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Penggunaan Estimator Robust Reweighted Minimum Covariance Determinant pada Diagram Kontrol T2 Hotelling untuk Monitoring Penyebaran Covid-19 di Korea Selatan

Authors

  • Andi Nur Fadhilah Utami Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Islam Bandung
  • Suwanda Universitas Islam Bandung

DOI:

https://doi.org/10.29313/jrs.v1i1.304

Keywords:

Estimator Robust, Diagram Kontrol T2 Hotelling, RMCD.

Abstract

Abstract. Control charts are one of the widest used techniques in statistical process control. Hotelling’s control chart are commonly used in process quality control to control the vector mean shift and the covariance matrix in individual observations. In phase I, it is possible that Hotelling’s  can’t detect observation that are out of control due to masking effect if there are outliers. In this paper we propose a robust alternative to Hotelling’s control chart with estimator robust Reweighted Minimum Covariance Determinant (RMCD) for individual observation. Robust Hotelling’s  multivariate control chart will be applied to monitoring growth index of new cases and growth index of daily death due to Coronavirus Disease-19 (Covid-19) in South Korean. This control chart is applied to the data using  and it obtained the result UCL = 9,47998 and LCL = 0. There are 5 observations that are out of control which is observation in 11, 39, 90, 158, and 167. Using estimators robust Reweighted Minimum Covariance Determinant is more effective in detecting outliers which is there are found 2 new observation that out of control. From these result it can be concluded that using control chart with RMCD estimator for Covid-19 in South Korean not controlled because there are data out of control.

Abstrak. Diagram kontrol merupakan salah satu metode yang paling banyak di gunakan dalam pengendalian kualitas proses. Diagram kontrol T2 Hotelling merupakan salah satu alat yang biasa digunakan dalam pengendalian kualitas proses untuk mengongtrol pergeseran vektor rata-rata dan matriks kovarians dalam hal pengamatan individu. Pada saat pengontrolan proses pada fase 1, diagram kontrol T2 Hotelling dimungkinkan tidak dapat mendeteksi pengamatan yang out of control akibat efek masking apabila terdapat outlier. Pada penelitian ini akan dibahas alternatif diagram kontrol T2 Hotelling dengan menggunakan estimator robust Reweighted Minimum Covariance Determinant (RMCD) untuk pengamatan individual. Diagram kontrol T2 Hotelling RMCD akan diaplikasikan pada pengontrolan Index Pertumbuhan Kasus Baru dan Index Pertumbuhan Kematian Harian karena Coronavirus Disease-19 (Covid-19) di Korea Selatan. Diagram kontrol ini diaplikasikan pada data menggunakan dan sehingga didapat nilai BKA = 9,47998 dan BKB = 0. Terdapat out of control sebanyak 5 pengamatan yaitu pengamatan ke 11, 39, 90, 158, 167. Menggunakan estimator robust Reweighted Minimum Covariance Determinant lebih efektif mendeteksi data yang mengandung outlier dimana terdapat 2 pengamatan baru yang terdeteksi sebagai data out of control. Dari hasil tersebut dapat disimpulkan bahwa dengan menggunakan diagram kontrol T2 RMCD kasus Covid-19 di Korea Selatan belum terkendali karena masih terdapat data out of control.

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Published

2021-10-26