Comparing Populations Using Confidence Bands

[Mark Clair]

Background: One method for comparing populations is to put confidence bands around each population and check for overlap. The check for overlap is to occur at a particular B-level. My understanding is that Waloddi Weibull used the B-10 level for his work with bearings.

Question: What criteria do you use to determine the best B-level to make the comparison at?

My thought is that the comparison is best made at a level where you have plotted points. For instance, if you have very few failures and a large quantity of non-failures then it would seem more appropriate to me to do the comparison at the B1 level rather than the B10 level since plotted failure points would be nearer the B1.

I'm interested in others opinions and also whether anyone knows of any research directly related to this specific question that could help.
Thanks.

[Pantelis]

Are you comparing population or are you comparing specific percentages? You start by mentioning populations and then change it to specific values?

[Mark Clair]

Thanks for the response. The comparison is for populations not for a specific B value. However, our instruction on The Double Bounds Overlap method of comparing populations is that rather than checking for any overlap at all we should select a particular B-level a-priori and check for overlap there -- if there is overlap at that B-level then we would conclude there is no significant difference between the two populations. My questions is: how do we select the B-level to make the comparison at. I'm glad that I got a response on this. Hopefully this clarifies my question.

[Pantelis]

The reason you do not know an exact B value is because there isn’t a specific one for what you are trying to do. If you are comparing overall populations a more correct approach is to look at it using contour plots instead of the method mentioned. Contour plots are confidence intervals on the parameters and in the parameter space. What you are looking for is overlaps in this plot.

For additional info on contour plots see:

http://www.weibull.com/LifeDataWeb/tests_of_comparison.htm

http://www.weibull.com/hotwire/issue18/relbasics18.htm

http://www.weibull.com/hotwire/issue19/relbasics19.htm

http://www.weibull.com/LifeDataWeb/likelihood_ratio_confidence_bounds_on_time_type_1. htm

http://www.weibull.com/LifeDataWeb/likelihood_ratio_confidence_bounds_on_reliability_ type_2.htm