New weighted adaptive CUSUM charts for monitoring the generalized variance of a bivariate normal process

Abstract

In modern and high volume manufacturing environments, it is vital to early detect a small sustained shift in a short period of time as it may have a serious impact on a manufacturing process. Adaptive memory-type control charts have the ability to swiftly detect a range of the shift sizes, and one such control chart is a weighted adaptive CUSUM (abbreviated as C) chart. In this paper, using a simple likelihood ratio test-statistic, we propose two types of the C charts (with and without the normalizing transformation) using three different shift estimators for monitoring the generalized variance (GV) of a bivariate normally distributed production process. In addition, the sensitivities of these control charts are also enhanced with the variable sampling interval feature. Monte Carlo simulations are used to compute the zero-state and steady-state run-length characteristics of the proposed charts. Based on detailed run-length comparisons, it is observed that the proposed charts may uniformly and substantially outperform the existing charts when detecting different kinds of shifts in the GV. A real dataset is also selected to illustrate the implementation of the newly proposed charts.