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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.
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Start & End Page |
1449 - 1456 |
Received Date |
2012-07-16 |
Revised Date |
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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 |
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Citation |
Petcharat[a] K., Areepong*[a] Y., Sukparungsee[a] S. and Mititelu[b] 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. |
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