An efficient MEWMA chart for Gumbel's bivariate Pareto distribution

Abstract

Control charts play a vital role in process monitoring to ensure the product's desired standards. Due to rapid improvements in data collection methods, multivariate charts are preferred over univariate charts. This paper proposes a bivariate exponentially weighted moving average chart for the simultaneous monitoring of the mean vector of Gumbel's bivariate Pareto type II (also known as the Lomax distribution) time-between-events data. The performance of the proposed chart is assessed through average run length, median run length, and the standard deviation of the run length criteria. To show the implementation of the chart in the real world, illustrative examples are also presented.

Keywords:

• Time-between-events
• bivariate Gumbel distribution
• EWMA chart
• average run length

Acknowledgments

The authors would like to thanks the comments and suggestions of the anonymous reviewers and editor to improve the presentation of the work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.