The data in Table 9E.1 represent individual observations on molecular weight taken hourly from a chemical process. The target value of molecular weight is 1,050 and the process standard deviation is thought to be about σ = 25.

(a) Set up a tabular CUSUM for the mean of this process. Design the CUSUM to quickly detect a shift of about 1.0in the process mean.
(b) Is the estimate of σ used in part (a) of this problem reasonable?

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TABLE 9E.1 Molecular Weight Observation Observation Number Number x x 1,045 2 1,055 1,037 4 1.064 1,095 6 1008 7 1,050 8 1,087 1.125 10 1,146 12 13 14 15 16 17 18 19 20 1.139 1.169 1,151 1.128 1,238 1,125 1,163 1.188 1,146 1,167 5