Sellyra, Eirene Christina (2025) Diagram Kontrol Adaptive Exponentially Weighted Moving Average Dengan Measurement Error Menggunakan Auxiliary Information Max (AEWMA ME AI Max). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Diagram kontrol yang pertama kali dikenalkan adalah diagram kontrol Shewhart yang baik mendeteksi pergeseran besar. Diagram kontrol Shewhart dilakukan secara individual monitoring yaitu pengamatan secara terpisah untuk rata-rata atau varians proses. Selanjutnya, diagram kontrol dikembangkan untuk mendeteksi pergeseran kecil dengan berbasis memori atau memory based control chart seperti Exponentially Weighted Moving Average (EWMA) dan Cummulative Sum. Untuk dapat mendeteksi pergeseran proses baik dalam rata-rata dan varians secara simultan atau jointly monitoring, telah dikenalkan diagram kontrol Max. Diagram kontrol EWMA memiliki asumsi bahwa karakteristik kualitas yang dikontrol harus tidak memiliki kesalahan pengukuran atau measurement error. Penelitian sebelumnya telah membuktikan bahwa adanya kesalahan pengukuran mengakibatkan ukuran kualitas proses yang sebenarnya tidak dapat digambarkan dengan akurat dan dapat mengurangi sensitifitas diagram kontrol EWMA oleh karena itu dapat ditangani terlebih dahulu sebelum melakukan pengendalian dengan diagram kontrol EWMA. Pendekatan penanganan kesalahan pengukuran ada tiga yaitu covariate method, multiple measurement, dan keadaan varians tidak konstan (linearly increasing variance). Selain itu, adanya varians proses yang turut tergambar oleh variabel lain yang berhubungan dengan karakteristik kualitas teramati maka dikenalkan diagram kontrol dengan memasukkan unsur variabel auxiliary didalamnya. Diagram kontrol EWMA baik untuk pergeseran kecil tetapi tidak lebih baik dari diagram kontrol Shewhart dalam mendeteksi pergeseran besar sehingga tidak efektif dalam pengambilan keputusan terkait kualitas. Oleh karena itu, dikenalkan fungsi skor adaptive yang dapat membuat diagram kontrol EWMA mampu menyesuaikan kondisi dimana terjadi pergeseran kecil atau pergeseran besar. Oleh karena itu, penelitian ini ingin mengembangkan diagram kontrol dengan menggabungkan unsur memory based, jointly monitoring, penanganan measurement error, penggunaan variabel auxiliary, dan fungsi skor adaptive sehingga menjadi diagram kontrol Adaptive Exponentially Weighted Moving Average dengan Measurement Error menggunakan Auxiliary Information Max (AEWMA ME AI Max). Untuk mengamati kebaikkan diagram kontrol dapat digunakan simulasi Average Run Length (ARL) dan penerapannya pada data sebenarnya.
Berdasarkan hasil analisis, didapatkan bahwa kesalahan pengukuran (σm^2/σx^2) berdampak negatif pada efisiensi diagram kontrol AEWMA ME AI Max ditandai dengan kenaikkan nilai ARL untuk setiap kenaikkan kesalahan pengukuran σm^2/σx^2 yang menandakan bahwa semakin lambat kemampuan diagram kontrol dalam mendeteksi adanya pergeseran proses baik dalam mean dan varians akibat adanya kesalahan pengukuran σm^2÷σx^2. Sebaliknya, Hubungan korelasi antara variabel karakteristik kualitas terukur Y dengan variabel auxiliary W (ρ) berdampak positif pada pada efisiensi diagram kontrol AEWMA ME AI Max ditandai dengan penurunan nilai ARL untuk setiap kenaikkan nilai korelasi ρ yang menandakan bahwa semakin cepat kemampuan diagram kontrol dalam mendeteksi adanya pergeseran proses baik dalam mean dan varians. Parameter intercept (A) dari model covariate tidak memiliki pengaruh yang signifikan terhadap efisiensi diagram kontrol AEWMA ME (Covariate) AI Max. Sedangkan, Parameter slope model covariate B berdampak negatif pada efisiensi diagram kontrol AEWMA ME (Covariate) AI Max ditandai dengan kenaikkan nilai ARL untuk setiap kenaikkan parameter slope model covariate B yang menandakan bahwa semakin lambat kemampuan diagram kontrol dalam mendeteksi adanya pergeseran proses. Parameter intercept model linearly increasing variance C tidak memiliki pengaruh yang signifikan terhadap efisiensi diagram kontrol AEWMA ME (Linearly increasing variance) AI Max. Parameter slope model linearly increasing variance D berdampak positif pada efisiensi diagram kontrol AEWMA ME (Linearly increasing variance) AI Max ditandai dengan penurunan nilai ARL untuk setiap kenaikkan parameter slope model linearly increasing variance D yang menandakan bahwa semakin cepat kemampuan diagram kontrol dalam mendeteksi adanya pergeseran proses baik dalam mean dan varians akibat kenaikkan nilai parameter slope model linearly increasing variance D. Untuk mendeteksi adanya pergeseran proses dalam rata-rata (γ) diagram kontrol AEWMA ME (Covariate) AI Max lebih sensitif dibandingkan diagram kontrol AEWMA ME (Linearly increasing variance) AI Max ditandai dengan nilai ARL yang lebih kecil. Dalam menteksi pergeseran proses dalam varians (δ), diagram kontrol AEWMA ME (Linearly Increasing Varians) Max cukup baik untuk mendeteksi kenaikkan varians proses tetapi kurang baik untuk mendeteksi penurunan varians proses. Diagram kontrol AEWMA ME AI Max bekerja lebih baik dibandingkan diagram kontrol Max-EWMA ME AI baik untuk pergeseran kecil atau besar baik dalam mendeteksi pergeseran rata-rata atau varians proses secara bersama-sama ditandai dengan nilai ARL yang lebih kecil. Diagram kontrol AEWMA ME AI Max dapat digunakan untuk data semen dan memiliki sensitifitas lebih tinggi dibandingkan diagram kontrol Max-EWMA ME AI yang ditandai dengan nilai statistik diagram kontrol yang lebih dekat dengan nilai batas kendali atas.
