1. Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

2. Basics of Statistical Process Control Statistical Process Control (SPC) developed by Walter A. Shewhart at Bell Lab in 1920. –monitoring production process to detect and prevent poor quality Sample –subset of items produced to use for inspection Control Charts –process is within statistical control limits UCL LCL

3. SPC in TQM SPC –tool for identifying problems and make improvements –contributes to the TQM goal of continuous improvements Real world Example: Honda

4. Control Chart –Purpose: to monitor process output to see if it is random deciding whether the process is in control or not –A time ordered plot represents sample statistics obtained from an ongoing process (e.g. sample means) –Upper and lower control limits define the range of acceptable variation

5. VariabilityVariability Random –common causes –inherent in a process –can be eliminated only through improvements in the system Non-Random –special causes –due to identifiable factors –can be modified through operator or management action

6. Process Control Chart 12345678910 Sample number Uppercontrollimit Processaverage Lowercontrollimit Out of control

7. Quality Measures Variable –a product characteristic that is continuous and can be measured –weight - length Attribute –a product characteristic that can be evaluated with a discrete response –good – bad; yes - no

8. Control Charts Types of charts –Variables mean (x bar – chart) range (R-chart) *Note: mean and range charts are used together –Attributes p-chart c-chart

9. Control Charts for Variables Mean control charts –Used to monitor the central tendency of a process. –X bar charts Range control charts –Used to monitor the process variability –R charts

10. 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 are beyond control limits  It is possible for sample averages to be in control, but ranges might be very large

11. Mean and Range Charts UCL LCL UCL LCL R-chart x-Chart Detects shift Does not detect shift (process mean is shifting upward) Sampling Distribution

12. 10-12 x-Chart UCL Does not reveal increase Mean and Range Charts UCL LCL R-chart Reveals increase (process variability is increasing) Sampling Distribution

13. 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 =

14. 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

15. ExampleExample measuring the weight/packet in grams Packet Sample 1 2 3 R i x-bar i 1424044 2354045 3444444 4404043 5414138 Total ___ ___ Average ___ ___

16. Example (cont.) # of samples = k = Sample size = n =

17. Example (cont.) X-bar chart

18. Example (cont.) R chart

19. Example (cont.)

20. Fa cto rs 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

21. Control Charts for Attributes  p-charts  uses portion defective in a sample  c-charts  uses number of defects in an item

22. p-Chartp-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

23. p-Chart Example (assume the sample size of 100) NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE 113 27 320 40 5 10 5 10totalaverage

24. P-Chart Example (cont.) P-Chart Example (cont.) Step 1: get sigma Step 2: get UCL and LCL

25. C-ChartC-Chart UCL = c + z  c LCL = c - z  c where c = number of defects per sample  c = c

26. C-Chart (cont.) Measuring number of fouls called on a team per game 1 37 2 9 3 22 4 25 5 32 TotalAvg. SAMPLE NUMBER OF FOULS

27. C-Chart (cont.) UCL= c + z  c LCL= c - z  c

28. Control Chart Patterns UCL LCL Sample observations consistently above the center line LCL UCL Sample observations consistently below the center line

29. Control Chart Patterns (cont.) LCL UCL Sample observations consistently increasing UCL LCL Sample observations consistently decreasing

30. Homework for Ch 6-II 6–30 Computer upgrade problem Computer upgrades take 80 minutes. Six samples of five observations each have been taken, and the results are as listed. Determine if the process is in control. You have to use appropriate chart(s) 1 2 3 4 5 6 79.2 80.5 79.6 78.9 80.579.7 78.8 78.7 79.6 79.4 79.680.6 80.0 81.0 80.4 79.7 80.480.5 78.4 80.4 80.3 79.4 80.880.0 81.0 80.1 80.8 80.6 78.881.1

31. Homework for Ch 6-II 6–31 Wrong account problem The operations manager of the booking services department of hometown bank is concerned about the number of wrong customer account numbers recorded by hometown personnel. Each week a random sample of 2,500 deposits is taken, and the number of incorrect account numbers is recorded. The results for the past 12 weeks are shown in the following table. Is the process out of control? Use appropriate control chart and use three sigma control limit, ie. Z=3. Sample number 1 2 3 4 5 6 7 8 9 10 11 12 wrong account 1512 19 2 19 4 24 7 10 17 15 3