Fuzzy nonlinear programming approach for evaluating and ranking process yields with imprecise data

Process yield, the percentage of processed product units passing inspection, is a standard numerical measure of process performance in the manufacturing industry. On the basis of the process yield expression, an index SpkSpk was developed to provide an exact measure of process yield for normally distributed processes. Most traditional studies measuring process capability are based on crisp estimates in which the output process measurements are precise. However, it is common that the measurements of process quality characteristics are insufficiently precise. Traditional approaches for evaluating process yield become unreliable in such cases. Therefore, this study formulates fuzzy numbers to describe the quality characteristic measurements and applies two methods to construct the fuzzy estimation for SpkSpk. A nonlinear programming approach is provided to solve the α-level sets of the estimator, and a testing procedure is presented for making decisions. Finally, this concept is illustrated with an example and extended to solve the ranking problem of multiple yield indices.