Yes it is indeed a matter of culture: in reliability, the failure rate can indicate the probability of occurrence at a given time t. If a unit has increasing failure rate, then it is more likely to fail at a large calendar time t, given there is no failure before (and vice versa). The phrase “estimate the model parameters” is hasty-my fault. Imagine you need to build an optimal maintenance policy for the given unit (with known failure rate). Now I need failure data (samples of the r.v. in my question) to calibrate the policy parameters, and to compare with others policies in order to determine which is the best. Hence model parameters should mean the policy parameters, not the probability distribution parameters!

]]>Thank you, Tuan. I presume it is a matter of culture: for me, defining a random variable by a failure rate carries no intuition. An additional question is why do you need simulated samples to estimate the model parameters?

]]>Sorry about this, wordpress is not a great repository for posting equations… When considering how easy it is to write those entries on Stack Exchange, that’s really a problem! In the current post, the same equations are available on my Cross Validated answer. In a more readable format.

]]>