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Quality Management

Quality Management. Chapter 8. Learning Goals. Statistical Process Control X-bar, R-bar, p charts Process variability vs. Process specifications Yields/Reworks and their impact on costs Just-in-time philosophy. Steer Support for the Scooter. Steer Support Specifications. Go-no-go gauge.

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Quality Management

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  1. Quality Management Chapter 8

  2. Learning Goals • Statistical Process Control • X-bar, R-bar, p charts • Process variability vs. Process specifications • Yields/Reworks and their impact on costs • Just-in-time philosophy

  3. Steer Support for the Scooter

  4. Steer Support Specifications Go-no-go gauge

  5. Control Charts

  6. Statistical Process Control (SPC) • SPC: Statistical evaluation of the output of a process during production/service • The Control Process • Define • Measure • Compare to a standard • Evaluate • Take corrective action • Evaluate corrective action

  7. 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

  8. 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 whencontrol has likely been lost and assignable cause variation has occurred • Investigatefor assignable cause • Find “Root Cause(s)” of Potential Loss of Statistical Control • Eliminate assignable cause • Need Corrective Action To Move Forward

  9. Statistical Process Control • Shewhart’s classification of variability: • Common (random) cause • assignable cause • Variations and Control • Random variation: Natural variations in the output of process, created by countless minor factors • temperature, humidity variations, traffic delays. • Assignable variation: A variation whose source can be identified. This source is generally a major factor • tool failure, absenteeism

  10. Two Types of Causes for Variation Common Cause Variation (low level) Common Cause Variation (high level) Assignable Cause Variation

  11. Mean and Variance • Given a population of numbers, how to compute the mean and the variance?

  12. Sample for Efficiency and Stability • From a large population of goods or services (random if possible) a sample is drawn. • Example sample: Midterm grades of OPRE6302 students whose last name starts with letter R {60, 64, 72, 86}, with letter S {54, 60} • Sample size= n • Sample average or sample mean= • Sample range= R • Standard deviation of sample means=

  13. Mean Sampling Distribution Sampling distribution is the distribution of sample means. Sampling distribution Variability of the average scores of people with last name R and S Process distribution Variability of the scores for the entire class Grouping reduces the variability.

  14. Normal Distribution normdist(x,.,.,1) normdist(x,.,.,0) Probab x Mean     95.44% 99.74%

  15. Cumulative Normal Density 1 prob normdist(x,mean,st_dev,1) 0 x norminv(prob,mean,st_dev)

  16. Normal Probabilities: Example • If temperature inside a firing oven has a normal distribution with mean 200 oC and standard deviation of 40 oC, what is the probability that • The temperature is lower than 220 oC =normdist(220,200,40,1) • The temperature is between 190 oC and 220oC =normdist(220,200,40,1)-normdist(190,200,40,1)

  17. Samplingdistribution Processdistribution Mean LCL Lowercontrollimit UCL Uppercontrollimit Control Limits Process is in control if sample mean is between control limits. These limits have nothing to do with product specifications!

  18. Setting Control Limits:Hypothesis Testing Framework • Null hypothesis: Process is in control • Alternative hypothesis: Process is out of control • Alpha=P(Type I error)=P(reject the null when it is true)= P(out of control when in control) • Beta=P(Type II error)=P(accept the null when it is false) P(in control when out of control) • If LCL decreases and UCL increases, we accept the null more easily. What happens to • Alpha? • Beta? • Not possible to target alpha and beta simultaneously, • Control charts target a desired level of Alpha.

  19. /2 /2 Mean LCL UCL Probabilityof Type I error Type I Error=Alpha Sampling distribution The textbook uses Type I error=1-99.74%=0.0026=0.26%.

  20. Statistical Process Control: Control Charts Process Parameter • 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”? Upper Control Limit (UCL) Center Line Lower Control Limit (LCL) Time

  21. Abnormal variationdue to assignable sources Out ofcontrol UCL Mean Normal variationdue to chance LCL Abnormal variationdue to assignable sources 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample number Control Chart

  22. UCL LCL 1 2 3 4 Sample number Observations from Sample Distribution

  23. Parameters for computing UCL and LCLthe Table method

  24. 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

  25. Control Charts: The X-bar ChartThe Table method 12 10 8 6 4 2 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 • 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

  26. Range Control Chart Multipliers D4 and D3 depend on n and are available in Table 8.2. EX: In the last five years, the range of GMAT scores of incoming PhD class is 88, 64, 102, 70, 74. If each class has 6 students, what are UCL and LCL for GMAT ranges? Are the GMAT ranges in control?

  27. 12 10 8 6 X-Bar 4 2 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 30 25 20 15 R 10 5 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 Control Charts: X-bar Chart and R-bar ChartFor the Call Center

  28. x-Chart UCL LCL X-bar and Range Charts: Which? (process mean is shifting upward) Sampling Distribution UCL Detects shift LCL Does notdetect shift R-chart

  29. UCL LCL X-bar and Range Charts: Which? Sampling Distribution (process variability is increasing) Does notreveal increase x-Chart UCL R-chart Reveals increase LCL

  30. Control Charts: The X-bar ChartThe Direct method • Compute the standard deviation of the sample averages • stdev(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)=1.5687 • Use type I error of 1-0.9974

  31. Process CapabilityLet us Tie Tolerances and Variability • Tolerances/Specifications • Requirements of the design or customers • Process variability • Natural variability in a process • Variance of the measurements coming from the process • Process capability • Process variability relative to specification • Capability=Process specifications / Process variability

  32. LowerSpecification UpperSpecification Process variability matches specifications LowerSpecification UpperSpecification Process variability well within specifications LowerSpecification UpperSpecification Process Capability: Specification limits are not control chart limits Sampling Distribution is used Process variability exceeds specifications

