1. Statistical Process Control Managing for Quality Dr. Ron Lembke

2. Goal of Control Charts  collect and present data visually  allow us to see when trend appears  see when “out of control” point occurs

3. Process Control Charts  Graph of sample data plotted over time UCL LCL Process Average ± 3  Time X

4. Process Control Charts  Graph of sample data plotted over time Assignable Cause Variation Natural Variation UCL LCL Time X

5. Definitions of Out of Control 1. No points outside control limits 2. Same number above & below center line 3. Points seem to fall randomly above and below center line 4. Most are near the center line, only a few are close to control limits 1. 8 Consecutive pts on one side of centerline 2. 2 of 3 points in outer third 3. 4 of 5 in outer two-thirds region

6. Attributes vs. Variables Attributes:  Good / bad, works / doesn’t  count % bad (P chart)  count # defects / item (C chart) Variables:  measure length, weight, temperature (x-bar chart)  measure variability in length (R chart)

7. Attribute Control Charts  Tell us whether points in tolerance or not p chart: percentage with given characteristic (usually whether defective or not) np chart: number of units with characteristic c chart: count # of occurrences in a fixed area of opportunity (defects per car) u chart: # of events in a changeable area of opportunity (sq. yards of paper drawn from a machine)

8. p Chart Control Limits # Defective Items in Sample i Sample i Size

9. p Chart Control Limits # Defective Items in Sample i Sample i Size z = 2 for 95.5% limits; z = 3 for 99.7% limits # Samples

10. p Chart Control Limits # Defective Items in Sample i # Samples Sample i Size z = 2 for 95.5% limits; z = 3 for 99.7% limits

11. p Chart Example You’re manager of a 500- room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control (use z = 3)? © 1995 Corel Corp.

12. p Chart Hotel Data No.No. Not DayRoomsReady Proportion 12001616/200 =.080 2200 7.035 320021.105 420017.085 520025.125 620019.095 720016.080

13. p Chart Control Limits

14. 16 + 7 +...+ 16

15. p Chart Solution 16 + 7 +...+ 16

16. p Chart Solution 16 + 7 +...+ 16

17. p Chart UCL LCL

18. R Chart  Type of variables control chart Interval or ratio scaled numerical data  Shows sample ranges over time Difference between smallest & largest values in inspection sample  Monitors variability in process  Example: Weigh samples of coffee & compute ranges of samples; Plot

19. You’re manager of a 500- room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control? Hotel Example

20. Hotel Data DayDelivery Time 17.304.206.103.455.55 24.608.707.604.437.62 35.982.926.204.205.10 47.205.105.196.804.21 54.004.505.501.894.46 610.108.106.505.066.94 76.775.085.906.909.30

21. R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange 17.304.206.103.455.555.32 7.30 + 4.20 + 6.10 + 3.45 + 5.55 5 Sample Mean =

22. R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange 17.304.206.103.455.555.323.85 7.30 - 3.45Sample Range = LargestSmallest

23. R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange 17.304.206.103.455.555.323.85 24.608.707.604.437.626.594.27 35.982.926.204.205.104.883.28 47.205.105.196.804.215.702.99 54.004.505.501.894.464.073.61 610.108.106.505.066.947.345.04 76.775.085.906.909.306.794.22

24. R Chart Control Limits Sample Range at Time i # Samples From Exhibit 6.13

25. Control Chart Limits

26. R R Chart Control Limits R k i i k      1 385427422 7 3894.... 

27. R Chart Solution From 6.13 (n = 5) R R k UCLDR LCLDR i i k R R        1 4 3 385427422 7 3894 (2.11)(3.894)8232 (0)(3.894)0..... 

28. R Chart Solution UCL

29.  X Chart Control Limits Sample Range at Time i # Samples Sample Mean at Time i

30.  X Chart Control Limits From Table 6-13

31.  X Chart Control Limits Sample Range at Time i # Samples Sample Mean at Time i From 6.13

32. Exhibit 6.13 Limits

33. R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange 17.304.206.103.455.555.323.85 24.608.707.604.437.626.594.27 35.982.926.204.205.104.883.28 47.205.105.196.804.215.702.99 54.004.505.501.894.464.073.61 610.108.106.505.066.947.345.04 76.775.085.906.909.306.794.22

34.  X Chart Control Limits X X k R R k i i k i i k           1 1 532659679 7 5813 385427422 7 3894........  

35.  X Chart Control Limits From 6.13 (n = 5) X X k R R k UCLXAR i i k i i k X            1 1 2 532659679 7 5813 385427422 7 3894 5813058 *38948060............  

36.  X Chart Solution From 6.13 (n = 5) X X k R R k UCLXAR LCLXAR i i k i i k X X             1 1 2 2 532659679 7 5813 385427422 7 3894 5813(058) 5813(058) (3.894) = 3.566............   (3.894) = 8.060

37.  X Chart Solution* 0 2 4 6 8 1234567  X, Minutes Day UCL LCL

38. Thinking Challenge You’re manager of a 500- room hotel. The hotel owner tells you that it takes too long to deliver luggage to the room (even if the process may be in control). What do you do? © 1995 Corel Corp. N

39.  Redesign the luggage delivery process  Use TQM tools Cause & effect diagrams Process flow charts Pareto charts Solution MethodPeople Material Equipment Too Long