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

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