Quality Control Process Based on Fuzzy Random Variables

Quality control processes are very important for monitoring applications where the aim is to identify special causes of variation and improve quality and productivity. However, in many real-world cases, elements of quality control processes may be observed or defined imprecisely. Many studies have been focused on quality control processes dealing with normal random variables. Notably, none of such research has come to a unified approach to investigate all aspects of quality control processes in fuzzy environment, such as control charts, process capability, confidence interval, and hypothesis testing. In the present study, almost all processes required by the classical statistical quality control are developed in a fully fuzzy environment with fuzzy observations, fuzzy mean, fuzzy variance, and fuzzy control limits. The results are presented in three parts: 1) fuzzy control charts, 2) fuzzy process capability, and 3) fuzzy hypothesis testing for fuzzy mean and fuzzy variance. For this purpose, first, the concept of sample variance and associated large sample were extended in a fuzzy environment. Then, a new methodology was formulated for constructing fuzzy confidence intervals for the fuzzy mean and fuzzy variance. Common control charts were also developed based on particular fuzzy control limits. Moreover, a popular process capability indicator and its estimator were developed based on fuzzy random variables. Finally, a method was proposed for statistical hypotheses testing regarding fuzzy process capability. To this end, we began with developing the classical critical value at a certain significance level. Then, applying the credibility index, a fuzzy test was introduced to accept/reject the fuzzy hypotheses to a particular degree of credibility. In order to clarify the subject matter, illustrative numerical examples were provided, and feasibility and effectiveness of the proposed methods were compared to those of existing counterparts. The results indicated that the proposed method is a powerful tool for quality control processes when fuzzy observations are taken from a normal distribution with fuzzy parameters.