Lesson 7.1 Quality Control

1. Lesson 7.1 Quality Control Today we will learn to… > use quality control charts to determine if a manufacturing process is out of control

2. A business hires someone to be in charge of “quality control” to ensure that they produce a quality product.

3. X Charts The X Chart is used to analyze the means of measured values to determine if a quality product is being produced.

4. R charts The R Chart is used to analyze the ranges of measured values to determine if the manufacturing process is consistent.

5. Step 2 – compute the Grand Mean ( XGM ) and the mean of the ranges (R) Step 1 – compute the mean and range of each sample Step 3 – compute upper and lower control limits Step 4 – plot control charts Step 5 – analyze the charts

6. UCLx XGM LCLx control chart for a process that is in control

7. UCLx XGM LCLx control chart for a process that is out of control

8. Why is a process out of control? Two types of variation that can occur in manufacturing process: 1) chance variation – random problem & cannot be eliminated entirely 2) assignable-cause variation – not random & must be eliminated to maintain quality of product

9. A manufacturer of rope tests the breaking strength of 6 samples of 5 ropes. R X 46 2 4 51 3 50 3 50 5 48 51 3 Step 1 – mean & range of samples n = 5

10. R = XGM = Step 2 – the mean of the means the mean of the ranges 49.3 3.33  49  3

11. UCLx = XGM+ A R LCLx = XGM – A R Step 3 – compute the upper control limit and the lower control limit A is a constant obtained from the Quality Control Table where n is the number of items in one sample.

12. UCLx = XGM+ A R LCLx = XGM – A R Step 3 – compute the upper control limit and the lower control limit 49 + (0.577)(3) =  51 50.7 49 - (0.577)(3) =  47 47.3 Step 4 – draw the chart

13. =51 UCLx =49 XGM =47 LCLx X Chart 52 51 50 49 48 47 46 1 2 3 4 5 6 the quality is out of control

14. UCLR = D4R LCLR = D3R Step 3 – compute the upper control limit and the lower control limit D4 and D3 are constants obtained from the Quality Control Table where n is the number of items in one sample.

15. R = UCLR = D4R LCLR = D3R n = D4 = 5 2.115 D3 = 3 0 (2.115)(3) = 6.345  6 (0)(3) = 0 Step 4 – draw the chart

16. 7 6 5 4 3 2 1 0 =6.3 UCLR R = 3 LCLR =0 R chart 1 2 3 4 5 6 The process is consistent!

17. A battery is designed to last for 200 hours. Ten samples of six batteries each were selected and tested. Construct and analyze a quality control X chart for the data. n = 6

18. R = XGM = Battery Tests How is this chart different from the first chart? 201.96 202.0 2.1

19. Step 3 – compute the upper control limit and the lower control limit R = XGM = UCLx = XGM+ A R LCLx = XGM – A R 202.0 n = 6 A = 0.483 2.1 202 + (0.483)(2.1) = 203 202 - (0.483)(2.1) = 201

20. R chart UCLx =203 XGM =202 LCLx =201 206 205 204 203 202 201 200 199 198 1 2 3 4 5 6 7 8 9 10 out of control (not consistent) The battery performance is

21. X charts quality of product is acceptable In control  quality of product is NOT acceptable Out of control  R charts quality is consistent In control  quality is NOT consistent Out of control 

22. Lesson 7.2 Quality Control Today we will learn to… > use quality control charts to determine if a manufacturing process is out of control

23. Product quality acceptable, manufacturing process consistent Product quality acceptable, manufacturing process not consistent Product quality not acceptable, manufacturing process consistent Product quality not acceptable, manufacturing process not consistent

24. Lesson 7.3 Attribute Charts Today we will learn to… > use attribute charts to determine if a manufacturing process is out of control

25. When manufacturing items, there is always some level of “acceptable” defects. Attribute Charts are used to determine if manufactured items are within the acceptable limits of defects.

26. The p chart is used to analyze the percent of defects per sample. The c chart is used to analyze the quality of and item by counting the number of defects per item p charts and c charts Two types of charts are used to measure attributes.

27. A company manufactures ball point pens. Five samples of 50 pens each are selected, and the number of defective pens in each sample is recorded. n = 50

28. Step 1 – find proportion of defective parts for each sample 0.06 0.02 0.08 0.04 0.10

29. p = p = 0.06 + 0.02 + 0.08 + 0.04 + 0.10 5 Step 2 – find the mean for the proportions of defective parts 0.06 n = 50

30. p (1 – p ) UCLp = p + 3 n p (1 – p ) LCLp = p – 3 n -3σ -2σ -1σ +1σ +2σ +3σ Step 3 – find the UCLp and LCLp ♪♫ Memories ♪♫

31. 0.06 (1 – 0.06 ) 0.06 + 3 50 0.06 (1 – 0.06 ) 0.06 – 3 50 Step 3 – find the UCLp and LCLp UCLp = UCLp = 0.16 LCLp = LCLp = – 0.042 = 0 Since proportions cannot be negative, we use zero.

32. 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0 UCLp =0.16 Step 4 – Draw the p chart p = 0.06 =0 LCLp 1 2 3 4 5 The number of defects per sample is acceptable.

33. Calculators are manufactured and checked for defects. Twelve of the defective calculators are checked for the number of defects per calculator. The defects might include soldering, lettering, cracked cases, and memory error.

34. Step 1 – find the average number of defects per item, c. c = The number of defects per calculator are: 6, 3, 2, 5, 6, 7, 4, 3, 7, 8, 9, 5 65  12 = 5.42  5

35. UCLc = c + 3 c LCLc = c – 3 c Step 2 – Find UCLc and LCLc = 11.7  12 = – 1.71 = 0 Since proportions cannot be negative, zero is used.

36. 12 10 8 6 4 2 0 UCLc = 12 c = 5 LCLc = 0 Step 3 – Draw the c chart 1 2 3 4 5 6 7 8 9 10 11 12 Since all points fall within the limits, The number of defects per calculator is acceptable.

37. p charts % of defective products is acceptable In control  % of defective products NOT acceptable Out of control  c charts # of defects per item is acceptable In control  # of defects per item is NOT acceptable Out of control 