Acita, Selly (2020) Kinerja Diagram Kendali Bivariate Exponentially Weighted Moving Average (BEWMA) Menggunakan Distribusi CARL dan Exceedance Probability Criterion (EPC). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Pada umumnya diagram kendali dikembangkan dengan asumsi karakteristik kualitas dari sebuah proses produksi berdistribusi normal dengan parameter yang diketahui. Namun dalam praktik, karakteristik kualitas tidak selalu berdistribusi normal dan parameter proses tidak selalu diketahui. Oleh karena itu perlu dilakukan estimasi parameter. Apabila data set yang digunakan pada Fase I berbeda-beda jumlahnya, maka kinerja diagram kendali pada Fase II akan bervariasi. Kinerja diagram yang bervariasi itu disebut “variabilitas praktisi ke praktisi”. Salah satu ukuran kinerja diagram kendali adalah Average Run Length (ARL), yaitu rata-rata banyaknya run sampai ditemukan out-of-control yang pertama. Ketika parameter proses di estimasi dari reference sampel in-control, run-length mengikuti distibusi conditional-nya yang disebut Conditional Average Run Length (CARL). Pada penelitian ini, akan dievaluasi kinerja diagram kendali Bivariate Exponentially Weighted Moving Average (BEWMA) dengan mempertimbangkan variabilitas praktisi ke praktisi menggunakan distribusi Conditional Average Run Length (CARL) dan Exceedance Probability Criterion (EPC). Nilai dari CARL pada penelitian ini dihitung menggunakan metode Rantai Markov. EPC digunakan untuk mengevaluasi variabilitas praktisi ke praktisis yang berkaitan erat dengan estimasi parameter. Hasil penelitian ini menunjukkan bahwa, untuk menjamin kinerja in-control dengan dengan probabilitas tinggi 1-p (yang merupakan kriteria EPC) dibutuhkan data Fase I yang cukup besar, yaitu lebih dari 10.000 data. Namun dalam praktiknya, sulit untuk mendapatkan data Fase I yang cukup besar. Sehingga untuk menghasilkan kinerja in-control yang baik dengan jumlah data Fase I yang tersedia harus dilakukan penyesuaian batas kendali.
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In general, control charts are developed with the assumption that the critical quality of a production process is normally distributed with known parameters. However, in practice, critical quality is not always normally distributed and process parameters are typically unknown. In such a case, it is necessary to estimate the parameters. If the number of observations in Phase I varies, the performance of the control chart in Phase II will also vary. The various performance charts are called practitioner to practitioner variability. One of the measures to evaluate the performance control charts is Average Run Length (ARL), which is the average number of runs until the first out-of-control detected. When the process parameters are estimated from an in-control reference sample, the run-length follows its conditional distribution so-called Conditional Average Run Length (CARL). In this study, the performance of the Bivariate Exponentially Weighted Moving Average (BEWMA) control chart will be evaluated by considering the practitioner to practitioner variability using the CARL distribution and the Exceedance Probability Criterion (EPC). The value of CARL is calculated using the Markov Chain method. The EPC is used to evaluate practitioner to practitioner variability that is closely related to parameter estimation. The results show that to guarantee the in-control performance with a high probability of 1-p (which is the EPC criterion), the large size of observations (more than 10.000 data) in Phase I data is needed. However, in practice, it is difficult to collect such a huge size of data in Phase I. Therefore, to produce the best in-control performance with available Phase I, the control limits are adjusted.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | RTSt 519.86 Aci k-1 2020 |
| Uncontrolled Keywords: | BEWMA, CARL, EPC, Rantai Markov |
| Subjects: | Q Science > QA Mathematics > QA274.7 Markov processes--Mathematical models. Q Science > QA Mathematics > QA76.9 Computer algorithms. Virtual Reality. Computer simulation. T Technology > TS Manufactures > TS156 Quality Control. QFD. Taguchi methods (Quality control) |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Selly Acita |
| Date Deposited: | 24 Dec 2024 07:38 |
| Last Modified: | 24 Dec 2024 07:38 |
| URI: | http://repository.its.ac.id/id/eprint/74427 |
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