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Analytical explicit formulas of average run length for long memory process with ARFIMA model on CUSUM control chart |
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| รหัสดีโอไอ | |
| Creator | 1. Wilasinee Peerajit 2. Yupaporn Areepong 3. Saowanit Sukparungsee |
| Title | Analytical explicit formulas of average run length for long memory process with ARFIMA model on CUSUM control chart |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2560 |
| Journal Title | Songklanakarin Journal of Science and Technology (SJST) |
| Journal Vol. | 39 |
| Journal No. | 6 |
| Page no. | 779 |
| Keyword | ARFIMA(p,d,q) process,numerical integral equation (NIE) method,exponential white noise |
| ISSN | 0125-3395 |
| Abstract | This paper proposes the explicit formulas for the derivation of exact formulas from Average Run Lengths (ARLs) usingintegral equation on CUSUM control chart when observations are long memory processes with exponential white noise. Theauthors compared efficiency in terms of the percentage of absolute difference to a similar method to verify the accuracy ofthe ARLs between the values obtained by the explicit formulas and numerical integral equation (NIE) method. The explicitformulas were based on Banach fixed point theorem which was used to guarantee the existence and uniqueness of thesolution for ARFIMA(p,d,q). Results showed that the two methods are similar in good agreement with the percentage ofabsolute difference at less than 0.23%. Therefore, the explicit formulas are an efficient alternative for implementation in realapplications because the computational CPU time for ARLs from the explicit formulas are 1 second preferable over the NIEmethod. |
