I need to predict when the next failure of a machine will be. I have a long history of its past failures, repairs, and preventive maintenance.

By common sense, I can guess there must be some positive or negative influence of the past incidents to the next failure. But I cannot find the right way to shape up a model counting all these past transactions.

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#### Best Answer

I think there is probably an interrogative process that needs to happen before a model can be recommended here.

In this process you or a domain expert may answer some of these questions. Additionally some of these assumptions might be investigated first by looking at the data. Lastly your interest in the results could be more clearly stated. When you predict do you hope to gain insight into the factors for a failure or do you simply want to anticipate/calculate these failures?

It might help you to know that there is a fairly mature body of literature called Reliability Engineering in which there are the usual variants of non-parametric, bayesian, stochastic, and fuzzy.

Some example questions:

- Can you assume that after a repair the machine is as good as a new machine, that it has aged by some factor, or that is in a second binary state (old)? You might consider Renewal Processes
- Do you expect/want to find out how time-to-failure is influenced by factors? You might consider Survival Analysis. It seems like you are suggesting this approach based upon your tags.
- Do you think there may be some hidden factors that govern the next failure time such as irregular jobs, faulty repair, or improper maintenance? You might consider Hidden Markov Models
- Is it your intuition that duration in time increases the chance of failure? Perhaps the number of previous failures increases the probability of another failure. You might research fitting Duration Dependence or Occurrence Dependence models respectively.

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