Exact Expression of Average Run Length of EWMA Chart for SARIMA (P,D,Q)(L) Procedure

The objective of Statistical Process Control (SPC) is to monitor the operation of in-control processes. One of efficient tools of SPC is the Exponentially Weighted Moving Average (EWMA) control chart which widely used in several of application such as pharmaceutics, engineering, industries and in other areas. 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 gold of this paper is to derive analytical solutions for ARL of the EWMA control chart for Seasonal Autoregressive Integrated Moving Average processes (SARIMA (P,D,Q)(L)) with Exponential white noise. Checking the accuracy of results, the results obtained from exact expressions with Numerical Integral Equation by Gauss-Legendre rule were compared. An excellent agreement between the exact expressions and numerical solutions was found. This fact is an additional indication that the exact expressions are sufficiently high accuracy.