Process Capability Cp Assessment for Auto-Correlated Data in the Presence of Measurement Errors

In this paper, we shall discuss some statistical properties of the estimator of [Formula: see text] when sample observations are autocorrelated and affected by measurement errors. The presence of autocorrelation in production units is very common in many industries like chemical, food processing, pharmaceutical, paper, and mineral. At the same time some amount of measurement error is invariably present in the sample observations due to inaccurate measurement process. In this paper, we discuss the case of a first-order stationary autoregressive process where measurement error follows a Gaussian distribution. The comparison of the statistical properties of the estimator in this case with the error-free case is the subject matter of this paper.