Measuring the process yield for circular profiles

Abstract

Two indices Cp(circular) and Cpk(circular) based on the functional method have been proposed to measure the process capability of circular profiles. However, these two indices only provide potential capability and a lower bound on the process yield, respectively. In this paper, we develop a new yield index Spk(circular) for circular profiles. This index provides an exact measure of process yield. The asymptotic normal distribution of the estimated index is derived. The statistical inferences such as hypothesis testing, confidence interval, and lower confidence interval can be easily constructed. A simulation study is conducted to assess the performance of the proposed method. The simulation results confirm that the estimates are close to the true value and the coverage rates of the confidence intervals are greater than the 95% lower limit of the stated nominal in most cases. One real data set is used to illustrate the applicability of the proposed method.