IJPAM: Volume 77, No. 2 (2012)
HYPEREXPONENTIAL TO EVALUATE
THE ARL FOR CUSUM CHART


Saowanit Sukparungsee



Faculty of Applied Science
King Mongkut's University of Technology
North Bangkok,Bangkok 10800, THAILAND

University of Technology Sydney
Broadway, NSW 2007, AUSTRALIA
Abstract. Explicit formulas for the Average Run Length (ARL) of Cumulative Sum
(CUSUM) chart are very complicated in regarding the analytical
derivation when observations are Long-tailed distributions. The
objective of this paper is to fitting Pareto distribution with the
hyperexponential distribution to evaluate ARL of CUSUM procedure.
The numerical results obtained from analytical solution for the ARL
and from numerical approximations are derived and we compared the
result with integral equations approach.
Received: February 11, 2012
AMS Subject Classification: 60A05
Key Words and Phrases: cumulative sum chart, average run length, hyperexponential distribution, stopping times
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 2