A sample of five units is taken from a process every half hour. It is known that the process standard deviation is in control with σ = 2.0. The x values for the last 20 samples are shown in Table 10E.7. Specifications on the product are 40 ± 8.

(a) Set up a modified control chart on this process. Use three-sigma limits on the chart and assume that the largest fraction nonconforming that is tolerable is 0.1%
3-sigma limits:
(b) Reconstruct the chart in part (a) using two-sigma limits. Is there any difference in the analysis of the data?
(c) Suppose that if the true process fraction nonconforming is 5%, we would like to detect this condition with probability 0.95. Construct the corresponding acceptance control chart.

TABLE 10E.7 Data for Exercise 10,9 Sample Number Sample Number 41.5 42.7 40.5 39.8 41.6 44.7 39.6 40.2 41.4 43.9 12 13 14 15 16 17 18 19 20 40.6 39.4 38.6 425 41.8 40.7 42.8 43.4 42.0 41.9 9 10