Reference no: EM132432454

A control chart is used for monitoring a process mean (??X¯??) that is normally distributed with a mean of u and a standard deviation of ?σ? _X¯ , and the sample size is n = 5.

A 3-sigma limit (u ??±?? 3??σ?? _X¯ ) is used as control limits.

Two decision rules are given here.

Rule 1: If one or more of the next seven samples yield values of the sample average that fall outside the control limits, conclude that the process is out of control.

Rule 2: If all of the next seven sample averages fall on the same side of the center line, conclude that the process is out of control.

If the mean of the quality characteristic shifts one standard deviation of the sample mean ??σ?? _X¯ , and remains there during the collection of the next seven samples, What is the B-risk (probability of Type II error) associated with each decision rule?

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