Two-tailed Buckley fuzzy testing for operating performance index.

This paper proposes an operating performance index (OPI) based directly on the Six Sigma process quality index. We considered the following case: the number of customers arriving at a store follows a Poisson process of rate λ and the sequence of inter-arrival times is an exponential random variable with mean τ , where τ = 1/ λ. In operating performance assessments, using the statistical testing to evaluate the OPI can lower the risk of misjudgment caused by sampling error. A smaller sample size entails a larger sampling error, while a larger sample size entails a smaller sampling error. Thus, using critical value for statistical testing can result in inconsistencies for different sample size. We therefore referred to the one-tailed fuzzy method proposed by Buckley (2005) for the parameters of population distributions and developed a two-tailed fuzzy test for the OPI to assess operating performance. The advantage of this approach is that conventional measurement methods can be used during data collection, and then the confidence interval of the OPI can be used to construct a fuzzy membership function for fuzzy testing. This not only lowers the risk of misjudgment caused by sampling error, but also enhances testing accuracy. [ABSTRACT FROM AUTHOR]