Modelling and joint monitoring of input and output of systems with arbitrary order autoregressive disturbance

Considerable studies have been done on modelling and joint monitoring of input and output of systems with autoregressive moving average (ARMA) disturbance. Most of these studies focus on systems with ARMA (1, 1) disturbance. However, many kinds of systems are not conform to ARMA(1, 1) disturbance. Motivated by the fact that an autoregressive (AR) model with high order can be implemented to approximate the stationary ARMA model at any precision, a new generic model and a joint monitoring scheme of systems with arbitrary order AR( p ) disturbance are developed. A minimum mean squared error (MMSE) controller with arbitrary order AR disturbance is designed to reduce the system variability. The mathematical expectation and average run length of MMSE-controlled outputs are derived. A new joint chart for monitoring the input and output simultaneously is explored. Two out-of-control rules for the joint monitoring chart are developed. The monitoring performances of the input chart, the output chart and the joint monitoring chart are also discussed. The results of simulation experiments and case studies validate the effectiveness of the developed model and joint monitoring chart.