An xbar chart with three-sigma limits has parameters as, Ask an Expert

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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?

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Operation Management, Management Studies

Category:- Operation Management
Reference No.:- M92589482

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