Sains Malaysiana 52(2)(2023): 641-653

http://doi.org/10.17576/jsm-2023-5202-24

Bayesian Estimation of Time to Failure Distributions Based on Skew Normal Degradation Model: An Application to GaAs Laser Degradation Data

(Anggaran Bayesian Masa untuk Taburan Kegagalan Berdasarkan Model Degradasi Normal Pencong: Aplikasi untuk Data Degradasi Laser GaAs)

LAILA NAJI BA DAKHN, MOHD AFTAR ABU BAKAR^* & KAMARULZAMAN IBRAHIM

Jabatan Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

Diserahkan: 30 Jun 2022/Diterima: 16 Disember 2022

Abstract

In this paper, the Bayesian method which involves informative and weakly informative priors are considered to estimate the parameters and percentiles of the time to failure distribution. The parameters of the time to failure distribution and its percentiles are determined based on linear degradation model where the degradation parameter is assumed to follow the skew normal distribution. For the prior distributions, location and scale parameters of the skew normal distribution is assumed to follow the uniform distribution while the shape parameter is assumed to follow gamma distribution. Two gamma priors are considered, either informative or weakly informative prior, depending on the assumed values of the hyper parameters. The performance of the method under the different prior assumptions is compared using a simulation study based on Markov Chain Monte Carlo method as well as a real data application. It is found that the parameter estimation based on informative prior is more precise as opposed to the weakly informative prior, especially in the case of small sample size. In addition, the skew normal degradation model is compared to the log-logistic degradation model through a simulation study and a real application of GaAs laser data. When modeling the percentiles of the time to failure distribution, results found based on the skew normal distribution is generally found to be more precise, particularly for the higher percentile values.

Keywords: Bayesian method; linear degradation model; log-logistic distribution; skew normal distribution; time to failure distribution

Abstrak

Dalam kertas ini, kaedah Bayesan yang melibatkan prior bermaklumat dan kurang bermaklumat dipertimbangkan untuk menganggar parameter dan persentil untuk taburan masa kegagalan. Parameter dan persentil bagi taburan masa kegagalan ditentukan berdasarkan model degradasi linear yang mana parameter degradasi diandaikan mengikuti taburan normal pencong. Untuk taburan prior, parameter skala dan lokasi bagi taburan normal pencong diandaikan mengikuti taburan seragam manakala parameter bentuk diandaikan mengikuti taburan gama. Dua prior gama yang dipertimbangkan, iaitu sama ada bermaklumat atau kurang bermaklumat, bergantung kepada nilai parameter hiper yang diandaikan. Prestasi kaedah berkenaan di bawah andaian yang berbeza dibandingkan menerusi kajian simulasi berdasarkan kaedah Rantai Markov Monte Carlo dan juga aplikasi data sebenar. Didapati bahawa penganggaran parameter berdasarkan prior bermaklumat adalah lebih persis berbanding prior kurang bermaklumat, khususnya apabila saiz sampel kecil. Seterusnya, model degradasi normal pencong dibandingkan dengan model degradasi log-logistik menerusi kajian simulasi dan aplikasi data laser GaAs. Bila memodelkan persentil bagi taburan masa kegagalan, secara amnya, hasil menunjukkan bahawa keputusan berdasarkan taburan normal pencong adalah lebih persis, khususnya untuk persentil yang bernilai tinggi.

Kata kunci: Kaedah Bayesian; model degradasi linear; taburan log-logistik; taburan masa kegagalan; taburan normal pencong

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^*Pengarang untuk surat-menyurat; email: aftar@ukm.edu.my