Minimax Multivariate Control Chart Using a Polynomial Function
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Date
2011
Authors
Adewara, J.A.
Adekeye, K.S
Asiribo, O.E
Adejuyigbe, S.B
Journal Title
Journal ISSN
Volume Title
Publisher
Applied Mathematics
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.
Description
Keywords
Minimax , Non-Linear Polynomial , Process , Maximum , Minimum