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ScienceAsia 41 (2015): 141-147 |doi: 10.2306/scienceasia1513-1874.2015.41.141

Exact solution of the average run length for the cumulative sum chart for a moving average process of order q

Kanita Petcharat, Saowanit Sukparungsee, Yupaporn Areepong*

ABSTRACT:     In this paper we use a Fredholm integral equation approach to derive an explicit formula for the average run length (ARL) of a cumulative sum (CUSUM) chart for random observations described by a moving average process of order q (MA(q)) with exponential white noise. We compare the computational times required for calculating the ARL from our exact formula with the computational times required for solving the Fredholm integral equations using a Gauss-Legendre numerical scheme. We find that the computational times are approximately 1 s for the explicit formula and approximately 13 min for the numerical integration scheme.

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Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800 Thailand

* Corresponding author, E-mail: yupaporna@kmutnb.ac.th

Received 13 Apr 2013, Accepted 27 Nov 2014