Parametric and nonparametric estimation of P(Y < X) for finite mixtures of lognormal components

In this paper, parametric and nonparametric estimators of the stressstrength reliability are obtained and compared when the random variables X and Y are independent and each of which is a mixture of lognormal components. 100(1 - α)% confidence bounds are obtained and compared in both of the parametric and nonparametric cases. Sin~ulation shows that the parametric point estimates are better than the nonparametric point estimates for all sample sizes. This is also true for interval estimates. particularly when the sample size N is small. As N increases: no great loss in precision occurs if Goviildarajulu's bounds arc used rather than the parametric bounds. The nonparanietric bounds are simpler and faster to obtain.