Developing new methods to monitor phase II fuzzy linear profiles

In some quality control applications, the quality of a process or a product is described by the relationship between a response variable and one or more explanatory variables, called a profile. Moreover, in most practical applications, the qualitative characteristic of a product/service is vague, uncertain and linguistic and cannot be precisely stated. The purpose of this paper is to propose a method for monitoring simple linear profiles with a fuzzy and ambiguous response. To this end, fuzzy EWMA and fuzzy Hotelling's $T^2$ statistics are developed using the extension principle. To monitor phase II of fuzzy linear profiles, two methods using fuzzy hypothesis testing, are presented based on these statistics. A case study in ceramic and tile industry, is provided. A simulation study to evaluate the performance of the proposed methods in terms of average run length (ARL) criterion showed that the proposed methods are very efficient in detecting various sized shifts in process profiles.