Construction and fuzzy hypothesis testing of Taguchi Six Sigma quality index

By taking process targeting as well as process variability into consideration, the Taguchi capability index ${C_{pm}} $Cpm gives a reasonable indication of process loss. This makes it an ideal tool for practical applications that depend on the evaluation of process quality. The ability of Six Sigma quality management to reduce process defect rates has led a number of researchers to investigate the relationship between ${C_{pm}} $Cpm and Six Sigma quality levels. Unfortunately, previous efforts indicate the quality level using only a range, rather than a specific value. Our objective in this study was to develop a Taguchi Six Sigma quality index ${Q_{pm}} $Qpm that retains the advantages of ${C_{pm}} $Cpm in the assessment of process performance, while providing a specific value for the quality level associated with the process in question. To ensure rigorous quality assessments, we employed the upper confidence limit of ${Q_{pm}} $Qpm in the design of a testing model for use by manufacturers. Fuzziness and stochastic uncertainty are unavoidable aspects of data collection. We, therefore, adopted a right half triangular-shaped fuzzy number for ${\hat{Q}_{pm}} $Qˆpm to deal with imprecise data. We also developed a method of the fuzzy hypothesis testing for ${Q_{pm}} $Qpm to make reliable decisions for process quality assessment.