TY - JOUR
T1 - Exact solution for average run length of CUSUM charts for MA(1) process
AU - Petcharat, Kanita
AU - Areepong, Yupaporn
AU - Sukparungsee, Saowanit
AU - Mititelu, Gabriel
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - CUSUM technique
KW - integral equations
KW - numerical integration
UR - https://hdl.handle.net/1959.7/uws:57779
UR - https://epg.science.cmu.ac.th/ejournal/journalDetail.php?journal_id=5287
M3 - Article
SN - 0125-2526
VL - 41
SP - 1449
EP - 1456
JO - Chiang Mai Journal of Science
JF - Chiang Mai Journal of Science
M1 - 45327
ER -