Question

6.15. Parts manufactured by an injection molding process are subjected to a compressive strength test. Twenty samples of five parts each are collected, and the compressive strengths (in psi) are shown in Table 6E.11. (a) Establish 7 and R control charts for compressive strength using these data. Is the process in statis- tical control? (b) After establishing the control charts in part (a), 15 new subgroups were collected and the com- pressive strengths are shown in Table GE.12. Plot the Tand R values against the control units from part (a) and draw conclusions. 6.16. Reconsider the data presented in Exercise 6.15. (a) Rework both parts (a) and (b) of Exercise 6.15 using the i and s charts. (b) Does the s chart detect the shift in process vari- ability more quickly than the R chart did origi- nally in part (b) of Exercise 6.15? TABLE 6E. 11 Strength Data for Exercise 6.15 Sample Number 12 13 Xs 7.3 2 3 4 5 6 7 8 9 10 83.0 81.2 78.7 75.7 77.0 79.1 88.6 78.3 78.8 71.0 84.2 80.2 17.6 85.7 75.8 84.3 75.2 81.0 80.4 10.4 80.3 74.4 82.5 74.1 75.7 77.5 8.4 83.4 78.4 82.6 78.2 78.9 80.3 5.2 75.3 79.9 87.3 89.7 81.8 82.8 145 74.5 78.0 80.8 73.4 79.7 77.3 7.4 79.2 84.4 81.5 86.0 74.5 81.1 11.4 80.5 86.2 76.2 64.1 80.2 81.4 9.9 75.7 75.2 71.1 82.1 74.3 75.7 10.9 80.0 81.5 78.4 73.8 78.1 78.4 7.7 80.6 81.8 79.3 73.8 81.7 79.4 8.0 82.7 81.3 79.1 82.0 79.5 80.9 3.6 79.2 74.9 78.6 77.7 75.3 77.1 4.3 85.5 82.1 82.8 73.4 71.7 79.1 13.8 78.8 79.6 80.2 79.1 80.8 79.7 2.0 82.178.2 755 78.2 82.1 79.2 6.6 84.576.9 83.5 81.2 79.2 81.1 7.6 79.0 77.8 81.2 84.4 81.6 80.8 6.6 84.5 73.1 78.6 78.7 80.6 78.6 78.7 80.6 79.1 114 TABLE 6E.12 New Data for Exercise 6.15, part (1) Sample Number * * * * 1 68.9 81.5 78.2 80.8 81.5 78.2 12.6 2 69.8 68.6 80.4 843 83.9 774 15.7 3 78.5 85.2 784 803 81.7 80.8 6.8 4 76.986.1 86.9 94.4 83.9 85.6 175 5 93.6 81.6 87.8 79.6 71.0 827 225 6 655 86,8 72.4 82.6 714 75.9 21.3 7 78.1 65.7 83.7 93.7 934 82.9 279 8 74.9 72.6 81.6 872 72.7 77.8 14.6 9 78.1 77.1 67.0 67.0 75.7 76.8 749 11.0 10 78.7 854 77.7 77.7 90.7 76.7 81.9 14.0 11 85.0 60.2 68.5 71.1 82.4 73.4 249 12 86.4 79.2 79.8 86.0 75.4 81.3 10.9 13 78.5 99.0 78.3 71.4 81.8 78.3 71.4 81.8 81.7 27.5 14 68.8 62.0 82.0 775 76.1 733 19.9 15 83.0 83.7 73.1 82.2 95.3 83.5 22.2 12 13 14 15 16 17 18 19 20

Answer 1

Sol:

6.15).

(a)

Step 1: Compute Xbarbar and Rbar X-Chart 86.00 UCLX - 2X_X. +&+... X = 79.53 84.00 k k 82.00 CLX ΣR, 80.00 R= R. +R+....R R = 8.73 k 78.00 76.00 LCLX 74.00 Values taken from control chart constants corresponding to sample size N Sample size, 5 D3 0 = 2.114 A2 = 0.577 72.00 = D4 70.00 68.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Step 2: Control limits for X-chart R-Chart 20.0 UCLR UCLX=+A, R = 84.57 18.0 LCLX = -A R = 74.49 16.0 14.0 12.0 10.0 Control limits for R-chart Step 3: CLR 8.0 A 6.0 UCLr =D, R = 18.46 4.0 2.0 0.0 LCLR LCLr =D, R = 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Step 4: Plot Control Charts and determine process control O Xbar-value lie outside of control limits. Therefore based on X-chart, the process is In Control O R-value lie outside of control limits. Therefore based on R-chart, the process is In Control

(b)

Step 1: Compute Xbarbar and Rbar X-Chart - 2X_X. +&+... X = 79.53 88 86 84 UCLX k k 82 80 ΣR, CLX R= R. +R+....R R = 8.73 k 78 76 A LCLX 74 Values taken from control chart constants corresponding to sample size N Sample size, 5 D3 0 = 2.114 A2 = 0.577 = 72 70 68 D4 66 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Step 2: Control limits for X-chart R-Chart 30.0 UCLX=+A, R = 84.57 25.0 LCLX = -A R = 74.49 20.0 MN UCLR Step 3: 15.0 Control limits for R-chart 10.0 CLR UCLr =D, R = 18.46 5.0 LCLR LCLr =D, R = 0.00 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Step 4: Plot Control Charts and determine process control 3 Xbar-value lie outside of control limits. Therefore based on X-chart, the process is Out of Control 7 R-value lie outside of control limits. Therefore based on R-chart, the process is Out of Control

Therefore, based on the previous control limits and new data of 15 subgroups, the process is NOT in statistical control .

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