## Question on Hypothesis testing for process control

Product is defective if thickness is below 997 or above 1003.
Population mean = 1000mm
Standard deviation = 1mm
The population is normally distributed.

Due to wear and tear, the process mean thickness may change and deviate from 1000mm, while standard deviation stays the same.

If the mean drifts to a position at which the process produces more than 5% defective products, process must be stopped.

Random sample of size 9 taken from the process from time to time, used to decide if the process needs to be stopped.

Beta, Type 2 error = 0.01

a)Find the critical points for sample mean X, such that if the sample mean X goes beyond these critical points, the process is stopped.

b) What is the implied alpha (type 1 error) under the decision rule determined in part C when the process mean thickness is at the target 1000mm?

Problem I'm facing is, 1. what is the implied alpha? 2. How do I make use of the information "if process produces more than 5% defective product, process must be stopped", how does this affect my sample mean, and hence finding the critical points.