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Analytical and numerical solutions of average run lengthintegral equations for an EWMA control chartover a long memory SARFIMA process |
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| รหัสดีโอไอ | |
| Creator | 1. Rapin Sunthornwat 2. Yupaporn Areepong 3. Saowanit Sukparungsee |
| Title | Analytical and numerical solutions of average run lengthintegral equations for an EWMA control chartover a long memory SARFIMA process |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2561 |
| Journal Title | Songklanakarin Journal of Science and Technology |
| Journal Vol. | 40 |
| Journal No. | 4 |
| Page no. | 885 |
| Keyword | average run length, EWMA control chart, SARFIMA process, composite midpoint rule, integral equation |
| URL Website | http://rdo.psu.ac.th/sjstweb/index.php |
| ISSN | 0125-3395 |
| Abstract | The efficiency of a process, especially a long memory seasonal autoregressive fractional integral moving average(SARFIMA) process, has commonly been measured through the quality control chart. In this paper, a generalized long memorySARFIMA process of the exponentially weighted moving average (EWMA) control chart is carried out and shown. Also,analytical and numerical average run length (ARL) were designed to measure the efficiency of the EWMA control. Existence anduniqueness by the fixed point theory are proven for the analytical ARL. Error and convergence of numerical integration equationsare also given for the numerical ARL. The findings indicated that the analytical ARL was evaluated more quickly and accuratelythan the numerical ARL. As a result, the analytical ARL is an alternative for measuring the efficiency of an EWMA control chartover a long memory SARFIMA process. |
