Optimization design of X̅ &EWMA control chart for minimizing mean number of defective units per out-of-control case

This article proposes X̅&EWMA chart (known as MD X̅&EWMA chart) that combines Shewhart X̅ chart and Exponentially Weighted Moving Average (EWMA) chart for minimizing the mean number of defective units (denoted as MD) produced per out-of-control case. The design algorithm not only optimizes the sample size, sampling interval and control limits of the X̅ chart and EWMA chart, but also optimizes the allocation of detection power between the two charts´ elements considering random process shift in mean. The Rayleigh distribution is used to characterize the random process shift. The design of the MD X̅&EWMA chart requires a few design parameters that can easily be determined. A comparative study shows that an optimal MD X̅&EWMA chart is significantly superior to a traditional MD X̅&EWMA chart.