Bagan Kendali Robust Multivariat untuk Pengamatan Individual

Authors

  • Erna Tri Herdiani

DOI:

https://doi.org/10.20956/jmsk.v15i2.5712

Abstract

AbstractThe most widely used of control chart in multivariate control processing is control chart T2 Hotelling. There are 2 kinds of control chart T2 Hotelling, namely T2 Hotelling for group observation and T2 Hotelling  for individual observation. In this paper, discuss the control chart T2 Hotelling for individual observation. This control chart is used for monitoring of mean vector and sample of covariance matrix.   Mean vector and sample of covariance matrix are very sensitive with respect to extreme point (outliers). Therefore, it is needed  an estimator of mean vector and has a stocky population covariance matrix to the outliers data. One method that can be used to detect data that contains outliers is  Minimum Covariance Determinant (MCD). From the calculation results, obtained that  control chart T2 Hotelling by using Fast-MCD algorithm is more sensitive to detect outliers data  than  T2 Hotelling classically.Keyword: T2 Hotelling, Minimum Covariance Determinant (MCD), robust, outlier AbstrakBagan kendali yang  paling banyak digunakan dalam pengendalian proses secara multivariat adalah bagan kendali T2 Hotelling. Ada 2 jenis dari bagan kendali  Hotelling yaitu bagan kendali  Hotelling untuk pengamatan kelompok dan individual. Pada tulisan ini membahas bagan kendali  Hotelling untuk pengamatan individual. Bagan kendali ini digunakan untuk memonitor vektor  rata-rata dan matriks kovariansi sampel. Vektor rata-rata dan matriks kovariansi sampel sangat sensitif terhadap titik ekstrim (outliers). Oleh karena itu dibutuhkan estimator vektor rata-rata dan matriks kovariansi populasi yang kekar terhadap data outliers. Salah satu metode yang dapat digunakan untuk mendeteksi data yang mengandung outliers adalah Minimum Covariance Determinant (MCD). Dari hasil perhitungan diperoleh bahwa bagan kendali T2 Hotelling dengan algoritma Fast-MCD lebih sensitif mendeteksi data outliers daripada T2 Hotelling klasik.Kata Kunci: T2 Hotelling, Minimum Covariance Determinant (MCD), robust, outlier.

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References

. Barnett V, Lewis T., 1994. Outliers in Statistical Data. Chichester: John Wiley & Sons, Ltd.

. Bothe, Davis,R.,1997. Measuring Process Capability. McGraw-Hill Companies, United States of America.

. Chenouri, S., Steiner, S. H., Variyath, A. M., 2009. A Multivariate Robust Control Chart for Individual Observations. Journal of Quality Technology, 41, (3).

. Erna, 2014. Bagan Kendali T2 Hotelling Dengan Sampel Ganda Dan Aplikasinya. Skripsi. Program Studi Matematika Fakultas Matematika dan Ilmu pengetahuan Alam. Makassar: Universitas Hasanuddin.

. Hotelling, H., 1947. In Techniques of Statistical Analysis, C. Eisenhart, H. Hastay, and W. A.Wallis, eds., pp. New York, NY: McGraw-Hill.

. Hubert, M dan Driessen, 2002. Fast and Robust Discriminant Analysis. Computational Statistics and Data Analysis.45.

. Johnson, Richard. Dean Wichern., 2007. Applied Multivariat Statistical Analysis, 5th ed. New Jersey: Prentice Hall.

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Published

2018-12-20

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