1. Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Statistical Process Control Operations Management - 6 th Edition Chapter 3 Roberta Russell & Bernard W. Taylor, III

2. Copyright 2006 John Wiley & Sons, Inc.4-2 Lecture Outline  Basics of Statistical Process Control  Control Charts  Control Charts for Attributes  Control Charts for Variables  SPC with Excel  Process Capability

3. Copyright 2006 John Wiley & Sons, Inc.4-3 Basics of Statistical Process Control  Statistical Process Control (SPC) monitoring production process to detect and prevent poor quality monitoring production process to detect and prevent poor quality  Sample subset of items produced to use for inspection subset of items produced to use for inspection  Control Charts process is within statistical control limits process is within statistical control limits UCL LCL

4. Copyright 2006 John Wiley & Sons, Inc.4-4 Variability  Random common causes common causes inherent in a process inherent in a process can be eliminated only through improvements in the system can be eliminated only through improvements in the system  Non-Random special causes special causes due to identifiable factors due to identifiable factors can be modified through operator or management action can be modified through operator or management action

5. Copyright 2006 John Wiley & Sons, Inc.4-5 SPC in TQM  SPC tool for identifying problems and make improvements tool for identifying problems and make improvements contributes to the TQM goal of continuous improvements contributes to the TQM goal of continuous improvements

6. Copyright 2006 John Wiley & Sons, Inc.4-6 Quality Measures  Attribute a product characteristic that can be evaluated with a discrete response a product characteristic that can be evaluated with a discrete response good – bad; yes - no good – bad; yes - no  Variable a product characteristic that is continuous and can be measured a product characteristic that is continuous and can be measured weight - length weight - length

7. Copyright 2006 John Wiley & Sons, Inc.4-7  Nature of defect is different in services  Service defect is a failure to meet customer requirements  Monitor times, customer satisfaction Applying SPC to Service

8. Copyright 2006 John Wiley & Sons, Inc.4-8 Applying SPC to Service (cont.)  Hospitals timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts  Grocery Stores waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors  Airlines flight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance flight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance

9. Copyright 2006 John Wiley & Sons, Inc.4-9 Applying SPC to Service (cont.)  Fast-Food Restaurants waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy  Catalogue-Order Companies order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time 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 billing accuracy, timeliness of claims processing, agent availability and response time

10. Copyright 2006 John Wiley & Sons, Inc.4-10 Where to Use Control Charts  Process has a tendency to go out of control  Process is particularly harmful and costly if it goes out of control  Examples at the beginning of a process because it is a waste of time and money to begin production process with bad supplies at the beginning of a process because it is a waste of time and money to begin production process with bad supplies before a costly or irreversible point, after which product is difficult to rework or correct before a costly or irreversible point, after which product is difficult to rework or correct before and after assembly or painting operations that might cover defects before and after assembly or painting operations that might cover defects before the outgoing final product or service is delivered before the outgoing final product or service is delivered

11. Copyright 2006 John Wiley & Sons, Inc.4-11 Control Charts  A graph that establishes control limits of a process  Control limits upper and lower bands of a control chart upper and lower bands of a control chart  Types of charts Attributes Attributes p-chart p-chart c-chart c-chart Variables Variables range (R-chart) range (R-chart) mean (x bar – chart) mean (x bar – chart)

12. Copyright 2006 John Wiley & Sons, Inc.4-12 Process Control Chart 12345678910 Sample number Uppercontrollimit Processaverage Lowercontrollimit Out of control

13. Copyright 2006 John Wiley & Sons, Inc.4-13 Normal Distribution  =0 1111 2222 3333 -1  -2  -3  95% 99.74%

14. Copyright 2006 John Wiley & Sons, Inc.4-14 A Process Is in Control If … 1.… no sample points outside limits 2.… most points near process average 3.… about equal number of points above and below centerline 4.… points appear randomly distributed

15. Copyright 2006 John Wiley & Sons, Inc.4-15 Control Charts for Attributes  p-charts  uses portion defective in a sample  c-charts  uses number of defects in an item

16. Copyright 2006 John Wiley & Sons, Inc.4-16 p-Chart UCL = p + z  p LCL = p - z  p z=number of standard deviations from process average p=sample proportion defective; an estimate of process average  p = standard deviation of sample proportion p =p =p =p = p(1 - p) n

