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

Abstract

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.

Keywords:

• autoregressive disturbance
• MMSE controller
• joint monitoring
• statistical process control
• engineering process control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 51275558]; National Key Science and Technology Research Program of China [grant number 2014ZX04015-021], and State Key Lab of Mechanical System and Vibration program [grant number MSVZD201503].