Exact Run Length Sensitivity of DEWMA Control Chart Based on Quadratic Trend Autoregressive Model
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One well-known process detection tool that is sensitive to even little shift changes in the process is the Double Exponentially Weighted Moving Average (DEWMA) control chart. The present study aims to provide exact average run length (ARL) on the DEWMA chart under the data that is underlying the quadratic trend autoregressive (AR) model. At that point, the computed ARL via the numerical integral equation (NIE) technique was compared in terms of accuracy to the exact one that was developed by using the percentage accuracy (%Acc). And then, the computational times of both were also compared. The results revealed that the ARL results of exact ARL and ARL via the NIE method show hardly any difference in terms of accuracy, but exact ARL outperformed in terms of computational times that were computed instantly, whereas the other way spent approximately 2-3 seconds computing. Thereafter, the proposed ARL operating on the DEWMA chart was compared to the CUSUM and EEWMA charts. It was found to be more effective in terms of detection performance. Especially when there are little shift changes in the process. The run length formulas, which are the standard deviation run length (SDRL) and the median run length (MRL), were measures of sensitivity evaluation and were used to verify their capability. The sensitivity of detecting changes of exact ARL running on the DEWMA chart was illustrated by the real data utilized in fields of economics about natural gas importing in Thailand (Unit: 100 MMSCFD at heat value of natural gas 1,000 BTU/SCF). Apparently, the exact ARL of the DEWMA chart is an excellent choice to detect small shift changes under this scenario, which represents properties as a quadratic trend AR model.
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