Time-Series Modeling for Statistical Process Control

TLDR

Statistical process control assumes i.i.d. data, yet real processes often exhibit autocorrelation and systematic time‑series effects that can mislead standard control charts. The authors propose modeling and fitting time‑series effects and then applying standard control‑chart procedures to the residuals.

Abstract

In statistical process control, a state of statistical control is identified with a process generating independent and identically distributed random variables. It is often difficult in practice to attain a state of statistical control in this strict sense; autocorrelations and other systematic time-series effects are often substantial. In the face of these effects, standard control-chart procedures can be seriously misleading. We propose and illustrate statistical modeling and fitting of time-series effects and the application of standard control-chart procedures to the residuals from these fits. The fitted values can be plotted separately to show estimates of the systematic effects.