FUZZY DEVELOPMENT OF MULTIVARIATE VARIABLE CONTROL CHARTS USING THE FUZZY LIKELIHOOD RATIO TEST

Abstract

This paper is an e ort to evolve multivariate variable control charts in a fuzzy environment where each observation in each sample is assumed to be a canonical fuzzy number. To do this, a likelihood ratio test should be exploited in a fuzzy environment, because multivariate variable control charts are constructed using this test. In this way, membership functions of likelihood ratio statistics applied to control the process mean and dispersion are obtained solving four non-linear programming problems. Using these membership functions, membership degrees of in and out of control states of both process mean and dispersion are computed. Hence contrary to the classic multivariate variable control charts categorizing the process into just two states, i.e. in and out of control, the process can be considered in several intermediate states, based on the computed membership degrees, bringing about more exibility in process analysis.

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