Capability measures for Weibull processes with mean shift based on Erto's-Weibull control chart

Abstract

Process capability indices (PCIs), which are effective tools for quality assurance and are guidance for process improvement, have been proposed in the manufacturing industry to provide numerical measures on process reproduction capability. PCIs are calculated under the assumption that the process is stable while the process mean and variation are not changeable. However, in practice, the process is dynamic. Under the Bothe’s adjustments, we showed the detection powers of the percentile-Weibull control chart, bootstrap-Weibull control chart, and the Bayes-Weibull control chart. It is realized that the Bothe’s adjustments are inadequate with data coming from Weibull processes. For this reason, the PCIs have to be adjusted. Bothe (2002) provided the adjustment method for normality processes. In this research, we consider Weibull processes, which cover a wide class of applications. We calculate the mean shift adjustments under various sample sizes n and Weibull parameter γ, with the power fixed to 0.5. Then, we implement the adjustments to accurately estimate capability index Cpk for Weibull processes with mean shift consideration. Finally, an application example is presented for illustration purpose. Key words: Dynamic Cpk, mean shift, process capability index, Weibull distribution,Weibull control chart.