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Chapter 7

Six Sigma Quality and Statistical Process Control. Chapter 7. Definition: Total Quality Management. Total Quality Management (TQ, QM or TQM) and Six Sigma (6 ) are sweeping “culture change” efforts to position a company for greater customer satisfaction, profitability and competitiveness.

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Chapter 7

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  1. Six Sigma Quality and Statistical Process Control Chapter 7

  2. Definition:Total Quality Management • Total Quality Management (TQ, QM or TQM) and Six Sigma (6) are sweeping “culture change” efforts to position a company for greater customer satisfaction, profitability and competitiveness. • TQ may be defined as managing the entire organization so that it excels on all dimensions of products and services that are important to the customer.

  3. Total Quality Is… • Meeting Our Customer’s Requirements • Doing Things Right the First Time; Freedom from Failure (Defects) • Consistency (Reduction in Variation) • Continuous Improvement • Quality in Everything We Do

  4. The Continuous Improvement Process Measurement Empowerment/ Shared Leadership Customer Satisfaction Measurement Business Results Measurement Process Improvement/ Problem Solving Team Management . . . Measurement

  5. Is 99% Quality Good Enough? • 22,000 checks will be deducted from the wrong bank accounts in the next 60 minutes. • 20,000 incorrect drug prescriptions will be written in the next 12 months. • 12 babies will be given to the wrong parents each day.

  6. 100K 10K 1K 100 10 1 2 3 4 5 6 7 But is Six Sigma Realistic? · IRS – Tax Advice (phone-in) · (66810 ppm) · · Restaurant Bills · Doctor Prescription Writing · Payroll Processing · · Average Company Order Write-up · Journal Vouchers Wire Transfers Air Line Baggage Handling · Defects Per Million Opportunities (DPMO) Purchased Material Lot Reject Rate (233 ppm) Best in Class Domestic Airline Flight Fatality Rate (3.4 ppm) (0.43 ppm) SIGMA

  7. Six Sigma Quality The objective of Six Sigma quality is 3.4 defects per million opportunities!

  8. UCL LCL Statistical Process Control • Take periodic samples from process • Plot sample points on control chart • Determine if process is within limits • Prevent quality problems

  9. Variation • Common Causes • Variation inherent in a process • Can be eliminated only through improvements in the system • Special Causes • Variation due to identifiable factors • Can be modified through operator or management action

  10. Types of Data • Attribute data • Product characteristic evaluated with a discrete choice • Good/bad, yes/no • Variable data • Product characteristic that can be measured • Length, size, weight, height, time, velocity

  11. SPC Applied to Services • Nature of defect is different in services • Service defect is a failure to meet customer requirements • Monitor times, customer satisfaction

  12. Service Quality Examples • Hospitals • Timeliness, responsiveness, accuracy of lab tests • Grocery Stores • Check-out time, stocking, cleanliness • Airlines • Luggage handling, waiting times, courtesy • Fast food restaurants • Waiting times, food quality, cleanliness, employee courtesy

  13. Service Quality Examples • Catalog-order companies • Order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time • Insurance companies • Billing accuracy, timeliness of claims processing, agent availability and response time

  14. Control Charts • Graph establishing process control limits • Charts for variables • Mean (x-bar), Range (R) • Chart for attributes • P Chart • C Chart

  15. Out of control Upper control limit Process average Lower control limit 1 2 3 4 5 6 7 8 9 10 Sample number Process Control Chart Figure 15.1

  16. A Process is In Control if No sample points outside limits Most points near process average About equal number of points above & below centerline Points appear randomly distributed

  17. Development of Control Chart • Based on in-control data • If non-random causes present, find the special cause and discard data • Correct control chart limits

  18. Control Chart for Attributes • p Charts • Calculate percent defectives in sample

  19. UCL = p + zp LCL = p - zp where z = the number of standard deviations from the process average p = the sample proportion defective; an estimate of the process average p = the standard deviation of the sample proportion p(1 - p) n p = p-Chart

  20. 95% 99.74% -3 -2 -1 =0 1 2 3 The Normal Distribution

  21. Control Chart Z Values • Smaller Z values make more sensitive charts • Z = 3.00 is standard • Compromise between sensitivity and errors

  22. NUMBER OF PROPORTION SAMPLE DEFECTIVES DEFECTIVE 1 6 .06 2 0 .00 3 4 .04 : : : : : : 20 18 .18 200 p-Chart Example 20 samples of 100 pairs of jeans Example 15.1

  23. NUMBER OF PROPORTION SAMPLE DEFECTIVES DEFECTIVE 1 6 .06 2 0 .00 3 4 .04 : : : : : : 20 18 .18 200 total defectives total sample observations p = = 200 / 20(100) = 0.10 p-Chart Example 20 samples of 100 pairs of jeans Example 15.1

