Exact Solution for Average Run Length of CUSUM Charts for MA(1) Process
Kanita Petcharat[a], Yupaporn Areepong*[a], Saowanit Sukparungsee[a] and Gabriel Mititelu[b]* Author for corresponding; e-mail address: yupaporna@kmutnb.ac.th
Volume: Vol.41 No.5/2 (OCTOBER 2014)
Research Article
DOI:
Received: 16 July 2012, Revised: -, Accepted: 11 November 2013, Published: -
Citation: Petcharat K., Areepong Y., Sukparungsee S. and Mititelu G., Exact Solution for Average Run Length of CUSUM Charts for MA(1) Process, Chiang Mai Journal of Science, 2014; 41(5/2): 1449-1456.
Abstract
In this paper we apply Fredhom type integral equations method to derive explicit formula of the average run length (ARL) for a Cumulative Sum (CUSUM) chart, when observations are described by a first order moving average MA(1) process, with exponential white noise. We compare the computational time between our analytical explicit expressions for the ARL performance with the one obtained via Gauss-Legendre numerical scheme for integral equations. We found that those methods are in excellent agreement however, the computational time of the former takes approximately 1 second while the latter method consumes the computational time 11 minutes approximately.