Summary: Several types of hazard (failure) rate functions are considered while analyzing the probability of termination for the Poisson (renewal) process. Each event can lead to the process termination with a given, dependent on history, probability. The black box hazard rate is defined as a conventional hazard (failure) rate of a continuous distribution function. The conditional hazard rate is defined by conditioning on information (history) at hand and the mean conditional hazard rate is the result of applying to the latter an operation of expectation. Some relationships between different types of hazard rate are considered. A simple reliability example is presented.