Capability measures for m-dependent stationary processes

Process capability indices, providing numerical measures on process potential and process performance, have received substantial research attention. Most research assumes that the process is normally distributed and the process data are independent. In real-world applications such as chemical, soft drinks, or tobacco/cigarette manufacturing processes, process data are often auto-correlated. In this paper, we consider the capability indices C_p, C_pk, C_pm, C_pmk for strictly m-dependent stationary processes. We investigate the statistical properties of their natural estimators. We derive the asymptotic distributions, and establish confidence intervals so that capability testing can be performed.