Please use excel function where appropriate. The general model for the control l

Question

Please use excel function where appropriate.

The general model for the control limits for a control chart for the sample statistic w is the following: UCL = Mu(w) + L*Sigma(w) CL = Mu(w) LCL = Mu(w) - L * Sigma(w) where: L is the distance of the control limit from the center line Mu(w) is the mean of the sample statistic w Sigma(w) is the standard deviation of the statistic w Assume that the sample statistic w is Normally distributed. Find the Probability Limits (value of L) if we want to have a control chart with a probability of 0.0001 of a type I error in each direction. What is the in-control Average Run Length (ARL) for this control chart?

Explanation / Answer

(a) As the probability of type -1 error is 0.0001. and as we are taking both sided control limit so

L will such that P( X > L ) = 0.0001/2 = 0.00005 where X follows N(0,1) distribution.

so , P(X <=L) = 1-0.00005 = 0.99995 , which implies L is the inverse probability function N(0,1) distribution.

So L = =NORM.INV(0.99995,0,1) = 3.8906( answer)

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