Cpk index estimation using fuzzy numbers

Process capacity indices (PCIs) were developed and have been successfully used by companies to compete in and dominate the high-profit markets by improving the quality and the productivity since the past two decades. There is an essential assumption, in the conventional application, wherein the output process measurements are precise and distributed as normal random variables. Since the assumption of normal distribution is untenable, errors can occur if the Cpk index is computed using non-normal data. In the present study, we address the situation that the output of data from measurement of the quality of a product is insufficiently precise or scarce. This is possible when the quality measurement refers to the decision-maker's subjective determination. In such a situation, the linguistic variable that is easier to capture the decision-maker's subjective perception is applied to construct the PCI Cpk. The present approach can mitigate the effect when the normal assumption is inappropriate and extends the application of Cpk index.