Construction of closed interval for process capability indices<i>C_pu</i>,<i>C_pl</i>, and<i>S_pk</i>based on Boole’s inequality and de Morgan’s laws

Abstract

Considerable effort has been spent on the development of confidence intervals for process capability indices (PCIs) based on the sampling distribution of the PCI or the transferred PCI. However, there is still no definitive way to construct a closed interval for a PCI. The aim of this study is to develop closed intervals for the PCIs Cpu, Cpl, and Spk based on Boole's inequality and de Morgan's laws. The relationships between different sample sizes, the significance levels, and the confidence intervals of the PCIs Cpu, Cpl, and Spk are investigated. Then, a testing model for interval estimation for the PCIs Cpu, Cpl, and Spk is built as a powerful tool for measuring the quality performance of a product. Finally, an applied example is given to demonstrate the effectiveness and applicability of the proposed method and the testing model.