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Sains Malaysiana 51(7)(2022):
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
Received: 29 August 2021/Accepted: 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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*Corresponding author; email: suparat.n@sci.kmutnb.ac.th
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