Process Improvement and 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= Yield of Process=

Rework / Elimination of Flow Units Step 1Test 1Step 2Test 2Step 3Test 3 Rework Step 1Test 1Step 2Test 2Step 3Test 3 Step 1Test 1Step 2Test 2Step 3Test 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 Process Parameter 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

The X-bar Chart: Application to Call Center 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

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  ˆ = R / d 2 33 Upper Specification Limit (USL) Lower Specification Limit (LSL) X-3  A X-2  A X-1  A X X+1  A X+2  X+3  A X-6  B X X+6  B Process A (with st. dev  A ) Process B (with st. dev  B ) x  C p P{defect}ppm 1  ,000 2  ,500 3  ,700 4   ,6 6  2.002x ,00

Attribute Based Control Charts: The p-chart UCL= + 3  ˆ LCL= - 3  ˆ  ˆ = Estimate average defect percentage Estimate Standard Deviation Define control limits DAV case: - calibration period (capability analysis) - conformance analysis =0.052 =0.013 =0.091 =0.014 Period n defects p

Attribute Based Control Charts: The p-chart

Statistical Process Control Capability Analysis Conformance Analysis Investigate for Assignable Cause Eliminate 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”

Minimum acceptable value Maximum acceptable value Target value Quality Good Bad Performance Metric Target value Quality Loss Performance Metric, x Loss = C(x-T) 2 Step 2: Reduce Variability in the Process The 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 F2F2 F1F1 Chewiness of Brownie=F 1 (Bake Time) + F 2 (Oven Temperature) Bake TimeOven 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% 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… ©