The Capability Index when Some Assumptions are not Satisfied: Analysis and Empirical Comparisons

Abstract

The process capability index (PCI) evaluates the ability of a process to produce items with certain quality requirements. The PCI depends on the process standard deviation, which is usually unknown and estimated by using the sample standard deviation. The construction of confidence intervals for the PCI is also an important topic. The usual estimator of the PCI and its corresponding confidence interval are based on various assumptions, such as normality, the fact that the process is under control, or samples selected from infinite populations. The main aim of this paper is to investigate the empirical properties of estimators of the PCI, and analyze numerically the effect on confidence intervals when such assumptions are not satisfied, since these situations may arise in practice.

Research on the reliability of X70 steel gas pipelines under SRB main control factors

“…The individual distribution labeling function was applied again to test the goodness‐of‐fit, the Weibull distribution model was used to transform the data, and p value was 0.679, which obeyed the normal distribution. [ 28 ] Furthermore, the transformation data were used to analyze the process capability, and was 0.51.…”