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Journals / Hacettepe Journal of Mathematics and Statistics / 2025 / Volume: 54 Issue: 6

A new MCUSUM chart for Gumbel's bivariate Pareto distribution

Ayesha Talib(Quaid-i-Azam University)0009-0001-3398-8532
Sajid Ali(Quaid-I-Azam University)0000-0003-4868-7932
Ismail Shah(University of Padua)0000-0001-5005-6991
Pages
—
Publication Date
2025-12-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The proposed chart is also compared with other members of the Archimedean copula family.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:A real data set and a simulated data set are considered to illustrate the implementation of the proposed chart compared to existing charts.
💡
Conclusion & Impact:The proposed chart is also compared with other members of the Archimedean copula family.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Average run length · bivariate Gumbel distribution · control chart

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.

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Cite This Article

Talib, A., Ali, S., Shah, I. (2025). A new MCUSUM chart for Gumbel's bivariate Pareto distribution. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 6. https://doi.org/10.15672/hujms.1705940

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