Fuzzy nonparametric estimation of capability index Cpk

Process capability indices have been widely used in the manufacturing industry to measure the potential performance. This paper proposes a nonparametric approach for estimating the proportion of non-conforming items and capability index C-pk, when sample observations and specification limits of a process are reported as imprecise numbers. In this approach, first the alpha-pessimistic values of the imprecise observations were first applied to determine an unbiased estimator for population variance and optimal bandwidth. Thereafter, the fuzzy proportion of non-conforming items based on kernel distribution function was obtained. Finally, the fuzzy proportion of non-conforming items was applied to obtain the membership function of fuzzy nonparametric capability index (C) over tilde (pk). Moreover, the proposed nonparametric methods are examined to compare with some other existing parametric methods and their performance will be cleared via some numerical examples and some comparison studies.