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An Analytical of Average Run Length for First Order of Autoregressive Observations on CUSUM Procedure

J. Busaba, S. Sukparungsee, Y. Areepong

Abstract


The objective of this article is to derive explicit formulas for the Average Run Length (ARL) on CUSUM procedure when observations are the first order of autoregressive (AR(1)) model with white noise exponential distribution by using integral equations approach. The accuracy of this formulas is compared with the results obtained from the numerical approximations of integral equations. We found that the explicit ARL obtained from the proposed formulas are in excellent agreement with the approximation ARL obtained from numerical integral equation. However, the computational times obtained from the explicit formulas is found to be approximately one second, which is much less than obtained from the numerical integral approximations.

Keywords


CUSUM, autoregressive, average run length, integral equation, numerical approximations.

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