Measuring One-Sided Process Capability Index for Autocorrelated Data in the Presence of Random Measurement Errors

Abstract Many quality characteristics in manufacturing industry are of one sided specifications. The well-known process capability indices C P ⁢ U C_{PU} and C P ⁢ L C_{PL} are often used to measure the performance of such type of production process. It is usually assumed that process observations are independent and measurement system is free of errors. But actually in many industry it has been proven that auto-correlation is an inherent nature of the production process, especially for chemical processes. Moreover, even with the use of highly sophisticated advanced measuring instruments some amount of measurement error is always present in the observed data. Hence gauge measurement error also needs to be considered. In this paper we discuss some inferential properties of one-sided process capability indices for a stationary Gaussian process in the presence of measurement errors. As a particular case of a stationary Gaussian process, we discuss the case of a stationary AR ⁡ ( 1 ) \operatorname{AR}(1) process where measurement error follows an independent Gaussian distribution.