Desain optimal diagram kendali variable sample size (VSS) max berdasarkan median run length (MRL)

Qori’atunnadyah, Marita (2022) Desain optimal diagram kendali variable sample size (VSS) max berdasarkan median run length (MRL). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Diagram kendali Max- XS atau biasa disebut Max Chart dikhususkan untuk memonitor rata-rata dan variabilitas proses. Diagram kendali ini dinilai lebih efisien karena dapat memonitor rata-rata dan variabilitas proses dalam satu diagram. Penelitian-penelitian sebelumnya telah melakukan penelitian mengenai kinerja diagram kendali menggunakan Average Run Length (ARL). Akan tetapi, bentuk distribusi run-length bisa berubah menyesuaikan dengan besarnya pergeseran rata-rata dan variabilitas, sehingga ARL dapat menjadi ukuran kinerja yang kurang tepat. Penggunaan persentil dari distribusi run-length dianggap lebih reflektif dan handal dibandingkan dengan rata-rata dari distribusi run-length untuk evaluasi kinerja diagram kendali untuk distribusi run-length yang miring (skewed). Diagram kendali Max biasanya menerapkan ukuran sampel yang tetap. Pada penelitian ini, ditambahkan fitur adaptif yaitu Variable Sample Size (VSS) untuk diagram kendali Max. Selain itu, pada penelitian ini dikembangkan desain optimal dari diagram kendali VSS Max, dengan meminimalkan Median Run Length di luar kendali (MRL1). Dua skema VSS dipertimbangkan dalam penelitian ini, yaitu ketika ukuran sampel kecil ( Sn ) dan ketika ukuran sampel besar ( Ln ) yang telah ditentukan sebelumnya untuk subgrup pertama ( 1 n ). Berdasarkan evaluasi kinerja dan penerapan pada data sintetis, diagram kendali VSS Max optimal 1 n = Ln memiliki performa yang lebih baik dibandingkan diagram kendali VSS Max optimal 1 n = S n hampir pada semua pergeseran rata-rata dan/atau variabilitas proses karena memiliki nilai MRL1 kecil yang berarti cepat dalam mendeteksi adanya outof- control. Berdasarkan hasil perbandingan kinerja diagram kendali, diagram kendali VSS Max optimal dapat meningkatkan kinerja dari diagram kendali Max. Penerapan diagram kendali VSS Max optimal pada data kandungan Nitrogen (N) dalam pupuk NPK Phonska 15-10-12 menujukkan proses belum terkendali secara statistik.
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Max Chart is used to monitoring the mean and variability process. This control chart is considered more efficient because it can monitor the mean and variability process in one chart. Previous studies have conducted research on the performance of control charts using Average Run Length (ARL). However, the shape of the run-length distribution can change according to the magnitude of the mean and variability shift, so ARL can be a confusing performance measure. The
use of percentiles from the run-length distribution is considered to be more reflective and reliable than the average run-length for evaluating the performance of the control chart for the skewed run-length distribution. Max chart usually apply a fixed sample size. In this study, an adaptive feature was added, namely Variable Sample Size (VSS). The optimal design of the VSS Max chart was developed, by minimizing the out-of-control Median Run Length (MRL1). Two VSS schemes
were considered, namely when the small sample size ( Sn ) and when the large sample size ( L n ) which was predetermined for the first subgroup ( 1n ). Based on the performance evaluation, the optimal VSS Max chart 1n = Ln has better performance than the optimal VSS Max chart 1n = Sn almost all mean and/or variability process shifts because it has a small MRL1 value which means it is fast in detecting out-of-control. Based on the comparison results of the control chart performance, the optimal VSS Max chart can improve the performance of the Max chart. The application of the optimal VSS Max chart on the Nitrogen (N) in Phonska 15-10-12 NPK fertilizer shows that the process is not statistically controlled.

Item Type:	Thesis (Masters)
Additional Information:	RTSt 519.86 Qor d-1 2022
Uncontrolled Keywords:	Max Chart, Median Run Length, Optimal, Variable Sample Size., Variable Sample Size.
Subjects:	H Social Sciences > HD Industries. Land use. Labor > HD9980.5 Service industries--Quality control.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Mr. Marsudiyana -
Date Deposited:	29 Apr 2026 07:35
Last Modified:	29 Apr 2026 07:35
URI:	http://repository.its.ac.id/id/eprint/132932

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