Functional process capability indices for a simple linear profile in fuzzy environment

In some practical applications, the quality of a process or a product is characterized by a relationship, namely a profile between a response variable and one or more explanatory variables. Assuring the capability of a profile to meet the process requirements is particularly important. Process capability indices (PCIs) are widely used to measure whether a process is capable of reproducing product items within the specification limits (SLs). Background literature on the PCIs for profiles mostly take crisp values for process data. However, in practice, the outcomes of a measurement are often imprecise. So, the basic assumption of crisp data for process capability analysis (PCA) in profiles is not valid. Hence, fuzzy methods are developed to analyze the capability of a fuzzy profile with fuzzy response data. To this end, we extend the functional approach based on fuzzy set theory for the situations in which the SLs and target values of the response variable are imprecise. The performance of the proposed indices is investigated through simulation studies. The simulation results confirm that the proposed method performs well regarding 𝐷𝑝,𝑞-distance between the estimated value and the true value of fuzzy PCIs. Furthermore, a case study shows the applicability of the proposed method.