Estimation of Structural Reliability Relative to a Dependent Bivariate Weibull Distribution

Consider a dependent bivariate distribution whose reliability function is \olF(x_1,x_2)=\exp\-(x_1^1/\alpha/\theta_1)^1/\delta+(x_2^1/\alpha/\theta_2)^1/\delta^\delta\, \;\;\;x_i>0,\,\alpha>0,\,1\geq\delta>0,\,\theta_i>0\;(i=1,2). Two kinds of stress-strength model are discussed respectively. Moment-type estimators of structural reliability for those models are proposed and their asymptotic properties are discussed. At last, a simulation result is given.