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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