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The first control chart introduced was the Shewhart control chart which was good at detecting large shifts. The Shewhart control chart was conducted individually, namely by observing the average or variance of the process separately. Furthermore, control charts were developed to detect small shifts based on memory or memory-based control charts such as Exponentially Weighted Moving Average (EWMA) and Cummulative Sum. To detect process shifts in both the average and variance simultaneously or jointly monitor, the Max control chart was introduced. The EWMA control chart assumes the controlled quality characteristics must have no measurement error. Previous research has shown that the presence of measurement errors results in the actual process quality measure not being accurately described and can reduce the sensitivity of the EWMA control chart, therefore it can be handled first before carrying out control with the EWMA control chart. There are three approaches to handling measurement errors, namely the covariate method, multiple measurements, and the state of non-constant variance (linearly increasing variance). In addition, the existence of process variance is also depicted by other variables related to the observed quality characteristics, so the control chart is introduced by including auxiliary variable elements in it. EWMA control chart is good for small shifts but not better than the Shewhart control chart in detecting large shifts so it is not effective in making decisions related to quality. Therefore, an adaptive score function is introduced that can make the EWMA control chart able to adjust conditions where small shifts or large shifts occur. Therefore, this study wants to develop a control chart by combining elements of memory-based, jointly monitoring, handling measurement errors, use of auxiliary variables, and adaptive score functions to become an Adaptive Exponentially Weighted Moving Average control chart with Measurement Error using Auxiliary Information Max (AEWMA ME AI Max). To observe the goodness of the control chart, the Average Run Length (ARL) simulation can be used as its application to real data.
Based on the analysis results, it was found that measurement error (σₘ²/σₓ²) has a negative impact on the efficiency of the AEWMA ME AI Max control chart, as indicated by an increase in the Average Run Length (ARL) with each increment in the measurement error ratio. This implies a slower detection capability of the control chart in identifying process shifts in both the mean and variance due to measurement error. Conversely, the correlation (ρ) between the measured quality characteristic (Y) and the auxiliary variable (W) exerts a positive effect on the efficiency of the AEWMA ME AI Max chart. This is reflected by a decrease in ARL with increasing ρ, indicating a faster and more accurate detection of process shifts in the mean and variance. The intercept parameter (A) of the covariate model shows no significant effect on the efficiency of the AEWMA ME (Covariate) AI Max control chart. However, the slope parameter (B) has a negative impact, evidenced by increasing ARL values as B increases, signifying a slower detection of process shifts. For the linearly increasing variance model, the intercept parameter (C) does not significantly affect the control chart’s efficiency, while the slope parameter (D) has a positive impact, shown by decreasing ARL values with increasing D. This indicates improved responsiveness in detecting shifts in both mean and variance due to increasing slope values. In detecting mean shifts (γ), the AEWMA ME (Covariate) AI Max chart is more sensitive than the AEWMA ME (Linearly increasing variance) AI Max chart, as indicated by lower ARL values. For variance shifts (δ), the AEWMA ME (Linearly increasing variance) AI Max chart performs well in detecting increases in process variance but is less effective in detecting decreases. Overall, the AEWMA ME AI Max control chart outperforms the Max-EWMA ME AI chart in detecting both small and large shifts in mean and variance simultaneously, demonstrated by consistently lower ARL values. The AEWMA ME AI Max control chart can be applied to cement data and demonstrates higher sensitivity compared to the Max-EWMA ME AI control chart, as indicated by its control chart statistic values being closer to the upper control limit.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Adaptif, AEWMA ME AI Max, EWMA, Pengendalian Kualitas; Adaptive, AEWMA ME AI Max, EWMA, Statistical Quality Control |
| Subjects: | H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics H Social Sciences > HD Industries. Land use. Labor > HD62.15 Total quality management. |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Eirene Christina Sellyra |
| Date Deposited: | 05 Aug 2025 02:14 |
| Last Modified: | 06 Aug 2025 07:51 |
| URI: | http://repository.its.ac.id/id/eprint/126193 |
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