Rasyid, Dwilaksana Abdullah (2025) Neo Normal Distribution Control Chart Menggunakan Highest Posterior Distributions. Doctoral thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Distribusi Neo Normal adalah kelompok distribusi yang fleksibel, yang dapat mendekati distribusi normal ketika parameternya memiliki nilai tertentu, namun tidak bersifat normal pada kondisi lainnya. Penelitian ini mengembangkan metode diagram kontrol berbasis distribusi Neo Normal yang menggunakan Highest Posterior Distributions (HPD) untuk mendeteksi kondisi tetap dalam data multivariat yang bersifat non-Gaussian dan non-stasioner. Pengembangan dimulai dengan memperkenalkan distribusi Univariate Modified Skew-Normal Burr (MSN-Burr) dan Exponential Power (EP), yang kemudian diperluas menjadi Bivariate Modified Skew-Normal Distribution (Bivariate MSN-Burr). Beberapa distribusi tersebut kemudian diterapkan pada model Markov Switching Autoregressive (MSAR) dan Markov Switching Vector Autoregressive (MSVAR), yang masing-masing dinamakan MSAR MSN-Burr, MSAR EP, dan MSVAR MSN-Burr. Model-model ini diestimasi menggunakan kombinasi algoritma No U-Turn Sampler (NUTS) dan Expectation Maximization (EM) untuk mendeteksi perpindahan status dalam data. Diagram kontrol yang dibangun dihitung menggunakan HPD pada setiap model, dan diterapkan pada data kualitas udara kota Yogyakarta serta data rekam medis Electroencephalography (EEG) pasien anak dengan epilepsi ringan untuk menghitung Upper Control Limit (UCL) dan Lower Control Limit (LCL). Penerapan pada data kualitas udara kota Yogyakarta yang dimodelkan dengan MSAR MSN-Burr berhasil menangkap pergeseran antara kondisi normal dan kondisi tidak normal. Penerapan pada data EEG, yang dimodelkan dengan MSAR EP dan Bivariate MSN-Burr, menunjukkan kemampuan model dalam mendeteksi perubahan aktivitas otak pasien secara lebih sensitif.
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Neo Normal distribution is a flexible group of distributions, which can approach the normal distribution when its parameters have certain values, but are not normal under other conditions. This study develops a Neo Normal distribution-based control chart method that uses Highest Posterior Distributions (HPD) to detect steady states in multivariate data that are non-Gaussian and non-stationary. The development begins by introducing the Univariate Modified Skew-Normal Burr (MSN-Burr) and Exponential Power (EP) distributions, which are then extended to the Bivariate Modified Skew-Normal Distribution (Bivariate MSN-Burr). These new distributions are applied to Markov Switching Autoregressive (MSAR) and Markov Switching Vector Autoregressive (MSVAR) models, which are named MSAR MSN-Burr, MSAR EP, and MSVAR MSN-Burr, respectively. These models are estimated using a combination of the No U-Turn Sampler (NUTS) and Expectation Maximization (EM) algorithms to detect state switching in the data. The control diagrams constructed were calculated using HPD in each model, and applied to Yogyakarta city air quality data and Electroencephalography (EEG) medical record data of pediatric patients with mild epilepsy to calculate the Upper Control Limit (UCL) and Lower Control Limit (LCL). The application to Yogyakarta city air quality data modeled with MSAR MSN-Burr successfully captured shifts between normal and abnormal conditions. The application to EEG data, modeled with MSAR EP and Bivariate MSN-Burr, demonstrated the model's ability to detect changes in patient brain activity more sensitively.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Uncontrolled Keywords: | Markov Switching Vector Autoregressive, Modified Stable Normal Burr Distribution, Hamiltonian Monte Carlo, Highest Posterior Distribution. |
| Subjects: | H Social Sciences > HA Statistics > HA30.3 Time-series analysis T Technology > TD Environmental technology. Sanitary engineering > TD883 Air quality management. |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis |
| Depositing User: | Dwilaksana Abdullah Rasyid |
| Date Deposited: | 06 Aug 2025 07:55 |
| Last Modified: | 06 Aug 2025 08:14 |
| URI: | http://repository.its.ac.id/id/eprint/127823 |
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