An Xbar chart with three-sigma limits has parameters as follows:
UCL = 104
Center line = 100
LCL = 96
n= 5
Suppose the process quality characteristic being controlled is normally distributed with a true mean of 98 and a standard deviation of 8. What is the probability that the control chart would exhibit lack of control by at least the third point plotted?
I know the answer and how to find Beta, but i'm confused:
Beta = chart doesn't signal; 1-Beta = chart does signal. So, the answer is 1 - (beta)^3. I was thinking that I could do (1-beta)^3 can you explain to me why I cannot do it the second way?