Process Capability Indices Based on the Highest Density Interval

For process capability indices (PCIs) of non-normal processes, the natural tolerance is defined as the difference between the 99.865 percentile and the 0.135 percentile of the process characteristic. However, some regions with relatively low probability density may still be included in this natural tolerance, while some regions with relatively high probability density may be excluded for asymmetric distributions. To take into account the asymmetry of process distributions and the asymmetry of tolerances from the viewpoint of probability density, the highest density interval is utilized to define the natural tolerance, and a family of new PCIs based on the highest density interval is proposed to ensure that regions with high probability density are included in the natural tolerance. Some properties of the proposed PCIs and two algorithms to compute the highest density interval are given. A real example is given to show the application of the proposed method.