Evaluating process performance based on the incapability index for measurements with uncertainty

Process capability indices are widely used in industry to measure the ability of firms or their suppliers to meet quality specifications. The index CPPCPP, which is easy to use and analytically tractable, has been successfully developed and applied by competitive firms to dominate highly-profitable markets by improving quality and productivity. Hypothesis testing is very essential for practical decision-making. Generally, the underlying data are assumed to be precise numbers, but in general it is much more realistic to consider fuzzy values, which are imprecise numbers. In this case, the test statistic also yields an imprecise number, and decision rules based on the crisp-based approach are inappropriate. This study investigates the situation of uncertain or imprecise product quality measurements. A set of confidence intervals for sample mean and variance is used to produce triangular fuzzy numbers for estimating the CPPCPP index. Based on the δδ-cuts of the fuzzy estimators, a decision testing rule and procedure are developed to evaluate process performance based on critical values and fuzzy p-values. An efficient computer program is also designed for calculating fuzzy p-values. Finally, an example is examined for demonstrating the application of the proposed approach.