Average Run Length Formulas for Mixed Double Moving Average - Exponentially Weighted Moving Average Control Chart

Abstract

This research aims to propose an explicit formula for average run length (ARL) for a mixed Double Moving Average - Exponentially Weighted Moving Average (DMA-EWMA) control chart. In addition, the performance of the DMA-EWMA control chart is compared with the existing control charts; Shewhart and Exponentially Weighted Moving Average (EWMA) control charts. The common criterion to measure the efficiency is the average run length, commonly measured by the out of control average run length (ARL₁). The in control average run length (ARL₀) is given to 370, and the process observations are from normal, exponential, gamma, and Laplace distributions. The numerical results found that the DMA-EWMA control chart performs better than other control charts for all magnitudes of changes (). Furthermore, the real applications are addressed to validate the proposed control chart.