Resumen
Our purpose is to estimate the expectation E?(X˜) where ? is a known function, X˜ is a random vector with mutually independent components. The distribution functions of the components are unknown but sample X(1),X(2),…,X(n) from the population is available. In addition components of X(i) are dependent random variables. In this paper various estimators of the expectation are proposed.

Resumen
A failure model with damage accumulation is considered. Damages occur according to a Poisson process and they degenerate into failures in a random time. The rate of the Poisson process and the degeneration time distribution are unknown. Two sample populations are available: a sample of intervals between damages and a sample of degeneration times. The case of small samples is considered. The purpose is to estimate the expectation and the distribution of the number of damages and failures at time t. We consider the plug-in and resampling estimators of the above mentioned characteristics. The expectations and variances of the suggested estimators are investigated. The numerical examples show that the resampling estimator has some advantages.