Modeling Failure Probability of a Repairable systems with affecting factors

[#1]

Hello Community,

I would like to ask for a bit of help in this topic, I've read most of the posts and guides available for JMP as well as couple webinars, but I still can't realize how to model the following situation correctly.

Imagine you run an experiment with N systems, running for a period T, in which you observe several units (u1 to uN), some of them do fail (and are repaired and back to operation) and some others do not fail at all, so you have censored data and its censoring indicator.

* Running time between repairs is recorded in this way and the last measured running time before T expires.

* Running condition (on/off), running time and several other sensor measurements are recorded hourly until T (end of the experiment), so you hope these sensors may partially explain the failure rate

Questions:

a) While using  Fit Parametric Survival you can add location and scale factors as a way to incorporate variables that may affect the survival, but I don't know how to incorporate those factors into the recurrence analysis, so is it possible to model a recurrence analysis with affecting factors?

b) If you are here to predict failure probability using the sensor's measurements at a certain point t, would a Parametric Survival or Recurrence analysis make sense at all? 

Thanks a lot!!

Raul

[#2 · Accepted solution]

Based on your description, you should use Recurrence Analysis. Fit Parametric Survival is for non-repairable systems.

If you are interested in what would happen if one incorrectly uses Fit Parametric Survival or Life Distribution to analyze recurrent data, check out this talk Life Distribution or Recurrence Analysis . Dr. Trindade gave a striking example which leads to totally opposite conclusions. Some key slides: page 21, 24, 27.

To incorporate factors in recurrence analysis, check out the "Fit Model" section within the chapter for Recurrence Analysis in the documentation. Here is the link to JMP16.2 doc Fit Model in Recurrence Analysis . This should answer (a).

For (b), you will not be able to make interpretation like "System X's failure probability in the next two weeks is 1%.", but something like this "System X's is expected to experience 0.01 failure in the next two weeks." Notice the failure is a fraction. If you have a fleet of 100 such systems, all with the same recurrence rate, then you should expect one system will fail in the next two weeks.

[#3]

Thanks for the advice, I really appreciate it, I will try that approach and post here how it goes,

Cheers,

[#4]

Hi!
Well, I checked the resources given, they were great! But now I am facing another issue, derived from the requirement of having 'Age' for recurrence analysis. My data only has time to next failure, so question is:

* What would be a good strategy to define the initial 'Age' if you don't know it?

I don't have much data, so imputing the 1st repair and take the 2nd as the 1st would be my very last resort. Is it there a formal or commonly method to workaround this situation?

Many thanks again!
Cheers,
Raul