Average Run Length for CUSUM control chart of ARMAX(1,1) process

Abstract

The objective of Statistical Process Control (SPC) is to monitor the operation of in control process. One of efficient tools of SPC is the Cumulative Sum (CUSUM) control chart which widely used in several of application such as pharmaceutics, engineering, economics and in the other area. For many processes of interest, observations which are closely spaced in time will be correlated. The measure of performance used is the average run length (ARL). The main goal of this paper is to derive explicitformulas for ARL of the CUSUM control chart for ARMAX(1,1) process and using exponential white noise. Checking the accuracy of results, the result obtained from explicit formulas with numerical integral equation by Gauss-Legendre rule were compared. An excellent agreement between the explicit solution and numerical solutions was found. This fact is an additional indication that the explicit formulas are sufficiently high accuracy.