17. Copyright 2006 John Wiley & Sons, Inc.4-17 p-Chart Example 20 samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE 16.06 20.00 34.04 ::: 2018.18 200

18. Copyright 2006 John Wiley & Sons, Inc.4-18 p-Chart Example (cont.) UCL = p + z = 0.10 + 3 p(1 - p) n 0.10(1 - 0.10) 100 UCL = 0.190 LCL = 0.010 LCL = p - z = 0.10 - 3 p(1 - p) n 0.10(1 - 0.10) 100 = 200 / 20(100) = 0.10 total defectives total sample observations p =

19. Copyright 2006 John Wiley & Sons, Inc.4-19 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Proportion defective Sample number 2468101214161820 UCL = 0.190 LCL = 0.010 p = 0.10 p-Chart Example (cont.)

20. Copyright 2006 John Wiley & Sons, Inc.4-20 c-Chart UCL = c + z  c LCL = c - z  c where c = number of defects per sample  c = c

21. Copyright 2006 John Wiley & Sons, Inc.4-21 c-Chart (cont.) Number of defects in 15 sample rooms 1 12 2 8 3 16 : : 15 15 190 190 SAMPLE c = = 12.67 19015 UCL= c + z  c = 12.67 + 3 12.67 = 23.35 LCL= c + z  c = 12.67 - 3 12.67 = 1.99 NUMBER OF DEFECTS

22. Copyright 2006 John Wiley & Sons, Inc.4-22 3 6 9 12 15 18 21 24 Number of defects Sample number 246810121416 UCL = 23.35 LCL = 1.99 c = 12.67 c-Chart (cont.)

23. Copyright 2006 John Wiley & Sons, Inc.4-23 Control Charts for Variables  Mean chart ( x -Chart )  uses average of a sample  Range chart ( R-Chart )  uses amount of dispersion in a sample

24. Copyright 2006 John Wiley & Sons, Inc.4-24 x-bar Chart x =x =x =x = x 1 + x 2 +... x k k = UCL = x + A 2 RLCL = x - A 2 R == where x= average of sample means =

25. Copyright 2006 John Wiley & Sons, Inc.4-25 x-bar Chart Example Example 15.4 OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 12345xR 15.025.014.944.994.964.980.08 25.015.035.074.954.965.000.12 34.995.004.934.924.994.970.08 45.034.915.014.984.894.960.14 54.954.925.035.055.014.990.13 64.975.065.064.965.035.010.10 75.055.015.104.964.995.020.14 85.095.105.004.995.085.050.11 95.145.104.995.085.095.080.15 105.014.985.085.074.995.030.10 50.091.15

26. Copyright 2006 John Wiley & Sons, Inc.4-26 UCL = x + A 2 R = 5.01 + (0.58)(0.115) = 5.08 LCL = x - A 2 R = 5.01 - (0.58)(0.115) = 4.94 = = x = = = 5.01 cm = xkxk 50.09 10 x- bar Chart Example (cont.) Retrieve Factor Value A 2

27. Copyright 2006 John Wiley & Sons, Inc.4-27 x- bar Chart Example (cont.) UCL = 5.08 LCL = 4.94 Mean Sample number |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | 10 5.10 – 5.08 – 5.06 – 5.04 – 5.02 – 5.00 – 4.98 – 4.96 – 4.94 – 4.92 – x = 5.01 =

28. Copyright 2006 John Wiley & Sons, Inc.4-28 R- Chart UCL = D 4 RLCL = D 3 R R =R =R =R = RRkkRRkkk where R= range of each sample k= number of samples

29. Copyright 2006 John Wiley & Sons, Inc.4-29 R-Chart Example OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR 15.025.014.944.994.964.980.08 25.015.035.074.954.965.000.12 34.995.004.934.924.994.970.08 45.034.915.014.984.894.960.14 54.954.925.035.055.014.990.13 64.975.065.064.965.035.010.10 75.055.015.104.964.995.020.14 85.095.105.004.995.085.050.11 95.145.104.995.085.095.080.15 105.014.985.085.074.995.030.10 50.091.15 Example 15.3

