Weibull fit for two groups, second group has no failuresHi folks.
In this old thread, @martindemel asked how to fit Weibull distributions to two groups simultaneously -- the first group has standard data, but the second group has only one failure. For the second group, user wished to fix the beta parameter, using the value from the first group, then estimate alpha. The answer was to use Fit Y by X , works like a charm.
I have a potential customer who wants to do the same thing, except group 2 has zero failures, only right-censored data. He claims this is possible in Weibull++, wants to replicate it in JMP. The method described earlier does not work here.
Any ideas? Attaching example dataset.
Thanks, Jordan
Re: Weibull fit for two groups, second group has no failuresNot sure how Weibull++ does it. Here is what first comes to my mind:
Launch Life Distribution with By
Fit Weibull to the first group, and here is Beta
The second group shows a rather peculiar report, this is for Weibayes analysis. If you see a regular Life Distribution, then you have tempered the preference at one point. In the report, enter the Beta value from the first group, make sure the check boxes are checked as in the screenshot. Click "Update". And you get a Weibayes estimate for Alpha, which is a conservative bound of Alpha. There is no point estimate.
When there are few or no failures, a full Bayesian approach can bring more useful result than Weibayes approach. But one needs to be knowledgeable about Bayesian inference and has prior knowledge distribution.
Re: Weibull fit for two groups, second group has no failuresSecond comes to my mind.
I see the data set is not real, but borrowed from Martin. So I have a question, what are the groups? Two suppliers, two designs? Or two temperatures, two voltages? If it is the latter, use a parametric relationship in Fit Life by X might be the answer. I attach a modified data with script.
The fitted model use a "Linear" relationship to associate the two groups. And here is the model result.
1/sigma is Weibull's Beta. and Exp(mu) is Weibull's Alpha. Plug in two values of G, you get two values of Alpha.
In addition, what products, materials, are they testing? Is it common to have all censored situation? If the grouping variable is indeed continuous, and they want to establish a relationship, they might have an ALT DOE problem.
Re: Weibull fit for two groups, second group has no failuresHi Peng, thank you for giving this some thought.
I think this is to assess the effectiveness of repairs and/or design changes. Here is a direct quote from the customer:
The scenario is creating an overlay plot with at least two distributions for fix effectiveness demonstration analyses. The first distribution would have failure and right censored data and the second distribution would just have passing (right censored data). With Weibull++, I can create a line for the second failure distribution by using the Weibull beta measured from the first distribution (just a simple 1P Weibull) and see how the distributions (particularly the eta values) compare. I also need to confidence lines to see how if they overlap as a statistical significance gauge.
Re: Weibull fit for two groups, second group has no failuresI suspect they are talking about Bayesian inference. Because Weibayes doesn't give point estimate for all-censored situation. If they see "a line" (assuming they mean some kind of center line) and "confidence line", that has to be Bayesian inference. For Bayesian inference in Weibull++, this page might be useful: Bayesian-Weibull Analysis in Weibull++
There is an data example towards the end of that page. And I attach a JMP data table to illustrate how to match the numbers.
JMP Table:
Launch dialog:
Check "Weibull":
Turn on "Bayesian Estimates"
Change to the "Location and Scale Priors".
Specify priors like what are in the following screenshot.
A short explanation about the choices:
The web page says:
Because location parameter = log(eta), so I use uniform with a very wide range.
The web page says:
That means, sigma = 1/beta, is lognormal(-0.9064, 0.3325).
And here is the result:
Their numbers:
Notice:
I consider that is a match, due to random nature of the inference, and their settings are not clear.
Since their data have no failures, they need to turn off the following preference in Life Distribution, in order to access Bayesian inference features. Default is On for Weibayes.
Attach the data table and script.
Re: Weibull fit for two groups, second group has no failuresLate update from the customer: it is indeed the Weibayes estimate that is displayed in his desired output from Weibull++. Here's the graph he wishes to reproduce:
Can we make a similar plot in JMP? I don't see a way to plot the Weibayes output.
Re: Weibull fit for two groups, second group has no failuresThe user has to make his/her own overlay in this case. Copy Frame Contents from the Weibayes CDF profiler and Paste Frame Contents to the CDF plot of the first group. One may need some trick to get rid of the unwanted artifacts, e.g. axes grid lines, and set Time=0 to get rid of the red cross reference lines.
