Advances and Applications in Statistics
Volume 50, Issue 1, Pages 21 - 36
(January 2017) http://dx.doi.org/10.17654/AS050010021 |
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EXPLICIT FORMULAS OF AVERAGE RUN LENGTH OF CUMULATIVE SUM CONTROL CHART FOR AUTOREGRESSIVE INTEGRATED MOVING AVERAGE WITH EXOGENOUS VARIABLE MODEL
Yupaporn Areepong and Saowanit Sukparungsee
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Abstract: This research presents explicit formulas for Average Run Length (ARL) using an integral equation on CUSUM control chart for Autoregressive Integrated Moving Average with Exogenous Variable process (ARIMAX) and an exponential white noise. To check the accuracy, the ARL results are compared with numerical integral equations (NIE) based on the Gauss-Legendre rule and compared efficiency in terms of the percentage of absolute difference. There was an excellent agreement between the explicit formulas and the numerical solutions. Additionally, the computational time between our explicit formulas for the ARL with the one obtained via NIE is compared. The computational time for the explicit formulas is 1 second preferable over the NIE method. In addition, the explicit analytical formulas for evaluating and can produce a set of optimal parameters which depend on the reference value and the width of control limit for designing CUSUM chart with a minimum
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Keywords and phrases: cumulative sum control chart (CUSUM), autoregressive integrated moving average with exogenous variable model (ARIMAX), explicit formulas, average run length (ARL). |
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