Newbie Question Re Pump Repair Data

[Joe]

I'm preparing to do a Weibull analysis on some pump repair data. Say there are 10 pumps in the population. (I realized this is a small sample size, just keeping it manageable for illustration)

Assume the repair history showed the following:
Pump 1 failed after 30 days, was rebuilt, put back in service, failed again in 30 days, was rebuilt, put back in service and ran without failure the remainder of the year.
Pump 2 failed after 60 days, was rebuilt, put back in service and ran without failure the remainder of the year.
Pump 3 failed after 90 days, was rebuilt, put back in service and ran without failure the remainder of the year.
Pump 4 was rebuilt at 30 days (no failure)
Pump 5 was rebuilt at 60 days (no failure)
Pump 6 was rebuilt at 90 days (no failure)
Pump 7 ran all year without incident
Pump 8 ran all year without incident
Pump 9 ran all year without incident
Pump 10 ran all year without incident

So my data input for Weibull analysis would look something like this:

For Pump 1: 30 days, censor=0 (the second failure is ignored?)
For Pump 2: 60 days, censor=0
For Pump 3: 90 days, censor=0
For Pump 4: 30 days, censor=1
For Pump 5: 60 days, censor=1
For Pump 6: 90 days, censor=1
For Pump 7: 365 days, censor=1
For Pump 8: 365 days, censor=1
For Pump 9: 365 days, censor=1
For Pump 10: 365 days, censor=1

Am I on the right track here? I'm specifically wondering:
A - This is annual repair data. All I know is at t=0=January 1 that the pumps are up and runnning. I don't know for how long they have been running. But that doesn't effect my analysis.

B - Once a pump experiences an event (a failure, for example) I record that and ignore any other events for that pump.

C - A censored time = a suspension that occurs before failure. In other words, If I rebuild a pump as part of a pre-emptive strategy to prevent an unplanned outage, that is treated as a suspension, the same way the pumps that ran all year are treated as suspensions. And once they are suspended, any other events are ignored.

Any guidance, links, recommended reading would be appreciated.

Thanks

[Al]

Just one small point..you could use a Mixed Weibull Distribution for the 2nd failure for Pump 1

[tarik]

The fact that you don’t know for how long your pumps were running when you started observing them on Jan 1st, unlike you said, DOES AFFECT your analysis. That is because when you observe the first failure, you need to know how long a pump was running for before it failed in order to mark the right operating duration. I recommend you read the following material regarding this subject.
http://www.weibull.com/LifeDataWeb/data_and_data_types.htm
http://www.weibull.com/LifeDataWeb/data_classification.htm
http://www.weibull.com/LifeDataWeb/data_types_and_weibull++.htm (http://www.weibull.com/LifeDataWeb/data_types_and_weibull%2B%2B.htm)

For example, for pump 1, you had a failure after 30 days from when you started observing that pump. Because you don’t know for how long pump 1 was working before, all that you can say is that pump 1 lived for at least 30 days. So how do you express that uncertainty, well you have 2 options:
- To ignore this failure and not record it, and just record the second failure and the suspension at the end of the year.
or
- To use this piece of information in the interval data type format in Weibull++, by making an assumption about the maximum duration that pump could have been in operation for before you observed the first failure. Let’s say that duration is 6 months. In the case of the pumps 7,8,9,10 we would also assume that they have been running for 6 months before you started observing them.

The following table is how your data would look like in Weibull++


Last---------State---Time-------ID
Inspected----F/S-----to F/S-------
----------------------------------
30----------F--------210---------1
30----------F--------30----------1
205---------S--------205---------1
60----------F--------240---------2
205---------S--------205---------2
90----------F--------270---------3
275---------S--------275---------3
30----------S--------30----------4
335---------S--------335---------4
60----------S--------60----------5
305---------S--------305---------5
90----------S--------90----------6
275---------S--------275---------6
365---------S--------365---------7
365---------S--------365---------8
365---------S--------365---------9
365---------S--------365---------10

However, if you feel that the pumps were installed right before the beginning of the test (Jan 1st) then you can assume that the life before testing is 0 and the Weibull++ table would look like this

State---Time-------ID
F/S-----to F/S------
-----------------------
30----------F---------1
30----------F---------1
205---------S---------1
60----------F---------2
205---------S---------2
90----------F---------3
275---------S---------3
30----------S---------4
335---------S---------4
60----------S---------5
305---------S---------5
90----------S---------6
275---------S---------6
365---------S---------7
365---------S---------8
365---------S---------9
365---------S---------10

Note also that I don’t agree with Al’s comment about using a Mixed Weibull Distribution for the 2nd failure for pump1. Mixed Weibull distribution can be used when you have different underlying failure modes and that would be used across all your data not just a particular failure.

The above discussing is valid when assuming that when you rebuild a pump that it starts again as a new pump. If that is not a valid assumption, you could consider performing a repairable system analysis. The following material can provide you with information about this type of analysis

http://www.reliasoft.com/RG/index.html
http://www.weibull.com/hotwire/issue40/relbasics40.htm
http://www.weibull.com/hotwire/issue41/relbasics41.htm

[Al]

>>Mixed Weibull distribution can be used when you have different underlying failure modes
>and that would be used across all your data not just a particular failure.

This was exactly my thinking. One failure mode for brand new pumps, one for rebuilt

[tarik]

Al,
What you are saying is not correct. Joe doesn’t imply that there are different failure modes, if that was the case he can specify a failure mode for each failure time and use the competing failure modes model or if he didn’t know what failure modes caused each failure he can use the mixed Weibull if he notices that his data doesn’t fit a simple Weibull model and that there are some curvatures in his probability plot.
Here is some more information about the mixed Weibull model
http://www.weibull.com/LifeDataWeb/mixed_weibull_background.htm