Proportional Integral Derivative Charts for Process Monitoring

Abstract

We introduce a new class of monitoring procedures based on the relationship between a proportional integral derivative (PID) feedback control scheme and the corresponding prediction scheme. The charts are obtained by applying the PID predictor to the autocorrelated data to get residuals and then monitoring the residuals. This class of procedures includes as special cases several charts that have been recently proposed in the literature and thus provides a unifying framework. The PID charts have three parameters that can be suitably tuned to achieve good average run length (ARL) performance for large or small mean shifts. Methods for determining chart parameters to obtain good ARL performance are discussed. Simulation studies for autoregressive moving average (1, 1) models show that PID charts are competitive with the special cause charts of Alwan and Roberts for detecting large shifts and perform better in detecting small to moderate shifts. The effects of model parameter misspecification and bias in estimating the variance of the residuals are investigated in a robustness study.

KEY WORDS :

• Exponentially weighted moving average
• Feedback control
• Statistical process control