Sains Malaysiana 53(9)(2024): 3215-3227

http://doi.org/10.17576/jsm-2024-5309-24

Bayesian Approach for Estimating the Parameters of the Time-to-Failure Distribution and Its Percentiles under Power Degradation Model

(Pendekatan Bayesian untuk Menganggar Parameter Taburan Masa Kegagalan dan Peratusannya di bawah Model Penurunan Kuasa)

LAILA NAJI BA DAKHN^1,2, MOHD AFTAR ABU BAKAR¹, RAZIK RIDZUAN MOHD TAJUDDIN^1,* & KAMARULZAMAN IBRAHIM¹

¹Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

²Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla, Hadhramout, Yemen

Received: 8 January 2024/Accepted: 9 July 2024

Abstract

The degradation models are often applied on the degradation data for studying time-to-failure distribution. In this study, the Bayesian approach is applied on the power degradation model for estimating the parameters of the time-to-failure distribution and its percentiles. Two different distributions are assumed for the degradation parameter of the model. The degradation parameter is firstly assumed to follow the skew-normal distribution with three jointly independently distributed parameters such that the gamma prior is assumed for the shape parameter, while the scale and the location parameters are assumed uniform. The second distribution assumed for the degradation parameter is the log-logistic distribution with two jointly independent random parameters where the shape parameter is assumed gamma, while the scale parameter is assumed uniform. Based on the Gibbs sampling method carried out under the JAGS platform, the models considered are applied on the simulated data and the NASA turbofan Jet engine dataset and the results found are compared. In modeling the time-to-failure distribution, it is shown that based on the simulated data and real data, the Bayesian approach for the power degradation model with the skew-normal degradation parameter outperformed the Bayesian approach for the power degradation model with the log-logistic degradation parameter.

Keywords: Bayesian approach; log-logistic distribution; power degradation model; skew-normal distribution; time-to-failure distribution

Abstrak

Model degradasi sering digunakan pada data degradasi untuk mempelajari taburan masa kegagalan. Dalam kajian ini, pendekatan Bayes digunakan pada model degradasi kuasa untuk menganggarkan parameter taburan masa kegagalan dan persentilnya. Dua taburan yang berbeza diandaikan untuk parameter degradasi model. Parameter degradasi pertama diandaikan mengikut taburan normal terpencong dengan tiga parameter yang tertabur secara tak bersandar dengan diandaikan prior gamma untuk parameter bentuk, sementara parameter skala dan lokasi diandaikan tertabur secara seragam. Taburan kedua yang diandaikan untuk parameter degradasi adalah taburan log-logistik dengan dua parameter rawak bercantum yang tak bersandar dengan andaian parameter bentuk tertabur secara gamma, sementara parameter skala tertabur secara seragam. Berdasarkan kaedah pensampelan Gibbs yang dilaksanakan di platform JAGS, model yang dipertimbangkan digunakan pada data simulasi dan set data enjin jet kipas turbo NASA dan hasil yang ditemui dibandingkan. Dalam pemodelan taburan masa kegagalan, didapati bahawa berdasarkan data yang disimulasikan dan data sebenar, prestasi pendekatan Bayes untuk model degradasi kuasa dengan parameter degradasi normal terpencong mengatasi prestasi pendekatan Bayes untuk model degradasi kuasa dengan parameter degradasi log-logistik.

Kata kunci: Masa kegagalan; model degradasi kuasa; pendekatan Bayes; taburan log-logistik; taburan normal terpencong

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*Corresponding author; email: rrmt@ukm.edu.my