Monitoring fuzzy linear quality profiles: A comparative study

Abstract

Quality profiles representing the quality of a process or product as the functional relationship between one or more dependent variables and one or more explanatory variables are nowadays widely recognized in statistical process control (SPC) applications by both researchers and practitioners. On the other hand, in many real-world cases, evaluation of process or product characteristics is carried out with ambiguity or conducted using linguistic values. The theory of fuzzy sets provides an appropriate approach to deal with uncertainty due to ambiguity in human subjective evaluations or vagueness in linguistic variables. The purpose of this study is to introduce two novel methods based on fuzzy regression modeling for monitoring fuzzy linear profiles in phase II of SPC. To accomplish this, fuzzified Hoteling’s T2 statistic and fuzzy hypothesis testing are used. Moreover, a simulation study is used to compare the performance of the proposed methods compared with previous methods, based on the average run length (ARL) criterion in order to assess the detectability of charts with regard to the step shifts in profile parameters. Finally, the results of a real-world example in the tile and ceramic industry are presented.