The nominal value of the mean of a quality characteristic is 100 and the standard deviation is 2. The process is controlled by an x-bar chart. Specification limits on the process are established at three-sigma, such that the lower specification limit is 96 and the upper specification limit is 104. When the process is in control at the nominal level of 100, the fraction of nonconforming product produced, assuming that the quality characteristic is normally distributed, is 0.0025. Suppose that the process mean shift to 102. The fraction of nonconforming product produced following the shift is approximately 0.0230. Suppose that we want the probability of detecting this shift on the first subsequent sample to be 0.50. Find the appropriate sample size for the x-bar chart and compare it to the sample size for a p-chart that has the same probability of detecting the shift.

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