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Minimax control chart uses the joint probability distribution of the maximum and minimum standardized sample means to obtain the control limits for monitoring purpose. However, the derivation of the joint probability distribution needed to obtain the minimax control limits is complex. In this paper the multivariate normal distribution is integrated numerically using Simpson's one third rule to obtain a non-linear polynomial (NLP) function. This NLP function is then substituted and solveddoi:10.4236/am.2011.212219 fatcat:2gh37heo6be4pauez2ufnclpni