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Statistical Process Control

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. Variation. Common Causes Variation inherent in a process

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Statistical Process Control

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  1. 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 2000 by Prentice-Hall, Inc

  2. 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 2000 by Prentice-Hall, Inc

  3. 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 2000 by Prentice-Hall, Inc

  4. SPC Applied to Services • Nature of defect is different in services • Service defect is a failure to meet customer requirements • Monitor times, customer satisfaction 2000 by Prentice-Hall, Inc

  5. 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 2000 by Prentice-Hall, Inc

  6. 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 2000 by Prentice-Hall, Inc

  7. Control Charts • Graph establishing process control limits • Charts for variables • Mean (x-bar), Range (R) • Charts for attributes • p and c 2000 by Prentice-Hall, Inc

  8. 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 2000 by Prentice-Hall, Inc

  9. 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 2000 by Prentice-Hall, Inc

  10. Development of Control Chart • Based on in-control data • If non-random causes present discard data • Correct control chart limits 2000 by Prentice-Hall, Inc

  11. Control Charts for Attributes • p Charts • Calculate percent defectives in sample • c Charts • Count number of defects in item 2000 by Prentice-Hall, Inc

  12. 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 2000 by Prentice-Hall, Inc

  13. 95% 99.74% -3 -2 -1 =0 1 2 3 The Normal Distribution 2000 by Prentice-Hall, Inc

  14. Control Chart Z Values • Smaller Z values make more sensitive charts • Z = 3.00 is standard • Compromise between sensitivity and errors 2000 by Prentice-Hall, Inc

  15. 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 2000 by Prentice-Hall, Inc

  16. 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 2000 by Prentice-Hall, Inc

  17. 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 2000 by Prentice-Hall, Inc

  18. 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 2000 by Prentice-Hall, Inc

  19. UCL = c + zc c = c LCL = c - zc c-Chart where c = number of defects per sample 2000 by Prentice-Hall, Inc

  20. SAMPLE NUMBER OF DEFECTS 1 12 2 8 3 16 : : : : 15 15 190 c = = 12.67 UCL = c + zc = 12.67 + 3 12.67 = 23.35 190 15 c-Chart The number of defects in 15 sample rooms LCL = c + zc = 12.67 - 3 12.67 = 1.99 Example 15.2 2000 by Prentice-Hall, Inc

  21. 24 UCL = 23.35 21 18 c = 12.67 15 Number of defects 12 9 6 LCL = 1.99 3 2 4 6 8 10 12 14 16 Sample number c-Chart 2000 by Prentice-Hall, Inc

  22. Control Charts for Variables • Mean chart ( x -Chart ) • Uses average of a sample • Range chart ( R-Chart ) • Uses amount of dispersion in a sample 2000 by Prentice-Hall, Inc

  23. UCL = D4R LCL = D3R • R k R = where R = range of each sample k = number of samples Range ( R- ) Chart 2000 by Prentice-Hall, Inc

  24. 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 2000 by Prentice-Hall, Inc Table 15.1

  25. 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 2000 by Prentice-Hall, Inc

  26. 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 2000 by Prentice-Hall, Inc

  27. x1 + x2 + ... xk k = x = = = UCL = x + A2R LCL = x - A2R where x = the average of the sample means = x-Chart Calculations 2000 by Prentice-Hall, Inc

  28. 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 2000 by Prentice-Hall, Inc

  29. 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 2000 by Prentice-Hall, Inc

  30. Using x- and R-Charts Together • Each measures the process differently • Both process average and variability must be in control 2000 by Prentice-Hall, Inc

  31. UCL UCL LCL LCL Sample observations consistently below the center line Sample observations consistently above the center line Control Chart Patterns Figure 15.3 2000 by Prentice-Hall, Inc

  32. UCL UCL LCL Sample observations consistently increasing LCL Sample observations consistently decreasing Control Chart Patterns Figure 15.3 2000 by Prentice-Hall, Inc

  33. = UCL 3 sigma = x + A2R Zone A = 2 3 2 sigma = x + (A2R) Zone B = 1 3 1 sigma = x + (A2R) Zone C = Process average x Zone C = 1 3 1 sigma = x - (A2R) Zone B = 2 3 2 sigma = x - (A2R) Zone A = LCL 3 sigma = x - A2R | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 Sample number Zones for Pattern Tests Figure 15.4 2000 by Prentice-Hall, Inc

  34. Control Chart Patterns 8 consecutive points on one side of the center line. 8 consecutive points up or down across Zones. 14 points alternating up or down. 2 out of 3 consecutive points in Zone A but still inside the control limits. 4 out of 5 consecutive points in Zone A or B. 2000 by Prentice-Hall, Inc

  35. SAMPLE x ABOVE/BELOW UP/DOWN ZONE 1 4.98 B — B 2 5.00 B U C 3 4.95 B D A 4 4.96 B D A 5 4.99 B U C 6 5.01 — U C 7 5.02 A U C 8 5.05 A U B 9 5.08 A U A 10 5.03 A D B Performing a Pattern Test 2000 by Prentice-Hall, Inc Example 15.5

  36. Sample Size Determination • Attribute control charts • 50 to 100 parts in a sample • Variable control charts • 2 to 10 parts in a sample 2000 by Prentice-Hall, Inc

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