The purity of a chemical product is measured every two hours. The results of 20 consecutive measurements are as follows:

(a) Set up a CUSUM control chart for this process. Use σ = 0.8 in setting up the procedure, and assume that the desired process target is 90. Does the process appear to be in control?

(b) Suppose that the next five observations are 90.75, 90.00, 91.15, 90.95, and 90.86. Apply the CUSUM in part (a) to these new observations. Is there any evidence that the process has shifted out of control?

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Sample Purity Sample Purity 1 89.11 11 88.55 90.59 90.43 2 12 91.03 3 13 91.04 88.17 4. 89.46 14 89.78 15 91.23 6. 90.05 16 90.92 90.63 17 88.86 8. 90.75 18 90.87 9. 89.65 19 90.73 89.78 10 90.15