The Conditional Probability of Failure (CPF) has been used in reliability theory for reparable units as for non-reparable units in the same way. However, they respond to different stochastic processes. This is why the Reliability Function is replaced by other distribution functions that better fit the events rate curve to obtain a better approximation of the desired estimation.The Probability of Failure for non-reparable units is derived here through a proof based on a mental experiment for non-reparable units, avoiding assumptions on the distribution of the random variable, letting the experiment reveals the nature of the phenomenon under test. The proof leads to a Conditional Probability of Failure, presented after a detailed discussion where it is also proved that the hazard rate in the traditional CPF can’t be a constant.
Here you will find the theorem that makes the Conditional Probability of Failure practical for any non-reparable device with only the events rate function.