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Decision-making in testing process performance with fuzzy data
Authors:Chien-Wei Wu
Institution:Department of Industrial Engineering and Systems Management, Feng Chia University, 100, Wenhwa Road, Seatwen, Taichung 40724, Taiwan
Abstract:Over the years, numerous process capability indices (PCIs) have been proposed to the manufacturing industry to provide numerical measures of process performance. Most research efforts have focused on developing and investigating PCIs that assess process capability by precise measurements of output quality. However, real observations of continuous quantities are not precise numbers; in practice, they are more or less imprecise. Since observations of continuous random variables are imprecise the values of related test statistics become imprecise. Therefore, decision rules for statistical tests have to be adapted to this situation. This article presents a set of confidence intervals that produces triangular fuzzy numbers for the estimation of Cpk index using Buckley’s approach with some modification. Additionally, a three-decision testing rule and step-by-step procedure are developed to assess process performance based on fuzzy critical values and fuzzy p-values. This concept is also illustrated with an example for testing process performance.
Keywords:Fuzzy data  Fuzzy hypothesis testing  Fuzzy p-values  Process capability indices
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