Process incapability index for autocorrelated data in the presence of measurement errors

Process incapability index is a useful tool for measuring the performance of a process to maintain the quality of products. In this article, we discuss some statistical properties of the estimator of process incapability index when process observations are autocorrelated and contaminated by measurement errors. In many industry, it has been proven that observed quality characteristics for consecutive items are autocorrelated. Moreover, some amount of measurement errors is always present in the observed data. Therefore, it is important to analyze the statistical properties of the estimator under the combined effect of autocorrelation and measurement error for commenting approximately on the ability of a manufacturing process.