Statistical Hypothesis Testing for Asymmetric Tolerance Index

Abstract

Many of the nominal-the-best quality characteristics of important machine tool components, such as inner or outer diameters, have asymmetric tolerances. An asymmetric tolerance index is a function for the average of the process and the standard deviation. Unfortunately, it is difficult to obtain the 100(1−α)% confidence interval of the index. Therefore, this study adopts Boole’s inequality and DeMorgan’s theorem to find the combined confidence region for the average of the process as well as the standard deviation. Next, using the asymmetric tolerance index for the target function and the combined confidence region for the feasible region, this study applies mathematical programming to find the confidence interval as well as employs this confidence interval for statistical hypothesis testing. Lastly, this study demonstrates the applicability of the proposed approach with an illustrative example.