Deteksi Proses Diluar Kendali Menggunakan Peta Kendali Multivariate Cumulative Sum (MCUSUM) Dengan Copula Clayton Dan Frank

Hariyono, Muhammad (2019) Deteksi Proses Diluar Kendali Menggunakan Peta Kendali Multivariate Cumulative Sum (MCUSUM) Dengan Copula Clayton Dan Frank. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pada pergeseran rata-rata proses yang relatif kecil, peta kendali multivariat merupakan peta yang digunakan dalam mendeteksi pergeseran rata-rata proses yang kecil. Salah satu peta kendali multivariat yang lebih baik terhadap pergeseran rata-rata proses yang relatif kecil adalah Peta Kendali Multivariate Cumulative Sum (MCUSUM). Peta kendali ini menghimpun secara langsung semua informasi di dalam barisan nilai-nilai sampel dengan menggambarkan jumlah kumulatif deviasi nilai sampel dari nilai target. Untuk menemukan model bersama dari variabel acak bivariat atau multivariat diperlukan metode Copula dengan mentransformasi data ke domain [0,1]. Copula pada Tugas Akhir ini adalah Copula Clayton dan Copula Frank. Berdasarkan hasil analisis, data model Copula Clayton dan data model Copula Frank berada dalam keadaan tidak terkendali (out of control), dan berdasarkan nilai ARL, diperoleh bahwa data model Copula Clayton lebih sensitif dalam mendeteksi proses di luar kendali.
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In a relatively small shift in the process average, a multivariate control chart is used to detect small shifts in process averages. One of the multivariate control charts that performs better for relatively small shifts in process averages is the Multivariate Cumulative Sum (MCUSUM) control chart. This control chart directly aggregates all information within a sequence of sample values by depicting the cumulative deviation of sample values from the target value. To find a joint model of bivariate or multivariate random variables, the Copula method is needed, which transforms the data into the domain [0,1]. The copulas used in this final project are the Clayton Copula and the Frank Copula. Based on the analysis results, the data under the Clayton Copula model and the data under the Frank Copula model are both found to be in an out-of-control condition, and based on the ARL values, the Clayton Copula model data is found to be more sensitive in detecting out-of-control processes.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Peta Kendali, MCUSUM, Copula, Pengendalian kualitas, ARL
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA278 Cluster Analysis. Multivariate analysis. Correspondence analysis (Statistics)
Divisions:	Faculty of Mathematics, Computation, and Data Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Hariyono Muhammad
Date Deposited:	05 Aug 2026 08:33
Last Modified:	05 Aug 2026 08:33
URI:	http://repository.its.ac.id/id/eprint/68737

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