A Method to Construct the Confidence Intervals for Process Capability Indices Based on Fuzzy Set Theory

摘要

Traditionally, the methods used for constructing the confidence intervals of process capability indices(PCIs) are based on probability density function. Normally the approximate confidence intervals are obtained according to the approximate distribution since it is not easy to get the accurate sampling distribution of PCIs estimations. In this article, a methodology based on fuzzy set theory and Buckley's fuzzy estimation approach has been presented in order to construct the confidence intervals for PCIs. By establishing the corresponding relationship between (1 -- a)100% confidence intervals and the a cuts of fuzzy estimators, the confidence intervals of PCIs are constructed with the rules of the fuzzy number operation. This method does not depend on the distribution of the estimator, and has a higher precision at the same confidence level.