. Suppose that we have p = 4 quality char-

acteristics, 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 //' = [0, 0, 0, 0]. .

(a) Write out the covariance matrix E.

(b) What is the chi-square control Limit for the chart, assuming that Q =

0.01?

(c) Suppose that a sample of observa-

tions results in the standardized observation vector y = [3.5, 3,5, 3.5, 3.5]. Calculate the value of the Tª statistic. Is an out-of-control sig-

nal gencrated?

(d) Calculate the diagnostic quantities di, i = 1, 2, 3, 4 from equation 10-22, Does this information assist in iden-

tifying which process variables bave shifted?

(e) Suppose that a sample of observa-

tions results in the standardized observation vector y' = [2.5, 2, - 1, 0]. Calculate the value of the T" sta-

tistic. Is an out-of-control signal generated?

(1) For the case in (e), calculate the diagnostic quantities di, I = 1, 2, 3, 4 from equation 10-22. Does this information assist in identifying which process variables have shifted?