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All Journal AKSIOMA: Jurnal Program Studi Pendidikan Matematika Transformasi: Jurnal Pengabdian Masyarakat AlphaMath: Journal of Mathematics Education Jurnal Elemen E-Dimas: Jurnal Pengabdian kepada Masyarakat HISTOGRAM: Jurnal Pendidikan Matematika Jurnal Abdimas BSI: Jurnal Pengabdian Kepada Masyarakat Indonesian Journal of Science and Mathematics Education Unisda Journal of Mathematics and Computer Science (UJMC) IRJE (Indonesian Research Journal in Education) Buana Matematika : Jurnal Ilmiah Matematika dan Pendidikan Matematika Martabe : Jurnal Pengabdian Kepada Masyarakat JEMST: Journal of Education in Mathematics, Science, and Technology JPM : Jurnal Pendidikan Matematika Dedication : Jurnal Pengabdian Masyarakat Jurnal Absis : Jurnal Pendidikan Matematika dan Matematika Jurnal Abdi Insani SEPREN: Journal of Mathematics Education and Applied Range : Jurnal Pendidikan Matematika Jurnal Statistika dan Matematika (Statmat) Journal of Science and Technology MATH-EDU: Jurnal Ilmu Pendidikan Matematika Fraktal: Jurnal Matematika dan Pendidikan Matematika Brillo Journal Edumatica: Jurnal Pendidikan Matematika Dedication : Jurnal Pengabdian Masyarakat IndoMath: Indonesia Mathematics Education Mathematical Journal of Modelling and Forecasting Journal of Mathematics Theory and Applications
Cecilia Novianti Salsinha
Program Studi Pendidikan Matematika, Universitas Timor
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Journal : Unisda Journal of Mathematics and Computer Science (UJMC)

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Estimasi Parameter Distribusi Weibull Dan Aplikasinya pada Pengendalian Mutu Dengan Memanfaatkan Kuantil Cecilia Novianti Salsinha
Unisda Journal of Mathematics and Computer Science (UJMC) Vol 5 No 01 (2019): Unisda Journal of Mathematics and Computer Science (UJMC)
Publisher : Mathematics Department of Mathematics and Natural Sciences Unisda Lamongan

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (654.829 KB) | DOI: 10.52166/ujmc.v5i01.1473

Abstract

Abstract. Weibull distribution is one of the continuous probability distributions. As the other distributions, Weibull distribution is also characterized by Mean, Variance and Moment Generation Function. The advantage of this distribution compared to other distributions is its flexibility, that is, this distribution can change to another distribution such as an exponential distribution depending on the value of the selected distribution parameters, namely scale parameters and form parameters. From the distribution graph, it can be shown that, the flexibility will appear very clear. One application of the Weibull distribution is in statistical process control. Because not all data is normally distributed, the Shewhart control chart cannot be used. One way to solve this problem is that the data is analyzed with Weibull control charts by utilizing quantiles, namely 0.00135, 0.5 and 0.99865. Quantile 0.00135 is the bottom quintile used to form the Lower Control Limit, the Middle Line is the median of the data, which is 0.5 which replaces the average and the last to form the Upper Control Limit the top quintile is 0.99865. By generating 200 data with Weibull distribution, if the data is analyzed by Shewhart control charts then there is a lot of data that is outside the control limit so it will be concluded that the graph is out of control. Therefore, if the data is not from a Normal distribution, the use of Shewhart control charts is not recommended. Keywords: Weibull Distribution, Maximum Likelihood Estimation (MLE), Quality Control, Weibull Control Charts Abstrak. Distribusi Weibull merupakan salah satu distribusi probabilitas kontinu. Sama halnya dengan distribusi lainnya, distribusi Weibull pun dicirikan dengan Mean, Variansi dan Fungsi Pembangkit Momen. Kelebihan distribusi ini dibandingkan dengan distribusi lainnya adalah fleksibilitasnya, yaitu distribusi ini dapat berubah menjadi distribusi lain seperti distribusi eksponensial tergantung pada nilai parameter distribusi yang dipilih yaitu parameter skala dan parameter bentuk. Jika dilihat dari grafik distribusinya maka akan tampak sangat jelas fleksibilitas tersebut. Salah satu aplikasi dari distribusi Weibull yaitu dalam pengendalian proses statistik. Oleh karena tidak semua data berdistribusi normal maka grafik pengendali Shewhart tidak dapat digunakan. Salah satu cara menyelesaikan masalah tersebut adalah data dianalisis dengan grafik pengendali Weibull dengan memanfaatkan kuantil-kuantil yaitu 0,00135, 0,5 dan 0,99865. Kuantil 0,00135 adalah kuantil bawah yang digunakan untuk membentuk Batas Pengendali Bawah, Garis Tengah adalah median dari data yaitu 0,5 yang menggantikan rata-rata dan untuk membentuk Batas Pengendali Atas digunakan kuantil atas yaitu 0,99865. Dengan membangkitkan data sebanyak 200 data berdistribusi Weibull, jika data tersebut dianalisis dengan grafik pengendali Shewhart maka terdapat banyak data yang berada diluar batas pengendali sehingga akan disimpulkan bahwa grafik tak terkendali. Oleh karena itu, jika data bukan berasal dari distribusi Normal, penggunaan grafik pengendali Shewhart tidak disarankan. Kata Kunci: Distribusi Weibull, Estimasi Maximum Likelihood, Pengendalian Mutu, Grafik Pengendali Weibull
Co-Authors Agustina Hoar Agustinus Giovandi Laki Aloisius Loka Son Amsikan Stanislaus Andhy Rudhito, Marcellinus Anunut, Ardi Plasidus Bano, Elinora Naikteas Bees, Nene Lodiana Bete, Elviana Bete, Hendrika Binsasi, Eva Bone, Dominifridus Chatarina Enny Murwaningtyas Deda, Yohanis Ndapa Dina Timutang Dominifridus Bone Ebenhaiser Liunokas Eduardus Beo Seso Delvion Eva Binsasi Farida Daniel Fitriani Fitriani Fitriani Fitriani Gotlif Onirca Sina Hall, Eric Steven Hendrika Yeni Meti Hermina Disnawati, Hermina Hijriani, Lailin Hijriani, Lailin Hongki Julie Januario Pareira Jeniana Martha Prima Asa Julita Clarita Bete Kasa, Andreas Roberto Kolloh, Fanda Apriani Kresentius Iku Kobesi Mada, Grandianus Maifa, Talisadika Serrisanti Marcelina Nikola De Albergati Luty Marcellinus Andhy Rudhito Margareta Rodrigues Gomes Maria Alfiado Leu Maria Erwinda Kefi, Winda Maria Naimnule Mau, Maria Sensiana Meiva M. L. Siahaan Melissa Aeudia Daullu Minanur Rohman mone, ferdinandus Mun, Beatrix Farena Naimnule, Maria Nifu, Martha Marsela Oktovianus Mamoh Sanbein, Anita Fanu Selestina Nahak Semuel Ibrahim Amalo Siahaan, Meiva Marthaulina Lestari Sihombing, Yeni Rafita Simamarta, Justin Eduardo Simarmata, Justin Eduardo Solo, Prudensius Manek Maria Fransiska Venidora Stanislaus Amsikan Stanislaus, Amsikan Sulasri Suddin Tefa, Maria Angela Christin Timo, Maria Elisabeth Timutang, Moses Wua Laja, Yosepha Patricia Yakoba Yusina Muanley Yanpitherszon Liunokas Yohanes Jefrianus Kehi Yovita Alves Amsikan Zulkaidah Nur Ahzan