Advances and Applications in Statistics
Volume 48, Issue 6, Pages 429 - 444
(June 2016) http://dx.doi.org/10.17654/AS048060429 |
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EXACT EXPRESSION OF AVERAGE RUN LENGTH FOR TWO-SIDED EXPONENTIAL CUSUM PROCEDURE
Saowanit Sukparungsee, Sophana Somran and Yupaporn Areepong
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Abstract: In this paper, we study average run length (ARL) for cumulative sum (CUSUM) chart when observations are exponential distributions for non-negative two-sided CUSUM chart. The explicit formulas for calculating ARL are analytically obtained by two approaches namely integral equation (IE) and numerical integration (NI). The comparison of accuracy results of the explicit solution is made by the integral equation approach; meanwhile, the numerical approximations are evaluated by numerical integration approach, which show results found by both approaches are in good agreement. The computational time for the IE approach is significantly much less than the computational times required for the NI approach. |
Keywords and phrases: explicit form, average run length, two-sided chart, exponential distribution. |
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