and in correlation form all four variables have variance unity and all pairwise correlation coefficients are 0.7. The in-control value of the process mean vector is ť = [0, 0, 0, 0]. a) Write out the covariance matrix E. b) What is the chi-square control limit for the chart, assuming that a = 0.01? c) Suppose that a sample of observations results in the standardized observation vector y' = [3.5, 3.5, 3.5, 3.5]. Calculate the value of the T statistic. Is an out-of-control signal generated? %3D

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Suppose that we have p = 4 quality characteristics,
and in correlation form all four variables have variance
unity and all pairwise correlation coefficients are 0.7.
The in-control value of the process mean vector is
µ = [0, 0, 0, 0].
(a) Write out the covariance matrix E.
(b) What is the chi-square control limit for the chart,
assuming that a =
(c) Suppose that a sample of observations results in
the standardized observation vector y' [3.5, 3.5,
3.5, 3.5]. Calculate the value of the T statistic. Is
an out-of-control signal generated?
%3D
= 0.01?
Transcribed Image Text:Suppose that we have p = 4 quality characteristics, and in correlation form all four variables have variance unity and all pairwise correlation coefficients are 0.7. The in-control value of the process mean vector is µ = [0, 0, 0, 0]. (a) Write out the covariance matrix E. (b) What is the chi-square control limit for the chart, assuming that a = (c) Suppose that a sample of observations results in the standardized observation vector y' [3.5, 3.5, 3.5, 3.5]. Calculate the value of the T statistic. Is an out-of-control signal generated? %3D = 0.01?
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