality Quality Loss
Loss = C(x-T) 2
Good Bad Minimum acceptable value Target value
Performance Metric
Maximum acceptable value It is not enough to look at “Good” vs “Bad” Outcomes Target value 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”
Performance Metric, x
Step 3: Accommodate Residual Variability Through Robust Design
F 1
Chewiness of Brownie=F 1 (Bake Time) + F 2 (Oven Temperature)
F 2 25 min.
30 min.
Bake Time Design A Design B
350 F
• Double-checking (see Toshiba) • Fool-proofing, Poka yoke (see Toyota) • Process recipe (see Brownie) Pictures from www.qmt.co.uk
375 F
Oven Temperature
The Case of Jesica Santillam
Jesica Santillam, 17, has waited three years for donor organs to become available.
(Photo: AP)
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)
“We didn’t have enough checks”, Ralph Snyderman, Duke University Hospital Not the first death in organ transplantation because of blood type mismatch 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.
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)
1 problem every 10,000 units
“Bad” outcome only happens Every 10 Mio units 99% correct
Case 2:
Process has built-in rework loops • Double-checking • Jesica’s case
99%
Good
99% 99% 1% 1% 1%
Bad “Bad” outcome only happens with probability (1-0.99) 3 Learning should be driven by process deviations, not by defects
The Three Steps in the Case of Jesica
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
To End with a Less Sad Perspective: Predicting Distance can be Important…
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