Fuzzy Development of Multivariate Variable Control Charts Using the Fuzzy Likelihood Ratio Test


1 Department of Industrial Engineering,Tarbiat Modares University

2 Department of Industrial Engineering,Amirkabir University of Technology


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.