Pengembangan Diagram Kendali Adaptive Exponentially Weighted Moving Average Max-M (AEWMA Max-MChart)

Zulfa, Latifatuz (2025) Pengembangan Diagram Kendali Adaptive Exponentially Weighted Moving Average Max-M (AEWMA Max-MChart). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

SPC (Statistical Process Control) adalah metode statistik yang sering digunakan dalam monitoring proses terbagi menjadi diagram kontrol univariat dan multivariat berdasarkan jumlah karakteristik kualitas produk yang dimonitor. Diagram kontrol univariat memonitor satu karakteristik kualitas, sedangkan diagram kontrol multivariat memonitor dua atau lebih karakteristik kualitas. Diagram kontrol Shewhart efektif dalam mendeteksi pergeseran besar dalam proses, sementara diagram kontrol EWMA kurang baik untuk pergeseran besar. Diagram kontrol AEWMA bekerja dengan menghitung nilai rata-rata bergerak yang diberi bobot eksponensial, di mana bobot ini disesuaikan secara adaptif berdasarkan besarnya error. Jika error kecil, bobot pada pengamatan sebelumnya akan lebih besar, sehingga AEWMA dapat dengan cepat mendeteksi pergeseran kecil begitu juga sebaliknya yang memungkinkan AEWMA untuk mendeteksi pergeseran besar dengan efisien. Pengembangan diagram kontrol AEWMA Max-chart menunjukkan performa yang lebih baik dibandingkan diagram kontrol EWMA Max-chart dan Max-chart pada pergeseran kecil dan besar. Dalam kasus multivariat, diagram kontrol EWMA Max-Mchart memberikan performa optimal dalam mendeteksi sinyal out-of-control dengan mempertimbangkan pembobot λ yang digunakan. Untuk lebih meningkatkan performa dari diagram EWMA Max-M, penggunaan Adaptive Exponentially Weighted Moving Average (AEWMA) dapat menjadi solusi yang efektif. AEWMA menyesuaikan bobot pada pengamatan sebelumnya berdasarkan besarnya error, sehingga dapat mendeteksi pergeseran kecil dan besar dengan lebih efisien. Berdasarkan hasil analisis, AEWMA Max-Mchart memiliki performa yang lebih baik dalam mendeteksi pergeseran proses, baik kecil maupun besar, dibandingkan dengan EWMA Max-Mchart. Kinerja Diagram Kontrol AEWMA Max-Mchart memberikan hasil yang cukup optimal. Hal ini ditandai dengan nilai ARL₁ yang dihasilkan semakin cepat mendekati nilai 1 berdasarkan pergeseran mean,varian, dan mean varian. Selain itu pada penerapan data langsung hasil monitoring pada data clinker di PT ABC dengan menggunakan diagram kontrol AEWMA Max-Mchart mampu memberikan hasil yang cukup optimal mendeteksi dengan tepat signal out-of-control dibandingkan control chart lain
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Statistical Process Control (SPC) is a widely used statistical method for process monitoring, categorized into univariate and multivariate control charts based on the number of quality characteristics involved. Univariate charts monitor a single variable, while multivariate charts handle multiple variables. Shewhart charts are effective for detecting large shifts, whereas EWMA charts are less responsive to such changes. The AEWMA (Adaptive Exponentially Weighted Moving Average) control chart works by calculating a moving average with exponentially weighted observations, where the weights are adjusted adaptively based on the magnitude of the error. When the error is small, more weight is given to past observations, enabling AEWMA to quickly detect small shifts. Conversely, when the error is large, less weight is assigned to past observations, allowing AEWMA to efficiently detect large shifts. The development of the AEWMA Max-chart has demonstrated better performance compared to the EWMA Max-chart and the traditional Max-chart in detecting both small and large shifts. In multivariate cases, the EWMA Max-M chart has shown optimal performance in detecting out-of-control signals, considering the weighting parameter λ used in the computation. To further, the use of the Adaptive Exponentially Weighted Moving Average (AEWMA) approach can be an effective solution. AEWMA adjusts the weights of past observations based on the magnitude of error, thereby improving its ability to detect both small and large shifts efficiently. Based on the analysis results, the AEWMA Max-M chart demonstrates better performance in detecting process shifts—both small and large—compared to the EWMA Max-M chart. The control chart performance of the AEWMA Max-M chart shows optimal results, as indicated by ARL₁ values that approach 1 more rapidly in response to mean shifts, variance shifts, and combined mean-variance shifts. Moreover, in the real data application, the monitoring of clinker data from PT ABC using the AEWMA Max-M control chart yields optimal results by accurately detecting out-of-control signals compared to other control charts.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Statistical Process Control, Diagram Kontrol, Control Chart, EWMA Max-Mchart, AEWMA Max-Mchart
Subjects:	H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics H Social Sciences > HA Statistics > HA31.38 Data envelopment analysis. 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:	Latifatuz Zulfa
Date Deposited:	04 Aug 2025 01:49
Last Modified:	04 Aug 2025 01:49
URI:	http://repository.its.ac.id/id/eprint/126511

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