Pengembangan Diagram Pengendali Exponentially Weighted Moving Average Robust Max-M (ERMM-Chart)

Radjid, Samin (2026) Pengembangan Diagram Pengendali Exponentially Weighted Moving Average Robust Max-M (ERMM-Chart). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pengendalian proses industri modern sering melibatkan beberapa karakteristik kualitas yang saling berkorelasi sehingga perubahan rata-rata dan variabilitas proses perlu dipantau secara simultan. Max-Mchart dapat digunakan untuk pemantauan tersebut pada pengamatan individual, tetapi karakteristiknya yang bertipe Shewhart menyebabkan diagram ini kurang sensitif terhadap pergeseran kecil. Selain itu, estimasi parameter secara konvensional rentan terhadap outlier. Penelitian ini bertujuan mengembangkan Exponentially Weighted Moving Average Robust Max-M Control Chart (ERMM-Chart) untuk memantau pergeseran rata-rata dan variabilitas proses multivariat secara simultan. ERMM-Chart dibentuk dengan menerapkan mekanisme EWMA pada statistik Robust Max-M, sedangkan vektor rata-rata dan matriks kovarians pada fase I diestimasi menggunakan Fast-MCD. Kinerja diagram dievaluasi berdasarkan Average Run Length pada kondisi in-control (ARL₀) dan out-of-control (ARL₁) untuk berbagai jumlah karakteristik kualitas, konstanta pembobot, tingkat korelasi, serta skenario pergeseran rata-rata, variabilitas, dan keduanya secara simultan. Kinerja ERMM-Chart juga dibandingkan dengan EMM-Chart serta diterapkan pada data sintetis dan data kualitas clinker semen. Hasil simulasi menunjukkan bahwa ERMM-Chart dapat dikalibrasi untuk menghasilkan ARL₀ mendekati 370 dan memiliki ARL₁ yang semakin kecil seiring meningkatnya besar pergeseran. Dibandingkan EMM-Chart, ERMM-Chart secara konsisten memberikan deteksi yang lebih cepat pada pergeseran variabilitas dan pergeseran simultan. Nilai λ=0,1 lebih sensitif terhadap pergeseran kecil, sedangkan λ=0,7 lebih responsif terhadap pergeseran besar. Pada data sintetis, pergeseran simultan terdeteksi paling cepat dengan run length sebesar satu. Penerapan pada data clinker tidak menghasilkan false alarm pada fase I dan mendeteksi masing-masing 93, 67, 45, dan 40 sinyal out-of-control untuk λ=0,1, 0,3, 0,5, dan 0,7. Dengan demikian, ERMM-Chart dapat digunakan sebagai alat deteksi awal yang robust dan sensitif terhadap perubahan pola proses multivariat.
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Modern industrial process control often involves multiple correlated quality characteristics, requiring simultaneous monitoring of changes in the process mean and variability. The Max-M chart can be used for this purpose with individual observations; however, its Shewhart-type characteristic makes it less sensitive to small shifts. Moreover, conventional parameter estimation is vulnerable to outliers. This study aims to develop the Exponentially Weighted Moving Average Robust Max-M Control Chart (ERMM-Chart) for simultaneously monitoring shifts in the mean and variability of a multivariate process. The ERMM-Chart is constructed by applying the EWMA mechanism to the Robust Max-M statistic, while the Phase I mean vector and covariance matrix are estimated using the Fast-MCD method. Chart performance is evaluated using the in-control and out-of-control Average Run Lengths, denoted by ARL₀ and ARL₁, respectively, under various numbers of quality characteristics, weighting constants, correlation levels, and shift scenarios involving the mean, variability, and both components simultaneously. The performance of the ERMM-Chart is also compared with that of the EMM-Chart and demonstrated using synthetic data and cement clinker quality data. The simulation results show that the ERMM-Chart can be calibrated to achieve an ARL₀ close to 370, while its ARL₁ decreases as the shift magnitude increases. Compared with the EMM-Chart, the ERMM-Chart consistently provides faster detection of variability and simultaneous shifts. A value of λ=0.1 is more sensitive to small shifts, whereas λ=0.7 responds more rapidly to large shifts. For the synthetic data, simultaneous shifts are detected most rapidly, with a run length of one. The clinker data application produces no false alarms in Phase I and detects 93, 67, 45, and 40 out-of-control signals for λ=0.1, 0.3, 0.5, and 0.7, respectively. Therefore, the ERMM-Chart can serve as a robust and sensitive early-detection tool for changes in multivariate process patterns.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	ARL, ERMM-Chart, EWMA, Fast-MCD, Max-Mchart, Robust ARL, ERMM-Chart, EWMA, Fast-MCD, Max-Mchart, Robust
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QA Mathematics > QA276 Mathematical statistics. Time-series analysis. Failure time data analysis. Survival analysis (Biometry) Q Science > QA Mathematics > QA279 Response surfaces (Statistics). Analysis of covariance. Q Science > QA Mathematics > QA76.9 Computer algorithms. Virtual Reality. Computer simulation. Q Science > QA Mathematics > QA278 Cluster Analysis. Multivariate analysis. Correspondence analysis (Statistics)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Samin Radjid
Date Deposited:	05 Aug 2026 02:16
Last Modified:	05 Aug 2026 02:20
URI:	http://repository.its.ac.id/id/eprint/143765

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