The nominal value of the mean of a quality characteristic is 50, and the standard deviation is 2. The process is controlled by an chart. Specification limits on the process are established at ±...

The nominal value of the mean of a quality characteristic is 50, and the standard deviation is 2. The process is controlled by an chart. Specification limits on the process are established at ± three-sigma, such that the lower specification limit is 44 and the upper specification limit is 56. When the process is in control at the nominal level of 50, the fraction of nonconforming product produced, assuming that the quality characteristic is normally distributed, is 0.0027. Suppose that the process mean were to shift to 52. The fraction of nonconforming product produced following the shift is approximately 0.0228. 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 thechart and compare it to the sample size for a p chart that has the same probability of detecting the shift.