Estimation of C_pm for autocorrelated data in the presence of random measurement errors

Abstract

Process capability analysis is a widely used process improvement metric. There are several capability indices used in industries to assess the performance of production process. $C_{pm}$ is one of the most important capability index which is often used in many industries for assessing the performance of the production process by taking into consideration the target value. Although capability indices are estimated under the assumption that the data are independent but in many industries, process outputs are often autocorrelated. At the same time, no measuring device gives accurate results. In this paper, we discuss the statistical properties of the estimator of $C_{pm}$ for autocorrelated data and in the presence of random measurement errors. Here, we show that under the combined effect of autocorrelation and measurement errors, the estimator of $C_{pm}$ behaves differently depending upon the variability of the measurement errors.

Keywords:

• Estimation
• Bias
• MSE
• Process capability index
• Stationary process

Acknowledgement

I thank the anonymous referees for their insightful comments that helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s)