process capability slides

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



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

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