Directionally sensitive homogeneously weighted moving average control charts

Abstract

One-sided control charts for monitoring changes in the mean level are proposed in this paper. The proposed charts are given in the form of a homogeneously weighted moving average technique that provides efficient monitoring of small shifts in the mean level. The charts accumulate observations that are above the target (or mean value) and truncated the observations that are less than the target to the target value in their computations. Average run length comparisons of the proposed charts with the existing one-sided charts, based on the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, show that the proposed charts are more efficient in detecting small shifts than the competing charts. We investigate the sensitivity of the charts to non-normality and show how they can be designed to be robust to non-normal distributions. We provide a step-by-step implementation of the proposed charts when their parameters are unknown and estimated from historical reference data sets. The advantage of the proposed charts over some existing one-sided charts is demonstrated via an illustrative example, involving monitoring mean lethal concentration (LC (Formula presented.)) from a k-nearest neighbours (KNN) regression-based Quantitative Structure-Activity Relationships (QSAR) model that relates LC (Formula presented.) to eight molecular descriptors.