# Question: Control charts for have been maintained on a process

Control charts for have been maintained on a process and have exhibited statistical control. The sample size is n = 6. The control chart parameters are as follows:

(a) Estimate the mean and standard deviation of the process.

(b) Estimate the natural tolerance limits for the process.

(c) Assume that the process output is well modeled by a normal distribution. If specifications are 703 and 709, estimate the fraction nonconforming.

(d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occurring on the first sample following the shift?

(e) For the shift in part (d), what is the probability of detecting the shift by at least the third subsequent sample?

(a) Estimate the mean and standard deviation of the process.

(b) Estimate the natural tolerance limits for the process.

(c) Assume that the process output is well modeled by a normal distribution. If specifications are 703 and 709, estimate the fraction nonconforming.

(d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occurring on the first sample following the shift?

(e) For the shift in part (d), what is the probability of detecting the shift by at least the third subsequent sample?

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