# Question

Consider a T2 control chart for monitoring p = 6 quality characteristics. Suppose that the subgroup size is n= 3 and there are 30 preliminary samples available to estimate the sample covariance matrix.
m = 30 preliminary samples, n = 3 sample size, p = 6 characteristics, a = 0.005
(a) Find the phase II control limits assuming that a = 0.005.
(b) Compare the control limits from part (a) to the chi-square control limit. What is the magnitude of the difference in the two control limits?
(c) How many preliminary samples would have to be taken to ensure that the exact phase II control limit is within 1% of the chi-square control limit?

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