  33. Process Capability Ratio When the process is centered, process capability ratio A capable process has large Cp. Example: The standard deviation, of sample averages of the midterm 1 scores obtained by students whose last names start with R, has been 7. The SOM requires the scores not to differ by more than 50% in an exam. That is the highest score can be at most 50 points above the lowest score. Suppose that the scores are centered, what is the process capability ratio? Answer: 50/42

  34. 3 Sigma and 6 Sigma Quality Upperspecification Lowerspecification Processmean +/- 3 Sigma +/- 6 Sigma

  35. X-2sA X+6sB X X-6sB X+3sA X+2s X+1sA X X-1sA X-3sA • Estimate standard deviation: • Or use the direct method with the excel function stdev() • Look at standard deviation relative to specification limits = / d s ˆ R 2 The Statistical Meaning of Six Sigma Lower Specification (LSL) Upper Specification (USL) Process A (with st. dev sA) x Cp P{defect} 1 0.33 0.317 2 0.67 0.0455 3 1.00 0.0027 4 1.33 0.0001 5 1.67 0.0000006 6 2.00 2x10-9 3 Process B (with st. dev sB)

  36. Use of p-Charts • p=proportion defective, assumed to be known • When observations can be placed into two categories. • Good or bad • Pass or fail • Operate or don’t operate • Go or no-go gauge

  37. =0.052 UCL= + 3 LCL= - 3 =0.013 = =0.014 =0.091 s s s ˆ ˆ ˆ Attribute Based Control Charts: The p-chart Period n defects p • Estimate average defect percentage • Estimate Standard Deviation • Define control limits

  38. Attribute Based Control Charts: The p-chart

  39. Inputs Transformation Outputs Acceptance sampling Acceptance sampling Process control Inspection • Where/When • Raw materials • Finished products • Before a costly operation, PhD comp. exam before candidacy • Before an irreversible process, firing pottery • Before a covering process, painting, assembly • Centralized vs. On-Site, my friend checks quality at cruise lines

  40. Discovery of Defects and the Costs End of Process Process Step Market Bottleneck Defectoccurred Defectdetected Defectdetected Defectdetected Defectdetected $ $ $ Cost of defect Based on labor andmaterial cost Based on salesprice (incl. Margin) Recall, reputation,warranty costs Recall Alert U.S. Consumer Product Safety Commission Office of Information and Public Affairs Washington, DC 20207 September 26, 2003 CPSC, Segway LLC AnnounceVoluntary Recall to Upgrade Software on Segway™ Human Transporters The following product safety recall was conducted by the firm in cooperation with the CPSC. Name of Product: Segway Human Transporter (HT) Units: Approximately 6,000

  41. Examples of Inspection Points

  42. Yield of Resource = Yield of Process = The Concept of Yields 90% 80% 90% 100% 90% Line Yield: 0.9 x 0.8 x 0.9 x 1 x 0.9

  43. 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 / Elimination of Flow Units Rework:Defects can be corrected Same or other resource Leads to variability Examples: - Readmission to Intensive Care Unit 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

  44. 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) “Bad” outcome only happens Every 100*10,000 units 1 problem every 10,000 units 99% correct • Case 2: Process has built-in rework loops • Double-checking 99% Good “Bad” outcome happens with probability (1-0.99)3 99% 99% 1% Bad 1% 1% Learning should be driven by process deviations, not by defects

  45. Rare events are not so rare: Chances of a Jetliner Crash due to Engine Icing • Engine flameout due to crystalline icing: Engine stops for 30-90 secs and hopefully starts again. • Suppose 150 single engine flameouts over 1990-2005 and 15 dual engine flameouts over 2002-2005. What are the annualized single and dual engine flameouts? 10=150/15 and 5=15/3 • Let N be the total number of widebody jetliners flying through a storm per year. Assume that engines ice independently to compute N. Set Prob(2 engine icing)=Prob(1 engine icing)2(5/N)=(10/N)2 which gives N=20 • There are 1200 widebody jetliners worldwide. It is safe to assume that each flies once a day. Suppose that there are 2 storms on their path every day, which gives us about M=700 widebody jetliner and storm encounter very year. How can we explain M=700 > N=20? The engines do not ice independently. With M=700, Prob(1 engine icing)=10/700=1.42% and Prob(2 engine icing)=5/700=0.71%. Because of dependence Prob(2 engine icing) >> Prob(1 engine icing) 2 . Unjustifiable independence leads to underestimation of the failure probabilities in operations, finance, engineering, flood control, etc.

  46. Just-in-Time Philosophy • Pull the operations rather than pushing them • Inventory reduction • JIT Utopia • 0-setup time • 0-non value added operations • 0-defects • Discover and reduce process variability

  47. Push vs Pull System • What instigates the movement of the work in the system? • In Push systems, work release is based on downstream demand forecasts • Keeps inventory to meet actual demand • Acts proactively • e.g. Making generic job application resumes today (e.g.: exempli gratia) • In Pull systems, work release is based on actual demand or the actual status of the downstream customers • May cause long delivery lead times • Acts reactively • e.g. Making a specific resume for a company after talking to the recruiter

  48. Push/Pull View of Supply Chains Procurement, Customer Order Manufacturing and Cycle Replenishment cycles PUSH PROCESSES PULL PROCESSES Customer Order Arrives Push-Pull boundary

  49. Direction of production flow upstream downstream Authorize productionof next unit Kanban Kanban Kanban Kanban Pull Process with Kanban Cards

  50. 100 75 50 25 100 50 Number ofdefects Cumulativepercents ofdefects Browser error Order entrymistake Wrong modelshipped Order number out off sequence Product shipped tobilling address Product shipped, butcredit card not billed Pareto Principle or 20-80 rule

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