I am in the process of building a a model in order to estimate the need for spare parts at a factory. I will do so through simulation software, and I am trying to find an appropriate probability distrubtion in order to generate defective parts (i.e. demand for spare parts).
I was initially looking at the exponential distribution, however the memoryless-property does not suit this situation very well. I have an estimate of the 'time until breakdown' for each part, and each part is more likely to break down closer to 'time until breakdown' than right after is has been fitted.
Any suggestions on what probability distribution might be suitable for such a model?
The Weibull distribution has a good history of use in reliability analysis. It has a "bell-like" distribution, not a constant decaying curve like the exponential density. There is a lot of literature on Weibull Analysis. I'll not reproduce it here, as a Google search will turn up lots of stuff.
A couple higher-level things to think about:
Make sure you verify that the conditions that produced your estimates will hold going forward (i.e., future parts will experience similar use intensity) -- othwise, you will be estimating using data that is not representative.
Consider if failures are correlated -- will the failure of one part pre-dispose other parts to failure, or are groups of parts subject to the same impact (e.g., brakes and tires are subject to partially correlated wear).