Diagram Kontrol Simultan Robust Max Half-Mchart Berbasis Cellwise Minimum Covariance Determinant

Hidayatullah, Syafi' Bariq' Syihabuddin (2026) Diagram Kontrol Simultan Robust Max Half-Mchart Berbasis Cellwise Minimum Covariance Determinant. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Salah satu alat utama dalam Statistical Process Control (SPC) untuk memantau kualitas adalah diagram kontrol. Diagram kontrol multivariat simultan banyak diterapkan untuk memonitor proses mean dan variabilitas secara bersamaan. Max-Half-Mchart merupakan diagram kontrol multivariat simultan bertipe Shewhart yang dapat mendeteksi pergeseran mean dan variabilitas yang kecil maupun besar. Kinerja diagram kontrol diketahui cukup sensitif terhadap keberadaan pencilan (outliers). Outliers dapat mempengaruhi estimasi parameter proses serta menyebabkan fenomena masking dan swamping effect. Studi terbaru telah menyoroti pentingnya kontaminasi sel, yang dapat mengurangi efektivitas estimator robust casewise. Untuk mengatasi keterbatasan ini, penelitian ini mengembangkan diagram robust Max-Half-Mchart berbasis estimator Cellwise Minimum Covariance Determinant (cellMCD). Hasil simulasi pada berbagai tingkat korelasi dan proporsi kontaminasi menunjukkan bahwa diagram robust Max-Half-Mchart berbasis cellMCD memberikan kinerja deteksi outlier yang lebih baik dibandingkan dengan Max-Half-Mchart konvensional dan robust Max-Half-Mchart berbasis Fast-MCD. Analisis ARL (Average Run Length) juga menunjukkan deteksi pergeseran kecil hingga sedang yang lebih cepat. Hasil penerapan data sintetis dan monitoring data kualitas semen OPC menunjukkan bahwa diagram robust Max-Half-Mchart berbasis cellMCD lebih sensitif dalam mendeteksi out-of-control.
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One of the main tools in Statistical Process Control (SPC) for monitoring quality is the control chart. Simultaneous multivariate control charts are widely applied to monitor the process mean and variability at the same time. The Max-Half-Mchart is a Shewhart-type simultaneous multivariate control chart that can detect both small and large shifts in the process mean and variability. However, the performance of control charts is known to be sensitive to the presence of outliers. Outliers can affect the estimation of process parameters and cause masking and swamping effects. Recent studies have highlighted the importance of cellwise contamination, which can reduce the effectiveness of casewise robust estimators. To overcome this limitation, this study develops a robust Max-Half-Mchart based on the Cellwise Minimum Covariance Determinant (cellMCD) estimator. Simulation results under various correlation levels and contamination proportions show that the robust Max-Half-Mchart based on cellMCD provides better outlier detection performance than the conventional Max-Half-Mchart and the robust Max-Half-Mchart based on Fast-MCD. The Average Run Length (ARL) analysis also indicates faster detection of small to moderate shifts. The application to synthetic data and OPC cement quality monitoring data shows that the robust Max-Half-Mchart based on cellMCD is more sensitive in detecting out-of-control observations.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	CellMCD, Diagram Kontrol Multivariat Simultan, Max-Half-Mchart, Outlier, Penaksir Robust, CellMCD, Simultaneous Multivariate Control Charts, Max-Half-Mchart, Outliers, Robust Estimator
Subjects:	H Social Sciences > HD Industries. Land use. Labor > HD56.25 Industrial efficiency--Measurement. Industrial productivity--Measurement. H Social Sciences > HD Industries. Land use. Labor > HD9980.5 Service industries--Quality control. Q Science
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Syafi~ Bariq~ Syihabuddin Hidayatullah
Date Deposited:	01 Aug 2026 02:04
Last Modified:	01 Aug 2026 02:04
URI:	http://repository.its.ac.id/id/eprint/141171

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