Diagram Kontrol Simultan Maximum Multivariate Control Chart dan Maximum Half-normal Multivariate Control Chart Berbasis Kernel (Max-K-Mchart) dan (Max-KH-Mchart)

Loka, I Melda Puspita (2024) Diagram Kontrol Simultan Maximum Multivariate Control Chart dan Maximum Half-normal Multivariate Control Chart Berbasis Kernel (Max-K-Mchart) dan (Max-KH-Mchart). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Diagram kontrol merupakan salah satu alat yang umum digunakan untuk memonitor kualitas. Terdapat tiga jenis diagram kontrol, yaitu tipe Shewhart, CUSUM, dan EWMA. Diagram kontrol tipe Shewhart dibentuk dengan asumsi data berdistribusi normal, namun dalam kasus riil khusunya pada kasus monitoring kualitas semen sering kali dijumpai data tidak memenuhi asumsi distribusi normal. Saat data tidak berdistribusi normal atau tidak diketahui distribusinya, maka perlu dilakukan monitoring kualitas menggunakan diagram kontrol non-parametrik. Metode non-parametrik berupa kernel beberapa penelitian sebelumnya menunjukkan hasil yang baik. Pada penelitian ini dilakukan monitoring kualitas semen berupa blaine, residu, dan free lime dengan mengggunakan diagram kontrol multivariat simultan berbasis kernel. Kernel digunakan untuk mendapatkan densitas yang bersesuaian dengan kondisi data. Diagram kontrol simultan digunakan karena lebih efektif dalam memonitor kualitas dibandingkan diagram kontrol konvesional. Diagram kontrol multivariat simultan yang digunakan adalah diagram Max-Mchart dan Max-Half-Mchart yang mampu mendeteksi pergeseran kecil dan besar pada rata-rata dan variabilitas proses. Saat data berdistribusi multivariat normal, maka perhitungan statistik diagram Max-Mchart dan Max-Half-Mchart menggunakan probabilitas chi-square, namun saat data tidak berdistribusi multivariat normal maka menggunakan probabilitas kernel. Monitoring kualitas semen berupa blaine, residu, dan free lime menggunakan diagram kontrol Max-Mchart dan Max-Half-Mchart berbasis kernel yang masing-masing disebut sebagai Max-K-Mchart dan Max-KH-Mchart. Max-KH-Mchart mampu mendeteksi pergeseran kecil dan besar pada mean dan variabilitas proses saat data berdistribusi Mgamma (2,2), sedangkan diagram Max-K-Mchart mampu mendeteksi pergeseran kecil pada mean proses saat data berdistribusi multivariat normal. Pada monitoring kualitas semen diagram Max-K-Mchart dan Max-KH-Mchart mampu menangkap out-of-control yang sama pada Fase I dan Fase II.
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Control charts are one of the commonly used tools for monitoring quality. There are three types of control charts, namely Shewhart, CUSUSM, and EWMA. Shewhart-type control charts are formed assuming the data follows a normal distribution. However, in the application in real cases, especially in the case of monitoring cement quality, it is often found that the data to be monitored for quality does not fullfil the assumption of normal distribution. When the data is not normally distributed or the distribution is unknown, it is necessary to monitor the quality using non-parametric control charts. Non-parametric methods in the form of kernels in several previous studies have shown good results. In this study, cement quality monitoring of blaine, residue, and free lime using kernel-based simultaneous multivariate control charts. Kernels are used to obtain densities that match the data conditions. Simultaneous control charts are used because they are more effective in monitoring quality than conventional control charts. The simultaneous multivariate control charts used are Max-Mchart and Max-Half-Mchart charts which are able to detect small and large shifts in the mean and variability of the process. When the data is multivariate normally distributed, the statistical calculation of Max-Mchart and Max-Half-Mchart diagrams uses chi-square probability, but when the data is not multivariate normally distributed, it uses kernel probability. Monitoring cement quality of blaine, residue, and free lime using kernel-based Max-Mchart and Max-Half-Mchart (Max-K-Mchart) and (Max-KH-Mchart) control charts. Max-KH-Mchart is able to detect small and large shifts in both mean and variability when the data is Mgamma (2,2) distributed, while Max-K-Mchart is able to detect small shifts in the process mean when the data is multivariate normal distributed. In monitoring cement quality, Max-K-Mchart and Max-KH-Mchart are able to detect the same out-of-control in Phase I and Phase II.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Kernel, Max-K-Mchart, Max-KH-Mchart, Non-parametrik, Non-parametric
Subjects:	H Social Sciences > HD Industries. Land use. Labor > HD31 Management--Evaluation Q Science Q Science > QA Mathematics > QA353.K47 Kernel functions (analysis)
Divisions:	Faculty of Mathematics, Computation, and Data Science > Statistics > 49101-(S2) Master Thesis
Depositing User:	I Melda Puspita Loka
Date Deposited:	12 Feb 2024 22:54
Last Modified:	12 Feb 2024 22:54
URI:	http://repository.its.ac.id/id/eprint/106947

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