Distibution Selection

[Anonymous]

When determining the best distribution fit for a group of 18 failures, Reliasoft's Weibull software suggested the use of Weibull 3 parameter (Weibull 2 parameter was ranked fourth). When determining the best distribution for a data set, what criteria does Reliasoft use to determine which is a better fit for a Weibull distribution (2 or 3 parameter)?

It has been presented to me that this data set, a 2 parameter analysis should be performed despite Reliasoft's predictions. Is there any reason (e.g. low number of failures) that this should be the case?

[Dr. Dave Olwell]

Choosing a distribution to model a data set involves both empirical evidence and the use of knowledge of the object being modeled.

The Weibull 3-parameter and the exponential 2-parameter distributions include translation parameters, denoted by gamma. If gamma is positive, that is equivalent to modeling a failure free period in the life of the product. If gamma is negative,that means that failures can occur before time zero. Sometimes this makes sense, and we use a translation parameter. Other times, even though a model with gamma fits the data best, it doesn't make sense to use a 3-p model given what we know about the product.

We go through examples in our life data analysis class that make this point.

If a translation parameter doesn't make sense, one can exclude it from consideration by adjusting the options in the distribution wizard.

As a footnote, I also exclude the lognormal distribution from time to time when modeling data if I think the failure rate behavior implied by the lognormal distribution is inappropriate.

These judgements do not have much to do with the amount of data, although as one gets more and more data --- assuming it is a random sample --- one should give the empirical fit higher weight when doing this sort of balancing.


Hope this helps. Thanks for a good question.

Dr. Dave Olwell