# Question

Suppose that we have p = 3 quality characteristics, and in correlation form all three variables have variance unity and all pairwise correlation coefficients are 0.8. The in-control value of the process mean vector is μ′ = [0, 0, 0].
(a) Write out the covariance matrix ∑.
(b) What is the chi-square control limit for the chart, assuming that a = 0.05?
(c) Suppose that a sample of observations results in the standardized observation vector y’ = [1, 2, 0]. Calculate the value of the T2 statistic. Is an out-of-control signal generated?
(d) Calculate the diagnostic quantities di = 1, 2, 3, from equation 11.22. Does this information assist in identifying which process variables have shifted?
(e) Suppose that a sample of observations results in the standardized observation vector y’ = [2, 2, 1]. Calculate the value of the T2 statistic.
(f) For the case in (e), calculate the diagnostic quantities di, i = 1, 2, 3 from equation 11.22. Does this information assist in identifying which process variables have shifted?

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