Diagram Robust Max-Half-Mchart Berbasis Minimum Regularized Covariance Determinant

Fahri, Farisi (2024) Diagram Robust Max-Half-Mchart Berbasis Minimum Regularized Covariance Determinant. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Diagram kendali banyak digunakan pada dunia industri untuk memantau rata-rata dan variabilitas proses produksi. Max-Half-Mchart merupakan diagram kendali simultan multivariat yang dapat diterapkan pada observasi individual maupun subgrup, namun kurang mampu dalam menangani keberadaan outlier dalam jumlah besar. Penelitian ini bertujuan untuk mengembangkan diagram kendali yang memiliki ketahahanan lebih baik dalam mengatasi outliers pada data. Minimum covariance determinant (MCD) adalah metode penduga matriks rata-rata dan kovarians yang sangat tahan terhadap outliers, tetapi kurang bagus dalam menangani data dengan jumlah pengamatan yang relatif sedikit dibandingkan jumlah variabel (‘fat data’). Minimum Regularized Covariance Determinant (MRCD) merupakan hasil pengembangan metode MCD yang mampu menjaga ketahanan terhadap outliers ketika diterapkan pada kasus ‘fat data’. Dalam penelitian ini Max-Half-Mchart dikembangkan menggunakan estimator MRCD. Kinerja deteksi outlier Robust Max-Half-Mchart berbasis MRCD dibandingkan dengan Max-Half-Mchart. Robust Max-Half-Mchart berbasis MRCD terbukti mampu memberikan hasil akurasi dan AUC yang lebih baik pada jumlah persentase outlier 10%, 20%, 30%, 40%. Hasil penerapan pada data karakteristik kualitas data menunjukkan bahwa Robust Max-Half-Mchart berbasis MRCD lebih baik dalam mendeteksi outlier dibandingkan dengan metode Max-Half-Mchart.
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Control charts are widely used in industry to monitor the mean and variability of the production process. Max-Half-Mchart is a multivariate simultaneous control chart that can be applied to individual observations and subgroups, but is less able to handle the presence of a large number of outliers. This research aims to develop a control chart that has better robustness in dealing with outliers in the data. Minimum covariance determinant (MCD) is a method of estimating the mean and covariance matrix that is very resistant to outliers, but is not good at handling data with relatively few observations compared to the number of variables ('fat data'). Minimum Regularized Covariance Determinant (MRCD) is the result of the development of the MCD method which is able to maintain resistance to outliers when applied to 'fat data' cases. In this research, Max-Half-Mchart is developed using MRCD estimator. The outlier detection performance of Robust Max-Half-Mchart based on MRCD is compared with Max-Half-Mchart. Robust Max-Half-Mchart based on MRCD is proven to be able to provide better accuracy and AUC results at the number of outlier percentages of 10%, 20%, 30%, 40%. The application results on data quality characteristics data show that MRCD-based Robust Max-Half-Mchart is better at detecting outliers compared to the Max-Half-Mchart method

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Diagram kontrol robust simultan multivariat, fat data, Max-Half-Mchart, Minimum Regularized Covariance Determinant (MRCD); Robust multivariate simultaneous control diagram, fat data, Max-Half-Mchart, Minimum Regularized Covariance Determinant
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:	Farisi Fahri
Date Deposited:	19 Feb 2024 07:16
Last Modified:	19 Feb 2024 07:16
URI:	http://repository.its.ac.id/id/eprint/107497

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