Pengembangan Diagram Kontrol Multivariat Simultan untuk Pengamatan Individual

Kruba, Rumaisa (2022) Pengembangan Diagram Kontrol Multivariat Simultan untuk Pengamatan Individual. Doctoral thesis, Instititut Teknologi Sepuluh Nopember.

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Abstract

Diagram kontrol digunakan dalam lingkup industri untuk memonitor rata-rata dan variabilitas proses baik secara simultan maupun secara terpisah. Diagram simultan merupakan diagram yang dikembangkan untuk memonitor rata-rata dan variabilitas proses secara bersamaan pada satu diagram tunggal. Terdapat tiga tipe diagram kontrol simultan, yaitu diagram tipe Exponentially Weighted Moving Average (EWMA), Cumulative Sum (CUSUM) dan Shewhart. Saat ini, pengembangan diagram simultan tipe Shewhart (Max-Mchart) hanya terbatas pada pengamatan subgrup. Pada pengamatan individu, statistik Generalized Variance (GV) tidak dapat dihitung karena hanya memiliki satu pengamatan. Akibatnya Max-Mchart tidak dapat digunakan pada pengamatan individual. Sehingga pada penelitian ini bertujuan mengembangkan diagram Max-Mchart dengan modifikasi matriks kovarians. Namun penerapan transformasi normal standar yang digunakan pada diagram Max-Mchart memiliki kelemahan, yaitu tidak dapat mendeteksi pergeseran kecil. Sehingga perlu diterapkan pendekatan transformasi yang berbeda dari Max-Mchart, yaitu pendekatan half-normal. Dengan demikian, penelitian ini menghasilkan dua pengembangan diagram kontrol simultan. Pertama, diagram kontrol simultan modifikasi statistik varibilitas proses dengan pendekatan transformasi normal standar (Max-Mchart). Kedua, diagram simultan modifikasi statistik varibilitas proses dengan pendetan transformasi half-normal (Max-Half-Mchart). Hasil studi simulasi ARL menunjukkan bahwa diagram Max-Half-Mchart memiliki performa yang lebih baik dibandingkan diagram Max-Mchart dalam mendeteksi pergeseran variabilitas proses. Sedangkan pergeseran rata-rata proses diagram Max-Half-Mchart memiliki performa yang lebih baik ketika korelasi lebih besar dari ρ=0.3. Penerapan diagram Max-Half-Mchart pada data benchmark menghasilkan false alarm yang lebih kecil dan hasil yang konsisten dengan diagram T2 Hotelling dan diagram kontrol dispersi. Diagram Max-Half-Mchart juga menunjukkan hasil yang lebih baik dibandingkan diagram Max-Mchart untuk data produksi clinker pada PT Solusi Bangun Andalas (SBA) di Aceh yang dicatat setiap dua jam. Diagram Max-Half-Mchart mencatat jumlah out-of-control yang sama dengan hasil yang dimonitor oleh pabrik PT SBA dengan mendeteksi pergeseran kecil pada variabilitas proses dengan lebih baik. ================================================================================================ Control charts are used in industrial evironments to monitor the process mean and the process variability for the simultaneous monitoring or separate monitoring. Simultaneous chart is a chart developed to monitor the process mean and the process variability simultaneously in a single diagram. There are three types of simultaneous control charts, namely Exponentially Weighted Moving Average (EWMA), Cumulative Sum (CUSUM) and Shewhart charts. Currently, the development the simultaneous chart of Shewhart-type (Max-Mchart) is only limited of subgroup observations. For the individual observation the GV cannot be used since it only has one observation, hence the Max-Mchart cannot be used for individual observation. Hence, this research aims to develop a Max-Mchart diagram with a modification of the covariance matrix. However, the application of the standard transformation used in the Max-Mchart has the disadvantage that cannot detect small shifts.So, it is necessary to apply a different transformation approach from Max-Mchart, called the half-normal approach. Furthermore, this study resulted two simultaneous control charts. First, the simultaneous control chart with modification of the statistical variability that use the standard normal transformation approach (Max-Mchart). Second, the simultaneous control chart with of the statistical variability variability use Half-Normal (Max-Half-Mchart) instead of normal standard. The results of the ARL simulation study show that the Max-Half-Mchart outperform than the Max-Mchart in detecting shifts in variability process. Meanwhile in the mean shift, the Max-Half-Mchar has a better performance when the correlation is greater than ρ=0.3. The application of the Max-Half-Mchart to the benchmark data resulted in smaller false alarms and consistent results with Hotelling's T2 chart and dispersion control chart.The Max-Half-Mchart also shows better results than the Max-Mchart for clinker production data at PT Solusi Bangun Andalas (SBA) in Aceh which is recorded every two hours. The Max-Half-Mchart chart records the same amount of out-of-control as the results monitored by the PT SBA factory by better detecting small shifts in process variability.

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: control chart, individual observation, simultaneously, shewhart’s chart, max-mchart, max-half-mchart. diagram kontrol simultan, pengamatan individu, diagram tipe shewhart.
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD9980.5 Service industries--Quality control.
Divisions: Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User: Rumaisa Kruba
Date Deposited: 18 Feb 2022 01:16
Last Modified: 18 Feb 2022 01:16
URI: https://repository.its.ac.id/id/eprint/94229

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