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 − 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.

The Process Capability Analysis to Assess Capacity of a Cleaning Liquid Product with Asymmetric Tolerances

Process capability indices are a powerful tool used by quality control engineering to measure the degree to which the process is or is not meeting the requirements. This paper studies the application of process capability indices in the evaluation of a process with asymmetric tolerances. The analyzed collected data of the cleaning liquid “Zahi”, was used to investigate the ability of the filling process to meet the requested specifications. Matlab software was used to plot control charts, normal probability, and histogram of the data gathered from the production line and further performed statistical calculations. It was observed from the control charts that the filling process is under control. In addition, it was revealed by the process capability indices that the process of filling the cleaning liquid bottle is not fitted with the target value but it is adequate.