Copula-based multivariate control charts for monitoring multiple dependent Weibull processes

Monitoring multivariate time between events (MTBE) data is critical in areas such as manufacturing and service operations. Monitoring of multiple dependent Weibull processes is often required in high quality processes, yet existing methods for monitoring Weibull time between events (TBE) data have been developed based on univariate processes. This paper develops multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) control charts for monitoring the mean vector of multiple dependent Weibull processes from the Normal, Clayton, Frank, Gumbel and Joe copula models. The performance of the two charts is evaluated using Monte Carlo simulation based on the average time to signal (ATS) metric for in-control and out-of-control states. To further illustrate the use of the chart, two applications are illustrated.