Exact expression for average run length of control chart of ARX(p) procedure

Abstract

Statistical Process Control (SPC) can be defined as the use of statistical methods and technicals to improve process productivity and product quality. One of efficient tools of SPC are the control charts. The Cumulative Sum (CUSUM) control chart and Exponentially Weighted Moving Average (EWMA) control chart are widely used in several applications such as economic, engineering and industries. For many processes of interest, observations are closely space in time which will be correlated. The measurement of performance used in the average run length. The main goal of this paper is to derive analytical solutions for average run length of the Cumulative Sum and Exponential Weighted Moving Average control charts for ARX(p) processes with exponential white noise. The comparing of control charts found that EWMA control chart is better when mean shift is small.