Multivariate nonparametric control chart with variable sampling interval

Abstract

• Adaptive exponentially weighted moving average control chart using variable sampling interval for multivariate processes. • Completely nonparametric and adaptive chart. • Control chart for multivariate processes based on the Mahalanobis depth. • Detecting white wine quality by using the proposed control chart. • Comparing the proposed method to several advanced methods. This paper proposes an adaptive, multivariate, nonparametric, exponentially weighted moving average control chart with variable sampling interval. A number of studies have discussed multivariate nonparametric control charts. However, the proposed multivariate nonparametric control charts usually have strict requirements. In this paper, we construct a control chart for multivariate processes that is based on the Mahalanobis depth. Specifically, we use the concept of the Mahalanobis depth to reduce each multivariate measurement to a univariate index. It is worth mentioning that this approach is completely nonparametric. We also discuss the optimal strategy for the parameters. This chart is an adaptive chart and has a variable sampling interval. A simulation study demonstrates that the proposed chart is efficient in detecting various magnitudes of shifts. A gravel data and a wine quality detection example are given to introduce the proposed control chart.