Modelling successive failure times

[Dominic]

Hi, if I have decided to assume that a single piece of equipment has renewal repairs (good as new) then I can say that the consecutive failure times are all independent and identically distributed. Can these times then be modelled using any distribution?

Also if I can, then is the measure of central tendency for this distribution i.e. the mean just the MTBF (between failures). I read in another discussion that this term should only be used for an exponential distribution. In my case why can I not use it for a weibull distribution.

Hope someone can help.

[Pantelis]

Well Dominic, on your first question yes. You can apply any distribution (one defined in the positive domain, i.e. 0 to infinity), as long as it fits the data. Furthermore when dealing with life data the failure rate behavior of the distribution should be considered when making a choice. As an example the exponential assumes a constant failure rate, an assumption that is more often than not incorrect.


As for the term MTBF, unfortunately it has been misused and misapplied. When fitting a distribution such as the Weibull, then the mean of the distribution is really the mean time to failure and not the mean time between failures, i.e. more correctly MTTF. Now the problem with the confusion is due to the fact that if the failure rate is assumed to be constant (exponential) then the Mean time “to” and mean time “between” are identical.

Now wrt central tendency, “central tendency" can refer to a wide variety of measures. The mean is the most commonly used measure of central tendency, but the median, and mode can also be used.

[Dominic]

Thanks Pantelis. I guess I thought I would use the term MTBF instead of MTTF as I was looking at the 2nd, 3rd, 4th etc. failure times. I have read in Ebeling - Intro to reliability... that the TBF refers to the operating time between failures. Therefore I thought it would be ok to then say that if these times are modelled by a distribution, then the mean of the distribution should be called the MTBF.

One other question if you don't mind, I know that in some cases assuming a renewal repair is not accurate. How much effect does this have on the results. Also are there any statements or things I can do to help justify my assumption of renewal repairs.

Thanks, again

Dominic

[Pantelis]

Yes MTBF would be appropriate if you are looking at times “between” failure. However you made the statement that each repair renders the “equipment as good as new” – and my answer is based on this assumption.

Now how accurate is this assumption – it depends on what the repair us doing. In general weibull analysis assumes as good as new. You can use growth models such as NHPP (http://www.weibull.com/RelGrowthWeb/n_h_h_p_.htm) if you want to assume as good as old, or use a more advanced type of analysis with a restoration factor (http://www.weibull.com/SystemRelWeb/imperfect_repairs.htm) for something in between.