Univariate and multivariate performance indices in fuzzy environment

In statistical quality control, there are two important issues including control cards and performance indicators. Control cards are used to check the stability of the process and after determining the stability, the main parameters of the process are estimated based on the available data. Process performance indicators are numerical criteria that measure the degree of product complianceProduction represents a process with specifications considered by customers or manufacturersthey give. If the quality of products depends on only one variable, one-variable indices are used, and in processes where the quality is related to two or more dependent variables, multivariate indices are used.In the real world, many measurements are inaccurate because of the ambiguity. Therefore, fuzzy logic is used to describe them. Here are the cases where the specifications of the variable / variables under study are fuzzy. Therefore, fuzzy indicators should be used to measure process efficiency.In this paper, for univariate processes, we introduce two univariate fuzzy efficiency indices. In addition, for multivariate processes, we provide a fuzzy multivariate efficiency index and a fuzzy multivariate efficiency vector. We use practical examples to show how to use the proposed indicators.