[Solution Library] A process is known to be in control on the first day of operation. It is observed to have an average run length of 20 on the first day,


Question:

A process is known to be in control on the first day of operation. It is observed to have an average run length of 20 on the first day, for a certain sensitizing rule. The next day the average run length is observed to be 16, and change is attributed to a shift in the mean that has caused the process to drift out of control.

  1. What is the probability that a randomly chosen sample will signal that the process is out of control on the first day?
  2. What is the probability that a randomly chosen sample on the second day will signal that the process is in control?

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