Sains Malaysiana 51(7)(2022): 2265-2281

http://doi.org/10.17576/jsm-2022-5107-26

 

Comparison Analysis on the Coefficients of Variation of Two Independent Birnbaum-Saunders Distributions by Constructing Confidence Intervals for the Ratio of Coefficients of Variation

(Analisis Perbandingan Pekali Variasi Dua Taburan Birbaum-Saunders tak Bersandar dengan Membina Selang Keyakinan untuk Nisbah Pekali Variasi)

 

WISUNEE PUGGARD, SA-AAT NIWITPONG & SUPARAT NIWITPONG*

 

Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

 

Diterima: 29 Ogos 2021/Diserahkan: 30 November 2021

 

Abstract

The fatigue failure of materials can be investigated by applying the Birnbaum-Saunders (BS) distribution to fatigue failure datasets. The coefficient of variation (CV) is an important descriptive statistic that is widely used to measure the dispersion of data. In addition, for two independent datasets following BS distributions, the ratio of their CVs can be used to compare their CVs, especially when the difference is small, and constructing confidence intervals for this scenario is of interest in this study. Hence, we propose new confidence intervals for the ratio of the CVs from two BS distributions by using the bootstrap confidence interval (BCI), the fiducial generalized confidence interval (FGCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval approaches. The performances of the proposed confidence intervals were compared with the generalized confidence interval (GCI) in terms of their coverage probabilities and average lengths via Monte Carlo simulations. The results indicate that the HPD interval outperformed the others when the coverage probabilities and the average lengths were both considered together. The efficacies of the proposed methods and GCI are illustrated using real datasets of the fatigue life of 6061-T6 aluminum coupons.

 

Keywords: Bayesian; Birnbaum-Saunders distribution; coefficients of variation; confidence interval; fatigue failure

Abstrak

Kegagalan lesu bahan boleh dikaji dengan menggunakan taburan Birnbaum-Saunders (BS) pada set data kegagalan lesu. Pekali variasi (CV) ialah statistik deskriptif penting yang digunakan secara meluas untuk mengukur serakan data. Di samping itu, untuk dua set data tak bersandar disebabkan taburan BS, nisbah CV mereka boleh digunakan untuk membandingkan CV mereka, terutamanya apabila perbezaannya kecil dan membina selang keyakinan untuk senario ini adalah penting dalam kajian ini. Oleh itu, kami mencadangkan selang keyakinan baharu untuk nisbah CV daripada dua taburan BS dengan menggunakan pendekatan selang keyakinan bootstrap (BCI), selang keyakinan umum fidusial (FGCI), selang boleh percaya Bayesian (BayCI) dan selang ketumpatan posterior tertinggi (HPD). Prestasi selang keyakinan yang dicadangkan telah dibandingkan dengan selang keyakinan umum (GCI) dari segi kebarangkalian liputan dan panjang purata melalui simulasi Monte Carlo. Keputusan menunjukkan bahawa selang HPD mengatasi yang lain apabila kebarangkalian liputan dan panjang purata kedua-duanya diambil kira secara bersama. Keberkesanan kaedah yang dicadangkan dan GCI diilustrasi menggunakan set data sebenar hayat lesu kupon aluminium 6061-T6.

 

Kata kunci: Bayesian; kegagalan lesu; pekali variasi; selang keyakinan; taburan Birnbaum-Saunders

 

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*Pengarang untuk surat-menyurat; email: suparat.n@sci.kmutnb.ac.th

       

 

 

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