Detection Capability of the Modified EWMA Chart for the Trend Stationary AR(1) Model
A performance of control chart is frequently evaluated by using the average run length (ARL) which is calculated with several methods. Regarding this research paper, an explicit formula is a presented technique for computing the ARL of the modified EWMA chart with the trend AR(1) model in the scope of exponential white noise. The numerical integral equation (NIE) method is compared to the performance with the explicit formula. Accordingly, the results show that the explicit formula can find the solutions correctly and quickly. Moreover, the modified EWMA chart is used to compare a capability with the EWMA scheme. As a result, the performance of the modified EWMA control chart is better for small and moderated shifts. In addition, this explicit formula of the ARL is applied by using the real data of a health field.