A note on statistical analysis of C pk for autocorrelated data in the presence of random measurement errors

Abstract

Process capability indices (PCIs) have been widely used for process performance assessment. It provides a quantitative measure of performance of an industrial production process. Several PCIs have been proposed in the literature. C p k is one of the most useful capability index. Statistical properties of the estimator of C p k have been discussed by many researches under the assumption of identically and independently normal distribution. Some statistical properties of the estimator of C p k for autocorrelated data in presence of gauge measurement errors have studied by Scagliarini (2010). However, we found some critical error in the expression of expectation and variance of the estimator when process is autocorrelated as well as measurement error is present. Through this article, we present a corrected version of expectation and variance of the estimator.