On fuzzy and probabilistic control charts

Abstract

In this article, different procedures of constructing control charts for linguistic data, based on fuzzy and probability theory, are discussed. Three sets of membership functions, with different degrees of fuzziness, are proposed for fuzzy approaches. A comparison between fuzzy and probability approaches, based on the Average Run Length and samples under control, is conducted for real data. Contrary to the conclusions of Raz and Wang (1990b) the choice of degree of fuzziness affected the sensitivity of control charts.