Copula-Based Monitoring Of Mean, Variance, And Dependency Shifts In Multivariate Processes

Chotimah, Machmuda Fauzia Husnul (2025) Copula-Based Monitoring Of Mean, Variance, And Dependency Shifts In Multivariate Processes. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Monitoring multivariate processes is challenging due to the complex interdependencies among variables. While much attention has been paid to detecting shifts in mean and variance, shifts in the dependence structure are equally critical yet remain underexplored. This study proposes a novel monitoring approach that integrates a copula-based framework with the nonparametric progressive mean sign statistic (NPPM-SN), enabling the direct detection of changes in the joint distribution rather than monitoring each variable in isolation. The proposed framework is evaluated using three monitoring strategies: Joint Probability Density Function (JPDF), Copula Probability Density Function (CPDF), and Marginal Probability Density Function (MPDF), under various shift scenarios involving changes in mean, variance, and dependency. A large-scale Monte Carlo simulation is conducted to estimate run lengths, and classification trees are employed to assess detection performance across different scenarios and dimensions. The results show that each method offers distinct advantages depending on the type and magnitude of the shift. JPDF performs best under moderate mean shifts, whereas CPDF is more effective in detecting dependency shifts when variances are heterogeneous. Tied performance (TIE) across methods is more likely when the mean shift is large, indicating overlapping detection capabilities in high-shift scenarios. These findings are consistent across higher-dimensional settings, confirming the scalability and robustness of the proposed framework.
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Pemantauan proses multivariat, atau multivariate process monitoring, merupakan tantangan karena adanya ketergantungan yang kompleks di antara variabel-variabel. Meskipun perhatian besar telah diberikan pada deteksi perubahan rata-rata dan varians, pergeseran dalam struktur ketergantungan juga sama pentingnya namun masih kurang dieksplorasi. Penelitian ini mengusulkan pendekatan pemantauan baru yang mengintegrasikan kerangka kerja berbasis copula dengan Nonparametric Progressive Mean Sign Statistic (NPPM-SN), yang memungkinkan deteksi langsung terhadap joint distribution daripada memantau setiap variabel secara terpisah. Kerangka kerja yang diusulkan dievaluasi menggunakan tiga strategi pemantauan, Joint Probability Density Function (JPDF), Copula Probability Density Function (CPDF), dan Marginal Probability Density Function (MPDF), di bawah berbagai scenario pergeseran yang melibatkan perubahan dalam rata-rata, varians, dan ketergantungan. Simulasi Monte Carlo berskala besar dilakukan untuk memperkirakan Average Run Length (ARL) dan classification tree digunakan untuk menilai kinerja deteksi di berbagai skenario dan dimensi. Hasilnya menunjukkan bahwa setiap metode memiliki keunggulan tersendiri tergantung pada jenis dan besarnya perubahan. JPDF memberikan kinerja terbaik pada perubahan rata-rata sedang, sedangkan CPDF lebih efektif dalam mendeteksi perubahan ketergantungan ketika varians tidak homogen. Kinerja yang seimbang (TIE) antar metode lebih mungkin terjadi ketika perubahan rata-rata besar, menunjukkan kemampuan deteksi yang hampir serupa dalam skenario pergeseran tinggi. Temuan ini konsisten di seluruh skenario, baik pada pengaturan berdimensi tinggi, mengonfirmasi skalabilitas dan robustness dari kerangka kerja yang diusulkan.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Copula, Multivariate Process Monitoring, Dependency Shift, Simulation, Pergeseran Ketergantungan
Subjects:	Q Science > QA Mathematics > QA278 Cluster Analysis. Multivariate analysis. Correspondence analysis (Statistics) T Technology > T Technology (General) > T57.62 Simulation
Divisions:	Faculty of Industrial Technology and Systems Engineering (INDSYS) > Industrial Engineering > 26101-(S2) Master Thesis
Depositing User:	Machmuda Fauzia Husnul Chotimah
Date Deposited:	04 Aug 2025 07:38
Last Modified:	04 Aug 2025 07:38
URI:	http://repository.its.ac.id/id/eprint/125866

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