Statistical Estimation for a Reliability Model Based on Shot-Noise Processes in a Case of Small Samples

A failure model based on shot-noise processes is considered. A discussed reliability system is subjected to shocks. Shocks of random magnitude occur according to a homogeneous Poisson process and decay with time according to the deterministic function h(t). The rate of the Poisson process and the distribution of magnitude values are unknown. Two sample populations are available: a sample of intervals between shocks and a sample of magnitude values. The case of small samples is considered. The purpose is to estimate the expectation of the system stress level at time t. We consider the plug-in and resampling estimators of the above mentioned characteristics. The expectation and variance of the suggested estimators are investigated. The numerical examples and simulation studies show that the resampling estimator has some advantages.