A Variable Sampling Interval Multivariate Exponentially Weighted Moving Average Control Chart for Monitoring the Gumbel’s Bivariate Exponential Data

Abstract

The general assumption for designing a multivariate control chart is that the multiple variables are independent and normally distributed. This assumption may not be tenable in many practical situations, because multiple variables with dependency often need to be monitored simultaneously to ensure the process is in-control. The Gumbel’s Bivariate Exponential (GBE) distribution is considered a better model for skewed data with dependency in reliability analysis. In this paper, a Multivariate Exponentially Weighted Moving Average (MEWMA) control chart with Variable Sampling Interval (VSI) feature is developed to monitor the mean vector of GBE model. Monte-Carlo simulations are used to calculate the ATS (Average Time to Signal) values of the proposed VSI MEWMA GBE chart for three different types of shifts. Meanwhile, some tables are provided to show the ATS performances of the proposed chart with different designed parameters. Furthermore, both zero- and steady-state ATS performances of the proposed VSI MEWMA GBE chart are compared with those of the FSI (Fix Sampling Interval) MEWMA chart. Comparative results show that the proposed chart is superior to its FSI counterpart in monitoring the GBE data. In addition, a numerical example is provided to show that the proposed chart performs well in monitoring GBE data.