Chiang Mai Journal of Science

Exact Solution for Average Run Length of CUSUM Charts for MA(1) Process

Paper Type	Contributed Paper
Title	Exact Solution for Average Run Length of CUSUM Charts for MA(1) Process
Author	Kanita Petcharat[a], Yupaporn Areepong*[a], Saowanit Sukparungsee[a] and Gabriel Mititelu[b]
Email	yupaporna@kmutnb.ac.th
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.
Start & End Page	1449 - 1456
Received Date	2012-07-16
Revised Date
Accepted Date	2013-11-11
Full Text	Download
Keyword	Statistical Process Control, Cumulative Sum, Moving Average Observation, Average Run Length, Fredholm Type Integral Equations, Numerical Approximations
Volume	Vol.41 No.5/2 (OCTOBER 2014)
DOI
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 J. Sci., 2014; 41(5/2): 1449-1456.
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