A Consistent Confidence Interval for Fuzzy Capability Index

Fuzzy process capability indices are used to determine whether a production process is capable of producing items within specification tolerance, where instead of precise quality we have two membership functions for specification limits. In practice these indices are estimated using sample data and it is of interest to obtain confidence limits for fuzzy capability index given a sample estimate. After introducing 100(1− α)% fuzzy confidence interval by Parchami et al. in 2005 and 2006, for fuzzy capability index C̃p, our observation leads us to propound an open problem about the consistency property for interval estimation of C̃p. In this paper we redefine some concepts about fuzzy confidence interval and then we show the consistency property of the fuzzy confidence interval proposed by Parchami et al. in 2006 holds for almost every α in [0, 1].