  24. NUMBER OF PROPORTION SAMPLE DEFECTIVES DEFECTIVE p = 0.10 1 6 .06 2 0 .00 3 4 .04 : : : : : : 20 18 .18 200 0.10(1 - 0.10) 100 p(1 - p) n UCL = p + z = 0.10 + 3 UCL = 0.190 0.10(1 - 0.10) 100 p(1 - p) n LCL = p - z = 0.10 - 3 LCL = 0.010 p-Chart Example 20 samples of 100 pairs of jeans Example 15.1

  25. 0.20 UCL = 0.190 0.18 0.16 0.14 0.12 p = 0.10 0.10 Proportion defective 0.08 0.06 0.04 0.02 LCL = 0.010 2 4 6 8 10 12 14 16 18 20 Sample number p-Chart

  26. C Chart • Used when you can’t calculate a proportion defective and an actual count is used. • Key –the number of defects is assumed to come from a large population • Ex. Defects in the paint job of a car

  27. C Chart con’t • The mean is the average counted number of defects per item (total divided number of samples • The sample standard deviation is √cbar (square root of the mean of C)

  28. Control Charts for Variables • Mean chart ( x -Chart ) • Uses average of a sample • Range chart ( R-Chart ) • Uses amount of dispersion in a sample

  29. UCL = D4R LCL = D3R • R k R = where R = range of each sample k = number of samples Range ( R- ) Chart

  30. nA2D3 D4 2 1.88 0.00 3.27 3 1.02 0.00 2.57 4 0.73 0.00 2.28 5 0.58 0.00 2.11 6 0.48 0.00 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.44 0.18 1.82 10 0.11 0.22 1.78 11 0.99 0.26 1.74 12 0.77 0.28 1.72 13 0.55 0.31 1.69 14 0.44 0.33 1.67 15 0.22 0.35 1.65 16 0.11 0.36 1.64 17 0.00 0.38 1.62 18 0.99 0.39 1.61 19 0.99 0.40 1.61 20 0.88 0.41 1.59 SAMPLE SIZE FACTOR FOR x-CHART FACTORS FOR R-CHART Range ( R- ) Chart Table 15.1

  31. OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 R-Chart Example Example 15.3

  32. R k 1.15 10 UCL = D4R = 2.11(0.115) = 0.243 LCL = D3R = 0(0.115) = 0 OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 R = = = 0.115 0.28 – 0.24 – 0.20 – 0.16 – 0.12 – 0.08 – 0.04 – 0 – UCL = 0.243 R = 0.115 Range LCL = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 10 | 7 Sample number R-Chart Example Example 15.3

  33. x1 + x2 + ... xk k = x = = = UCL = x + A2R LCL = x - A2R where x = the average of the sample means = x-Chart Calculations

  34. OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 • x k 50.09 10 = x = = = 5.01 cm UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08 LCL = x - A2R = 5.01 - (0.58)(0.115) = 4.94 = = x-Chart Example Example 15.4

  35. 5.10 – 5.08 – 5.06 – 5.04 – 5.02 – 5.00 – 4.98 – 4.96 – 4.94 – 4.92 – UCL = 5.08 OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 • x k 50.09 10 = x = = = 5.01 cm = x = 5.01 Mean UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08 LCL = x - A2R = 5.01 - (0.58)(0.115) = 4.94 = = LCL = 4.94 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 Sample number x-Chart Example Example 15.4

  36. Using x- and R-Charts Together • Each measures the process differently • Both process average and variability must be in control

  37. Sample Size Determination • Attribute control charts • 50 to 100 parts in a sample • Variable control charts • 2 to 10 parts in a sample

  38. Process Capability • Process limits (The “Voice of the Process” or The “Voice of the Data”) - based on natural (common cause) variation • Tolerance limits (The “Voice of the Customer”) – customer requirements • Process Capability – A measure of how “capable” the process is to meet customer requirements; compares process limits to tolerance limits

  39. Process Capability • Range of natural variability in process • Measured with control charts. • Process cannot meet specifications if natural variability exceeds tolerances • 3-sigma quality • Specifications equal the process control limits. • 6-sigma quality • Specifications twice as large as control limits

  40. Design Specifications (a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time. Process Design Specifications (b) Design specifications and natural variation the same; process is capable of meeting specifications most the time. Process Process Capability Figure 15.5

  41. Design Specifications (c) Design specifications greater than natural variation; process is capable of always conforming to specifications. Process Design Specifications (d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification. Process Process Capability Figure 15.5

  42. = x - lower specification limit 3 , Cpk = minimum = upper specification limit - x 3 Process Capability Measures Process Capability Index

  43. = x - lower specification limit 3 , Cpk = minimum = minimum , = 0.83 = upper specification limit - x 3 9.50 - 8.80 3(0.12) 8.80 - 8.50 3(0.12) Computing Cpk Net weight specification = 9.0 oz  0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz Example 15.7

  44. Interpreting the Process Capability Index Cpk < 1 Not Capable Cpk > 1 Capable at 3 Cpk > 1.33 Capable at 4 Cpk > 1.67 Capable at 5 Cpk > 2 Capable at 6

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