Pengembangan Diagram Kontrol Maximum Multivariate Cumulative Sum Untuk Data Multivariat Berautokorelasi

Khusna, Hidayatul (2020) Pengembangan Diagram Kontrol Maximum Multivariate Cumulative Sum Untuk Data Multivariat Berautokorelasi. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Diagram kontrol Maximum Multivariate Cumulative Sum (Max-MCUSUM) merupakan salah satu diagram simultan yang dikembangkan untuk memonitor rata-rata dan variabilitas pada pengamatan multivariat yang independen. Namun, diagram Max-MCUSUM yang telah dikembangkan oleh peneliti sebelumnya memiliki in-control Average Run Length (ARL0) empiris yang jauh lebih rendah dari target ARL0 teoritis. Untuk mengatasi kelemahan tersebut, pada penelitian ini dikembangkan diagram Max-MCUSUM dengan cara menetapkan reference value pada proses monitoring Phase I serta dengan menggunakan metode bootstrap untuk perhitungan batas kontrol. Studi simulasi menunjukkan hasil bahwa diagram Max-MCUSUM dengan pendekatan bootstrap memiliki performa yang lebih baik daripada diagram Max-MCUSUM dengan pendekatan Markov chain. Diagram Max-MCUSUM dengan pendekatan bootstrap juga memiliki performa yang lebih baik daripada diagram improved T2 Hotelling dan diagram Generalized Variance (GV) apabila digunakan untuk memonitor data komposisi grit. Dalam aplikasi banyak ditemukan pengamatan yang berautokorelasi, sementara diagram yang sudah dikembangkan hanya dapat digunakan pada pengamatan yang bersifat random. Oleh karena itu, pada penelitian ini juga dikembangkan diagram Max-MCUSUM berbasis residual model Multioutput Least Square Support Vector Regression (MLS-SVR) dan diagram Max-MCUSUM berbasis pengamatan yang disebut dengan modified Max-MCUSUM untuk memonitor pengamatan yang berautokorelasi. Hasil studi simulasi menunjukkan bahwa semakin kecil reference value maka semakin sensitif diagram Max-MCUSUM berbasis residual model MLS-SVR dalam mendeteksi pergeseran vektor rata-rata. Sebaliknya, diagram tersebut semakin sensitif dalam mendeteksi pergeseran matriks kovarians apabila reference value semakin besar. Dibandingkan dengan diagram MCUSUM V berbasis residual model MLS-SVR, diagram Max-MCUSUM berbasis residual model MLS-SVR menghasilkan false alarm yang lebih kecil pada saat digunakan untuk memonitor data kualitas air Perusahaan Daerah Air Minum (PDAM) Kota Surabaya yang diamati setiap jam. Adapun statistik diagram modified Max-MCUSUM dikembangkan dengan cara melibatkan matriks cross-covariance lag ke nol dari historis data yang in-control. Sementara batas kontrol diagram modified Max-MCUSUM dihitung menggunakan kombinasi antara metode bootstrap dengan simulasi Monte Carlo sehingga memenuhi target ARL0. Hasil studi simulasi menunjukkan bahwa diagram modified Max-MCUSUM semakin sensitif apabila karakteristik kualitas yang diamati semakin banyak. Diagram modified Max-MCUSUM menunjukkan performa yang lebih baik daripada diagram MCUSUM V berbasis residual apabila digunakan untuk memonitor data kualitas komponen lampu fluorescent.
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The Maximum Multivariate Cumulative Sum (Max-MCUSUM) control chart is one of the single control charts developed for joint monitoring the mean and variability of independent observation. However, the Max-MCUSUM chart previously developed by researcher has empirical in-control Average Run Length (ARL0) which is smaller than the theoretical ARL0 target. To overcome those limitation, this research aims to develop the Max-MCUSUM chart by predetermining its reference value in Phase I monitoring process and by utilizing the bootstrap method to calculate its control limit. The simulation study indicates that the bootstrap-based Max-MCUSUM chart outperforms the Markov chain-based Max-MCUSUM chart. The bootstrap-based Max-MCUSUM chart also has better performance than both improved T2 Hotelling and Generalized Variance (GV) charts when applied to monitor grit composition data. In application, it is frequently found many autocorrelated observations, while the control charts which have been developed only can be utilized for random observations. Therefore, this research develops Max-MCUSUM control chart based on the residuals of Multioutput Least Square Support Vector Regression (MLS-SVR) model and an observation-based Max-MCUSUM chart referred as modified Max-MCUSUM chart for monitoring autocorrelated processes. The results of simulation studies show that the smaller the reference value, the more sensitive the MLS-SVR-based Max-MCUSUM chart in detecting mean vector shift. On the contrary, that control chart is more sensitive in detecting covariance matrix shift if the reference value is larger. Compared to the MLS-SVR-based MCUSUM V control chart, the MLS-SVR-based Max-MCUSUM chart produces smaller false alarm when utilized to monitor the hourly water quality data produced by Perusahaan Daerah Air Minum (PDAM) in Surabaya. The statistic of modified Max-MCUSUM chart is developed by involving the cross-covariance matrix at lag zero from historical in-control data. The control limit of modified Max-MCUSUM chart is computed using the combination of bootstrap method and Monte Carlo simulation such that satisfying the target of ARL0. The simulation studies prove that the modified Max-MCUSUM chart is more sensitive if the number of quality characteristics are larger. The modified Max-MCUSUM chart also provides the better performance than residual-based MCUSUM V chart when utilized to monitor the data of the quality of fluorescent lamp component.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	ARL, bootstrap, diagram kontrol simultan, Max-MCUSUM berbasis residual model MLS-SVR, modified Max-MCUSUM
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics > QA276 Mathematical statistics. Time-series analysis. Failure time data analysis. Survival analysis (Biometry) T Technology > TS Manufactures > TS156 Quality Control. QFD. Taguchi methods (Quality control)
Divisions:	Faculty of Mathematics, Computation, and Data Science > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Mrs. Hidayatul Khusna
Date Deposited:	23 Jul 2026 03:24
Last Modified:	23 Jul 2026 03:24
URI:	http://repository.its.ac.id/id/eprint/72143

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