Diagram Pengendali Functional T² Hotelling Berbasis Successive Difference Covariance Matrix

Afrinah, Ayu (2026) Diagram Pengendali Functional T² Hotelling Berbasis Successive Difference Covariance Matrix. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pengendalian proses berbasis data fungsional menjadi pendekatan yang semakin relevan dalam pemantauan proses modern yang menghasilkan data berdimensi tinggi dan berkorelasi kuat, seperti spektrum near-infrared (NIR). Penelitian ini mengusulkan diagram pengendali Functional Hotelling’s T² berbasis Successive Difference Covariance Matrix (SDCM) untuk meningkatkan sensitivitas deteksi pergeseran kecil pada proses kontinu. Data spektrum direpresentasikan sebagai fungsi halus menggunakan pendekatan Functional Data Analysis (FDA) dan direduksi dimensinya melalui Functional Principal Component Analysis (FPCA). Berbeda dari pendekatan konvensional yang menggunakan matriks kovarians sampel, SDCM dibangun dari selisih berturut-turut antar pengamatan fungsional sehingga mampu menekan pengaruh baseline drift dan meningkatkan kestabilan estimasi kovarians. Batas kendali ditentukan melalui simulasi untuk mencapai nilai in-control Average Run Length (ARL) yang diinginkan. Hasil evaluasi menunjukkan bahwa pendekatan yang diusulkan memiliki kemampuan deteksi pergeseran kecil yang lebih baik dibandingkan metode berbasis kovarians klasik, tanpa mengorbankan stabilitas kondisi terkendali. Metode ini memberikan alternatif yang efektif untuk pemantauan proses berbasis spektrum dan data fungsional berdimensi tinggi.
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Functional data based process control has become an increasingly relevant approach for monitoring modern processes that generate high-dimensional and strongly correlated data, such as near-infrared (NIR) spectra. This study proposes a Functional Hotelling’s T² control chart based on the Successive Difference Covariance Matrix (SDCM) to enhance sensitivity in detecting small shifts in continuous processes. The spectral data are represented as smooth functions using the Functional Data Analysis (FDA) framework and their dimensionality is reduced through Functional Principal Component Analysis (FPCA). Unlike conventional approaches that rely on the sample covariance matrix, the SDCM is constructed from successive differences between functional observations, which helps suppress baseline drift effects and improves the stability of covariance estimation. Control limits are determined via simulation to achieve a desired in-control Average Run Length (ARL₀). The evaluation results indicate that the proposed approach exhibits superior capability in detecting small shifts compared to classical covariance-based methods, without sacrificing in-control stability. The proposed method provides an effective alternative for monitoring spectral processes and high-dimensional functional data.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	FDA, Hotelling T^2, NIR Spectroscopy, SPC, SDCM,FDA, Hotelling’s T², SDCM, SPC, NIR Spectroscopy
Subjects:	H Social Sciences > HD Industries. Land use. Labor > HD9980.5 Service industries--Quality control.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Ayu Afrinah
Date Deposited:	22 Jan 2026 08:48
Last Modified:	22 Jan 2026 08:48
URI:	http://repository.its.ac.id/id/eprint/130094

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