X-MR control chart for autocorrelated fuzzy data using D p,q -distance

Abstract

A control chart is a tool for investigating whether the variation in a production process is random or assignable. X − M R control chart is a binary control chart on which average values of process and moving range between observations are used to discover the variability in the process. In an ordinary control chart, the data are crisp values but sometimes, the data are generated as vague and uncertain values because of some of environmental conditions and other factors. In such cases, fuzzy sets theory is a useful tool for analyzing data. On the other hand, the assumption of independence between observations cannot be accepted because the probability of false warning will increase if the data are autocorrelated and their correlation is ignored. In this article, we will discuss the construction of fuzzy control charts for autocorrelated fuzzy observations and employment of ranking method in order to find out whether the observations are in or out of control. In fact, by using defined D p,q -distance between fuzzy numbers, we calculate their variance, covariance, and autocorrelation coefficient. The autocorrelation coefficient is used in order to modify the limit of control chart. By using D p,q -distance, we present a new approach for constructing control charts.