Statistical Analysis Of Fatigue Life Distribution Of Birnbaum - Saunders

In the reliability life test, the failure of product has various reasons. Due to the periodic stress, product cracks. If the crack length reaches or exceeds a certain value,product fails. The fatigue life distribution of Birnbaum-Saunders is one of the reliability analysis distribution, and it is commonly used in reliability analysis. Due to complexity of its density function, it is difficult to do estimation for the parameter. So finding an effective parameter estimation method has great theoretical significance and application value.In this paper, firstly, article gives background of Birnbaum- Saunders distribution,such as the shape of density function, shape of failure rate function,1X-distribution,the variation coefficient, skewness, moments, maximum likelihood estimation. It is concluded that the shape of density function and failure rate function are both inverted tub graphs. Using torque estimation, inverse moment estimation and quantile estimation to estimate the parameters and using Monte Carlo simulation to compare them. We may draw the conclusion that the estimation effect is good when a,b are small, and the effects of several methods are similar, the precision of moment simulation is worse than the Maximum likelihood estimation’s. The application of it is not convenient. Other methods are more convenient. Secondly we put forward the three parameters Birnbaum-Saunders( BSI(m,a,b)) fatigue life distribution. Based on the BS distribution we add the location parameter, hence we derive the three parameters distribution. In addition, torque estimation and quantile estimation are obtained for the parameters, the stochastic simulation and examples are presented afterwards. In the end we give the background of the three parameters fatigue life distribution( BSII(m,a,b)) and make some exploration for the density function and failure rate function for it.