Abstract
The Birnbaum–Saunders (BS) distribution was derived to model failure times of materials subjected to fluctuating stresses and strains. Motivated by applications in the characterizations of materials, in 1991 Rieck and Nedelman proposed a log-linear model for the BS distribution. This model has many applications, for instance, to compare the median time life of several populations or to assess the effect of covariates on accelerated life testing. In addition to the model studied under the classical approach, we considered Markov chain Monte Carlo (MCMC) and we made an implementation in WinBUGS to get a Bayesian approach under noninformative priori distribution. Similar results for both classical and Bayesian approaches were obtained. This implementation was also adapted for censoring and we assessed the influence of different percentages of censored data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Achcar, J.A., Martinez, M.: Bayesian methods in accelerated life test considering a log-linear model for the Birnbaum–Saunders distribution. Rev. Bras. Estat. 52, 47–68 (1991)
Birnbaum, Z.W., Saunders, S.C.: A new family of life distributions. J. Appl. Probab. 6, 319–327 (1969)
Brown, M.W., Miller, K.J.: Biaxial fatigue data. Report CEMR1/78, University of Sheffield, Department of Mechanical Engineering (1978)
Dos Santos, M.F.: Estimaçãao e modelagem com a distribuiçãao Birnbaum-Saunders: uma nova reparametrizaçãao. Dissertation (Master: Estatística Matemática), Universidade Federal de Pernambuco, Recife (2010)
Rieck, J.R.: Statistical analysis for the Birnbaum Saunders fatigue life distribution. Unpublished Ph.D. thesis, Clemson University, Department of Mathematical Science (1989)
Rieck, J.R., Nedelman, J.R.A.: Log-linear model for the Birnbaum–Saunders distribution. Technometrics 33(1), 51–60 (1991)
Villegas, C.M.: Modelos log-Birnbaum-Saunders mistos. Tese (Doctorate: Estatística), Universidade de São Paulo, São Paulo (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Patiño, E. (2015). Bayesian Estimation of Birnbaum–Saunders Log-Linear Model. In: Polpo, A., Louzada, F., Rifo, L., Stern, J., Lauretto, M. (eds) Interdisciplinary Bayesian Statistics. Springer Proceedings in Mathematics & Statistics, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-12454-4_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-12454-4_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12453-7
Online ISBN: 978-3-319-12454-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)