Modeling a repair process


I really like the power of Stan and I have used it for some simpler models so far.
I would like to use Stan for modelling a Marcov like progress. Currently I cannot assess if Stan provides the means to model this type of problem and if yes, what is the right approach to do so?

Depending on the age of a unit the probability increases that the next status ( broken ) is reached. After a certain time ( repair process) the unit returns to service with a reduced risk of failure, and it starts to age again.
The thing is the process is not memory less, as far as I understand it. Because the probability of failure depends on the age of the unit. But maybe I am interpreting the requirements for a Marcov Chain not correctly.

Do you have a suggestion for an approach in Stan or is it not the right tool for this kind of task?


Stan uses Markov Chain Monte Carlo to obtain samples from a Bayesian posterior distribution. The process that the Bayesian posterior models doesn’t necessarily have anything to do with Markov chains.


Absolutely. That’s what is umder the hood, as far as I red. But is it also possible to use Stan to model the roughly described presses with the benefit of Bayesian inference?


That depends. How would you describe your problem in mathematical notation?