Enhancing the detection power of multivariate time between events control charts for Gumbel’s bivariate exponential distribution

Abstract

One of the most important goals of statistical process control is quickly detecting any changes in the processes and consequently reducing process variability. Control charts are graphical tools that are widely used to achieve these goals. In this regard, monitoring methods based on the time between events (TBEs) have received much attention in recent years. These methods are widespread for monitoring high-quality processes and temporal quality characteristics. Although univariate TBE control charts have been extensively studied in the literature, multivariate TBE control charts need more investigation. In this paper, the performance of the multivariate exponentially weighted moving average (MEWMA), paired individual exponentially weighted moving average (PEWMA), and multivariate cumulative sum (MCUSUM) control charts for the bivariate TBEs which follow Gumbel's bivariate exponential (GBE) distribution are compared based on the average time to signal (ATS) metric. Also, the multivariate rate (MRA) control chart is proposed for enhancing the performance of the multivariate TBE control charts. Real-world examples are used to illustrate the applicability of the proposed monitoring scheme. The results of the performance evaluation show that the proposed approach can considerably enhance the performance of the multivariate TBE control charts.