A SYNTHETIC CONTROL CHART FOR MONITORING THE PROCESS MEAN OF SKEWED POPULATIONS BASED ON THE WEIGHTED VARIANCE METHOD

摘要

A synthetic control chart for detecting shifts in the process mean integrates the Shewhart X chart and the conforming run length chart. It is known to outperform the Shewhart X chart for all magnitudes of shifts and is also superior to the exponentially weighted moving average chart and the joint X-exponentially weighted moving average charts for shifts of greater than 0.8σ in the mean. A synthetic chart for the mean assumes that the underlying process follows a normal distribution. In many real situations, the normality assumption may not hold. This paper proposes a synthetic control chart to monitor the process mean of skewed populations. The proposed synthetic chart uses a method based on a weighted variance approach of setting up the control limits of the X/S sub-chart for skewed populations when process parameters are known and unknown. For symmetric populations, however, the limits of the new X/S sub-chart are equivalent to that of the existing X/S sub-chart which assumes a normal underlying distribution. The proposed synthetic chart based on the weighted variance method is compared by Monte Carlo simulation with many existing control charts for skewed populations when the underlying populations are Weibull, lognormal, gamma and normal and it is generally shown to give the most favourable results in terms of false alarm and mean shift detection rates.