On the hazard rate process for imperfectly monitored multi-unit systems

The aim of this communication is to present a stochastic model to characterize the failure distribution of multi-unit systems when the current units state is imperfectly monitored. The definition of the hazard rate process given by (Arjas 1981a) with perfect monitoring is extended to the case where the units failure time are not always detected (non-detection events). The so defined observed hazard rate process is calculated on a practical industrial system (two parallel units). Its monotony property is,studied when the monitoring quality deteriorates (increase of the non-detection probabilities).