Statistical Hypothesis Testing for Asymmetric Tolerance Index

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 - alpha)% 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.

Automated summary

This study utilizes mathematical tools to find the confidence interval for the asymmetric tolerance index of important machine tool components, and conducts statistical hypothesis testing.