30. Copyright 2006 John Wiley & Sons, Inc.4-30 R-Chart Example (cont.) Example 15.3 RkRk R = = = 0.115 1.15 10 UCL = D 4 R = 2.11(0.115) = 0.243 LCL = D 3 R = 0(0.115) = 0 Retrieve Factor Values D 3 and D 4 Retrieve Factor Values D 3 and D 4

31. Copyright 2006 John Wiley & Sons, Inc.4-31 R-Chart Example (cont.) UCL = 0.243 LCL = 0 Range Sample number R = 0.115 |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | 10 0.28 – 0.24 – 0.20 – 0.16 – 0.12 – 0.08 – 0.04 – 0 –

32. Copyright 2006 John Wiley & Sons, Inc.4-32 Using x- bar and R-Charts Together  Process average and process variability must be in control.  It is possible for samples to have very narrow ranges, but their averages is beyond control limits.  It is possible for sample averages to be in control, but ranges might be very large.

33. Copyright 2006 John Wiley & Sons, Inc.4-33 Sample Size  Attribute charts require larger sample sizes  50 to 100 parts in a sample  Variable charts require smaller samples  2 to 10 parts in a sample

34. Copyright 2006 John Wiley & Sons, Inc.4-34 SPC with Excel UCL=0.19 LCL=0.01

35. Copyright 2006 John Wiley & Sons, Inc.4-35 SPC with Excel: Formulas

36. Copyright 2006 John Wiley & Sons, Inc.4-36 Process Capability  Tolerances design specifications reflecting product requirements design specifications reflecting product requirements  Process capability range of natural variability in a process what we measure with control charts range of natural variability in a process what we measure with control charts

37. Copyright 2006 John Wiley & Sons, Inc.4-37 Process Capability (b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time. Design Specifications Process (a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time. Design Specifications Process

38. Copyright 2006 John Wiley & Sons, Inc.4-38 Process Capability (cont.) (c) Design specifications greater than natural variation; process is capable of always conforming to specifications. Design Specifications Process (d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification. Design Specifications Process

39. Copyright 2006 John Wiley & Sons, Inc.4-39 Process Capability Measures Process Capability Ratio Cp==Cp== tolerance range process range upper specification limit - lower specification limit 6 

40. Copyright 2006 John Wiley & Sons, Inc.4-40 Computing C p Net weight specification = 9.0 oz  0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz C p = = = 1.39 upper specification limit - lower specification limit 6  9.5 - 8.5 6(0.12)

41. Copyright 2006 John Wiley & Sons, Inc.4-41 Process Capability Measures Process Capability Index C pk = minimum x - lower specification limit 3  = upper specification limit - x 3  =,

42. Copyright 2006 John Wiley & Sons, Inc.4-42 Computing C pk Net weight specification = 9.0 oz  0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz C pk = minimum = minimum, = 0.83 x - lower specification limit 3  = upper specification limit - x 3  =, 8.80 - 8.50 3(0.12) 9.50 - 8.80 3(0.12)

43. Copyright 2006 John Wiley & Sons, Inc.4-43 Fact ors nA2D3D4nA2D3D4 SAMPLE SIZEFACTOR FOR x-CHARTFACTORS FOR R-CHART 21.880.003.27 31.020.002.57 40.730.002.28 50.580.002.11 60.480.002.00 70.420.081.92 80.370.141.86 90.440.181.82 100.110.221.78 110.990.261.74 120.770.281.72 130.550.311.69 140.440.331.67 150.220.351.65 160.110.361.64 170.000.381.62 180.990.391.61 190.990.401.61 200.880.411.59 Appendix: Determining Control Limits for x-bar and R-Charts Return

44. Copyright 2006 John Wiley & Sons, Inc.4-44 CP &C pk Index  Cp < 1.0 the process range is greater than the tolerance range. Process is not capable of producing within specification all the time.  Cp =1 the tolerance range and the process range are the same.  Cp >1 the tolerance range is greater than the process range.  Cp ≥ 1 would indicate that the process is capable of meeting specification.  C pk index is greater than 1.0 then the process is capable of meeting design specification.  If C pk < 1.0 then the process mean has moved closed to one of the upper or lower design specifications, and it will generate defects.  If C pk = Cp then process mean is centered on the design target.