Advances and Applications in Statistics
Volume 57, Issue 1, Pages 41 - 59
(July 2019) http://dx.doi.org/10.17654/AS057010041 |
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THE EXACT SOLUTION OF ARL ON EWMA CHART FOR NON SEASONAL AR MODEL WITH EXOGENOUS VARIABLES
Yupaporn Areepong
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Abstract: The performance of a control chart monitoring a statistical process is regularly measured in terms of the average run length (ARL) which is calculated with several methods. This research is to present explicit formulas for average run length (ARL) on exponentially weighted moving average (EWMA) control chart for autoregressive with exogenous variable process To check the accuracy, the ARL results are compared with numerical integral equations (NIE) method based on the Gauss-Legendre rule. The performance is compared in term of the absolute percentage relative error (APRE). Accordingly, both methods had similarly excellent agreement with the APRE at less than 0.05%. Meanwhile, the explicit formulas consumed less CPU time than the NIE method. In addition, the real observations from stock price of Thailand with some Thailand’s economic indicators as the exogenous variables are the example for evaluating ARL on EWMA control chart. Moreover, EWMA chart is used to compare a capability with the CUSUM scheme. As a result, the performance of the EWMA control chart is better for all magnitude of shifts. |
Keywords and phrases: average run length (ARL), exponentially weighted moving average control chart (EWMA), autoregressive with exogenous variable model explicit formulas.
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