The β -Birnbaum–Saunders distribution: An improved distribution for fatigue life modeling

Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies. For the first time, based on this distribution, the so-called β -Birnbaum–Saunders distribution is proposed for fatigue life modeling. Various properties of the new model including expa...

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Bibliographic Details
Published in:	Computational statistics & data analysis 2011-03, Vol.55 (3), p.1445-1461
Main Authors:	Cordeiro, Gauss M., Lemonte, Artur J.
Format:	Article
Language:	eng
Subjects:	Beta distribution Birnbaum–Saunders distribution Data processing Density Deviation Distribution theory Exact sciences and technology Fatigue failure Fatigue life Fatigue life distribution General topics Lifetime data Mathematical analysis Mathematical models Mathematics Maximum likelihood estimation Mean deviation Multivariate analysis Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Statistics
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Summary:	Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies. For the first time, based on this distribution, the so-called β -Birnbaum–Saunders distribution is proposed for fatigue life modeling. Various properties of the new model including expansions for the moments, moment generating function, mean deviations, density function of the order statistics and their moments are derived. We discuss maximum likelihood estimation of the model’s parameters. The superiority of the new model is illustrated by means of three failure real data sets.
ISSN:	0167-9473 1872-7352