The development of target-based posterior process capability indices and confidence intervals

One of the most popular quality engineering tools is the process capability index (PCI), which relates the allowable spread of a process defined by engineering specifications to the natural spread of a process. The traditional PCI does not account for the loss in quality when product characteristics fail to achieve their process target value. This research, in contrast, proposes indices, namely posterior PCIs, that consider the underlying result of observations after inspection. Utilising a truncated distribution as the basis for measurement along with a target-based quality loss function for capability analyses, several posterior indices are developed in this paper. A simulation technique is implemented to compare the proposed posterior PCIs with traditional measures. Finally, the confidence interval approximations for the posterior PCIs are derived. Our results suggest using the proposed posterior indices for capability analyses when industrial processes require that non-conforming products be scrapped prior to shipping to the customer.