A new MCUSUM chart for Gumbel's bivariate Pareto distribution

Abstract

Statistical process control aims to quickly detect any changes that occur in the process and design strategies to reduce variability and improve the process accordingly. A control chart is a widely used SPC tool that is used to track changes in a process. Time-between-events control schemes efficiently monitor temporal quality characteristics and are especially effective for monitoring high-quality processes. The time-between-events datasets are not normally distributed and follow a skewed distribution. This study proposes a multivariate cumulative sum control chart to monitor Gumbel’s bivariate Pareto type II data. Monte Carlo simulations are used to compute and compare the run length characteristics of the proposed chart with the existing ones. A real data set and a simulated data set are considered to illustrate the implementation of the proposed chart compared to existing charts. The proposed chart is also compared with other members of the Archimedean copula family.

Keywords

• Average run length
• bivariate Gumbel distribution
• control chart
• cumulative sum
• Archimedean copula

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