Design for Six Sigma and Process Capability Using Penthagorean Fuzzy Sets

Abstract

Design for six sigma (DFSS) is a structured approach for designing new products, processes and/or services or redesigning the existing ones. It builds quality into the product during the development and ensures the customer expectations are understood, met, or exceed. In DFSS, variation is aimed to be minimized by applying the techniques of the six sigma approach. Some of these techniques are process control and process capability analysis. Vagueness and impreciseness in these analyses such as the statistical distribution of the considered process can be handled by the fuzzy set theory. Recently, ordinary fuzzy sets have been extended to several new types of fuzzy sets such as Pythagorean fuzzy sets, spherical fuzzy sets, picture fuzzy sets, and intuitionistic fuzzy sets. In this paper, we propose a new extension of intuitionistic fuzzy sets, which is called Penthagorean fuzzy sets and employ it in the process capability analysis of a production process. Penthagorean fuzzy process capability indices are developed and applied to an Autonomous Underwater Vehicle (AUV) design example.