Detection Sensitivity of a Modified EWMA Control Chart with a Time Series Model with Fractionality and Integration

Abstract

Among the many statistical process control charts, the modified exponentially weighted moving average (EWMA) control chart has been designed to swiftly detect a small shift in a process parameter. Herein, we propose two explicit formulas for the average run length (ARL) for integrated moving average (IMA) and fractional integrated moving average (FIMA) models combined with the modified EWMA control chart for time series prediction. The application of the suggested control chart procedures depends on the residuals of the IMA and FIMA models. The performance of the control chart with both models is evaluated by using the ARL. Explicit formulas for the ARL for the two models with the modified EWMA statistic are derived and their precision is compared with the numerical integral equation method. The explicit formulas could accurately predict the true ARL while markedly decreasing the computational processing time compared to the numerical integration method. The capabilities of the IMA and FIMA models with the modified EWMA control chart were studied by varying g times the last term and exponential smoothing parameter λ, with the relative mean index being used to evaluate these situations. The results show that the modified EWMA control chart with either model performed better than the original EWMA control chart. Furthermore, the modified EWMA control chart with either model was highly efficient when g increased and λ was small. Two applications involving energy commodity prices are used to illustrate the efficacies of the proposed approaches, the results of which were in accordance with the experimental study. Doi: 10.28991/ESJ-2022-06-05-015 Full Text: PDF

Keywords

• explicit formula
• average run length
• fractionally integrated moving average
• modified exponentially weighted moving average.