Diagram Kontrol Simultan Robust Maximum Half-Normal Multivariate Control Chart (Max-Half-Mchart) untuk Memonitor Data Ordinary Portland Cement (OPC)

R, Awang Putra Sembada (2024) Diagram Kontrol Simultan Robust Maximum Half-Normal Multivariate Control Chart (Max-Half-Mchart) untuk Memonitor Data Ordinary Portland Cement (OPC). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Setiap perusahaan melakukan evaluasi secara rutin dalam upaya untuk memberikan produk atau jasa yang berkualitas baik. Salah satu alat yang berguna dalam evaluasi adalah diagram kontrol. Diagram kontrol simultan multivariat digunakan untuk memonitor rata-rata dan variabilitas secara bersamaan. Beberapa contoh diagram kontrol simultan multivariat adalah Max-Mchart, Max-Half-Mchart, Max-MEWMA, dan Max-MCUSUM. Diagram kontrol Max-Half-Mchart memiliki kelebihan yaitu dapat mendeteksi pergeseran kecil dan besar pada rata-rata dan matriks kovarians. Pada diagram kontrol Max-Half-Mchart, outlier dapat menyebabkan fungsi distribusi kumulatif chi-square bernilai mendekati satu sehingga akan menghasilkan invers distribusi kumulatif normal standar yang mendekati tak hingga. Selain itu, efek masking dan swamping terjadi apabila data mengandung outlier. Oleh karena itu, penaksir robust diperlukan untuk mengestimasi rata-rata dan matriks kovarians. Fast-MCD dan Det-MCD merupakan penaksir robust yang cepat dalam mengestimasi rata-rata dan matriks kovarians karena menggunakan C-Step. Hasil deteksi outlier menunjukkan diagram kontrol robust Max-Half-Mchart berbasis Det-MCD memiliki kinerja terbaik pada jumlah outlier yang sedikit, sementara robust Max-Half-Mchart berbasis Fast-MCD dan robust Max-Half-Mchart berbasis Det-MCD memiliki kinerja terbaik pada jumlah outlier yang banyak. Berdasarkan kinerja pergeseran proses, robust Max-Half-Mchart berbasis Fast-MCD dan robust Max-Half-Mchart berbasis Det-MCD dapat mendeteksi pergeseran proses. Hasil monitoring data kualitas semen OPC dan penerapan pada data sintesis menunjukkan bahwa robust Max-Half-Mchart berbasis Det-MCD paling sensitif terhadap data outlier.
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Every company carries out regular evaluations to provide good quality products or services. One tool that is useful in evaluation is a control chart. Multivariate simultaneous control charts are used to monitor mean and variability simultaneously. Some examples of multivariate simultaneous control charts are Max-Mchart, Max-Half-Mchart, Max-MEWMA, and Max-MCUSUM. The Max-Half-Mchart control chart has the advantage of being able to detect small and large shifts in the mean and covariance matrix. In a Max-Half-Mchart control chart, outliers can cause a chi-square cumulative distribution function to approach one, resulting in an inverse of the standard normal cumulative distribution that approaches infinity. In addition, masking and swamping effects occur when the data contains outliers. Therefore, a robust estimator is needed to estimate the mean and covariance matrix. Fast-MCD and Det-MCD are robust estimators that are fast in estimating the mean and covariance matrix because they use C-Step. The outlier detection results show that the robust Max-Half-Mchart control chart based on Det-MCD has the best performance on a small number of outliers, while the robust Max-Half-Mchart based on Fast-MCD and the robust Max-Half-Mchart based on Det-MCD have the best performance on a large number of outliers. Based on process shift performance, robust Max-Half-Mchart based on Fast-MCD and robust Max-Half-Mchart based on Det-MCD can detect process shifts. The results of monitoring OPC cement quality data and application to synthetic data show that robust Max-Half-Mchart based on Det-MCD is the most sensitive to outlier data.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Det-MCD, Simultaneous Control Chart, Fast-MCD, Multivariate, OPC Cement, Diagram Kontrol Simultan, Multivariat, Semen OPC
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.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Awang Putra Sembada R
Date Deposited:	18 Feb 2024 12:37
Last Modified:	18 Feb 2024 12:37
URI:	http://repository.its.ac.id/id/eprint/107334

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