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S. M. Rump, “Ten Methods To Bound Multiple Roots of Polynomials,” Journal of Computational and Applied Mathematics, Vol. 156, No. 2, 2003, pp. 403-432. doi:10.1016/S0377-0427(03)00381-9

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• TITLE: Minimax Multivariate Control Chart Using a Polynomial Function

  AUTHORS: Johnson Ademola Adewara, Kayode Samuel Adekeye, Osebekwin Ebenezer Asiribo, Samuel Babatope Adejuyigbe

  KEYWORDS: Minimax, Non-Linear Polynomial, Process, Maximum and Minimum

  JOURNAL NAME: Applied Mathematics, Vol.2 No.12, December 27, 2011

  ABSTRACT: 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 solved numerically using Newton Raphson method to obtain the control limits for the minimax control chart. The approach helps to overcome the problem of obtaining the joint probability distribution needed for estimating the control limits of both the maximum and the minimum statistic for monitoring multivariate process.