Abstract
Multivariate memory-type control charts that use information from both the current and previous process observations have been proposed. They are designed to detect shifts in both upper and downward directions with equal precision when monitoring the process mean vector. The absence of directional sensitivity can limit the charts' application, particularly when users are interested in detecting variations in one direction than the other. This article proposes one-sided and two one-sided multivariate control charts for monitoring shifts in the process mean vector. The proposed charts are presented in the form of the multivariate homogeneously weighted moving average approach that yields efficient detection of shifts in the mean vector. We provide simulation studies under different shift sizes in the process mean vector and evaluate the performance of the proposed charts in terms of their run length properties. We compare the average run length (ARL) results of the charts with the conventional charts as well as the one-sided and two one-sided multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) charts. Our simulation results show that the proposed charts outperform the existing charts used for the same purpose, particularly when interest lies in detecting small shifts in the mean vector. We show how the charts can be designed to be robust to non-normal distributions and give a step-by-step implementation efficient application of the charts when their parameters are unknown and need to be estimated. Finally, an illustrative example is provided to show the application of the proposed charts.
Highlights
Multivariate process control (MPC) is used to monitor processes comprising several correlated characteristics or features
The proposed charts are obtained in the forms of the multivariate homogeneously weighted moving average approach that yield an efficient way to detect small shifts in the process mean
We provided simulation results under different shift sizes in the process mean vector and evaluated the performance of the proposed charts in terms of their run length properties
Summary
Multivariate process control (MPC) is used to monitor processes comprising several correlated characteristics or features. To enhance the sensitivity of the χ 2 chart to detect small shifts in the process mean vector, different multivariate memory-type tools that use information from both the current and previous process observations have been proposed in the literature. The multivariate charts and their enhancements mentioned above are directional invariant charts They are proposed to detect shifts in all directions (i.e., upper and downward) with equal precision when monitoring the process mean vector. On the other hand, using a one-sided chart can improve the speed in detecting an upward or a downward change in the process mean vector To this end, [24] proposed a one-sided MCUSUM chart. We provide two one-sided versions of the one-sided charts that can be used to detect irregular changes (i.e., both upward and downward shifts) in the process mean vector.
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