The concentration of a chemical product is measured by taking four samples from each batch of material. The average concentration of these measurements for the last 20 batches is shown in the following table:

(a) Suppose that the process standard deviation is σ = 8 and that the target value of concentration for this process is 100. Design a CUSUM scheme for the process. Does the process appear to be in control at the target?

(b) How many batches would you expect to be produced with off-target concentration before it would be detected by the CUSUM control chart if the concentration shifted to 104? Use Table 15-10.

Table 15-10

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Concentration Batch Concentration Batch 1 104.5 11 95.4 99.9 12 94.5 106.7 3 13 104.5 4 105.2 14 99.7 97.7 94.8 15 94.6 6. 16 97 104.4 17 95.8 99.4 100.3 100.3 97.4 99 18 19 10 20 102.6