The beta-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 @b-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.

[1]  Víctor Leiva,et al.  A Non-Central Version of the Birnbaum-Saunders Distribution for Reliability Analysis , 2009, IEEE Transactions on Reliability.

[2]  J. Hosking.  L‐Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics , 1990 .

[3]  S. Nadarajah,et al.  The beta Gumbel distribution , 2004 .

[4]  Debasis Kundu,et al.  On the hazard function of Birnbaum-Saunders distribution and associated inference , 2008, Comput. Stat. Data Anal..

[5]  Jianrong Wu,et al.  Improved interval estimation for the two-parameter Birnbaum-Saunders distribution , 2004, Comput. Stat. Data Anal..

[6]  Y. H. Abdelkader,et al.  Computing the moments of order statistics from nonidentical random variables , 2004 .

[7]  Frank Proschan,et al.  Theoretical Explanation of Observed Decreasing Failure Rate , 2000, Technometrics.

[8]  Frank G. Garvan,et al.  The MAPLE Book , 2001 .

[9]  Sam C. Saunders,et al.  Estimation for a family of life distributions with applications to fatigue , 1969, Journal of Applied Probability.

[10]  Gauss M. Cordeiro,et al.  The beta generalized half-normal distribution , 2010, Comput. Stat. Data Anal..

[11]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[12]  D. S. Jones.  INCOMPLETE BESSEL FUNCTIONS. II. ASYMPTOTIC EXPANSIONS FOR LARGE ARGUMENT , 2007, Proceedings of the Edinburgh Mathematical Society.

[13]  Simos G. Meintanis.  Inference procedures for the Birnbaum-Saunders distribution and its generalizations , 2010, Comput. Stat. Data Anal..

[14]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[15]  J. R. Wallis,et al.  Probability Weighted Moments: Definition and Relation to Parameters of Several Distributions Expressable in Inverse Form , 1979 .

[16]  F. Famoye,et al.  BETA-NORMAL DISTRIBUTION AND ITS APPLICATIONS , 2002 .

[17]  Timothy A. Davis,et al.  MATLAB Primer , 1994 .

[18]  Francisco Cribari-Neto,et al.  Bootstrap-based improved estimators for the two-parameter Birnbaum–Saunders distribution , 2008 .

[19]  Narayanaswamy Balakrishnan,et al.  A General Purpose Approximate Goodness-of-Fit Test , 1995 .

[20]  R. Terras.  A miller algorithm for an incomplete bessel function , 1981 .

[21]  Frank E. Harris,et al.  Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions , 2008 .

[22]  José A. Díaz-García,et al.  A new family of life distributions based on the elliptically contoured distributions , 2005 .

[23]  W. J. Padgett,et al.  A Bootstrap Control Chart for Weibull Percentiles , 2006, Qual. Reliab. Eng. Int..

[24]  G. A. Watson.  A treatise on the theory of Bessel functions , 1944 .

[25]  Z. Birnbaum,et al.  A new family of life distributions , 1969 .

[26]  Francisco Cribari-Neto,et al.  Improved statistical inference for the two-parameter Birnbaum-Saunders distribution , 2007, Comput. Stat. Data Anal..

[27]  D. S. Jones.  INCOMPLETE BESSEL FUNCTIONS. I , 2007, Proceedings of the Edinburgh Mathematical Society.

[28]  Richard L. Smith,et al.  A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution , 1987 .

[29]  Samuel Kotz,et al.  The beta exponential distribution , 2006, Reliab. Eng. Syst. Saf..

[30]  James R. Rieck,et al.  A moment-generating function with application to the birnbaum-saunders distribution , 1999 .