Pengembangan Diagram Pengendali Exponentially Weighted Moving Average Max-Mchart (EWMA Max-Mchart)

Rifki, Kevin Agung Fernanda (2024) Pengembangan Diagram Pengendali Exponentially Weighted Moving Average Max-Mchart (EWMA Max-Mchart). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Diagram pengendali simultan adalah alat yang dirancang untuk memonitor rata-rata dan variabilitas proses secara bersamaan dalam satu tampilan. Ada tiga jenis diagram pengendali simultan, yaitu menggunakan metode Exponentially Weighted Moving Average (EWMA), Cumulative Sum (CUSUM), dan Shewhart. Saat menghadapi data multivariat dan individu di industri, yang sudah ada adalah diagram pengendali simultan tipe Shewhart (Max-Mchart). Namun terdapat kekurangan pada penerapan Max-Mchart, terutama dalam mendeteksi pergeseran kecil. Oleh karena itu, diperlukan peningkatan sensitivitas dari Max-Mchart melalui proses tambahan. Beberapa penelitian menunjukkan bahwa penggunaan proses EWMA dapat meningkatkan sensitifitas dari berbagai statistik diagram pengendali, seperti EWMA-Max dan EWMA-CUSUM. Proses EWMA diterapkan ketika statistik sebelumnya sudah didapatkan dan meghasilkan performa yang bagus dan sensitif. Oleh karena itu, penelitian ini akan mengintegrasikan proses EWMA dengan Max-Mchart untuk menghasilkan pengembangan baru yang disebut Exponentially Weighted Moving Average Max Multivariate atau EWMA Max-M. Hasil analisis akan mencakup penentuan batas pengendali yang optimal menggunakan nilai L dan λ dalam proses EWMA dan performa yang dihasilkan dilihat dari pergerakan Average Run Length 0 (ARL0). Batas pengendali yang dihasilkan mengikuti dua parameter yaitu nilai parameter L dan λ. Dengan membandingkan performa diagram EWMA Max-M dan Max-M berdasarkan hasil ARL1, performa EWMA Max-M lebih unggul dari tiga parameter, yaitu p banyaknya karakterisik kualitas, ρ korelasi antar karakteristik dan λ pembobot baik dari pergeseran vektor mean, matriks kovarian, dan simultan keduanya. Pengaplikasian data sintesis dan data ril semen dilakukan dengan menggunakan EWMA Max-M dan Max-M menunjukkan hasil bahwa EWMA Max-M lebih unggul dan lebih sensitif dengan konfigurasi λ = 0,1.
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Simultaneous control charts are tools designed to monitor process averages and variability simultaneously in one view. There are three types of simultaneous control charts, namely using the Exponentially Weighted Moving Average (EWMA), Cumulative Sum (CUSUM), and Shewhart methods. When dealing with multivariate and individual data in industry, what already exists is the Shewhart (Max-Mchart) type simultaneous control chart. However, there are shortcomings in the application of Max-Mchart, especially in detecting small shifts. Therefore, it is necessary to increase the sensitivity of Max-Mchart through additional processes. Several studies show that the use of the EWMA process can increase the sensitivity of various control chart statistics, such as EWMA-Max and EWMA-CUSUM. The EWMA process is applied when previous statistics have been obtained and produce good and sensitive performance. Therefore, this research will integrate the EWMA process with Max-Mchart to produce a new development called Exponentially Weighted Moving Average Max Multivariate or EWMA Max-M. The results of the analysis will include determining optimal control limits using L and λ values in the EWMA process and the resulting performance seen from the movement of Average Run Length 0 (ARL0). The resulting control limits follow 3 parameters, namely the values of L, ρ and λ. By comparing the performance of EWMA Max-M and Max-M diagrams based on ARL1 results, the performance of EWMA Max-M is superior to 3 parameters p number of quality characteristics, ρ correlation between characteristics and λ good weighting of the mean vector shift, covariance matrix, and both simultaneous. The application of synthetic data and real cement data using EWMA Max-M and Max-M shows that EWMA Max-M is good and more sensitive with λ = 0,1.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Diagram pengendali simultan, EWMA-Max, Max-Mchart, Pengamatan individu, Individual observations, Simultaneous control chart
Subjects:	Q Science Q Science > QA Mathematics
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Kevin Agung Fernanda Rifki
Date Deposited:	14 Feb 2024 08:29
Last Modified:	14 Feb 2024 08:29
URI:	http://repository.its.ac.id/id/eprint/107023

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