Contour plot

[Pravin Kadekodi]

How do I use the contour plot? The plot is Eta on x axis vs beta on y axis.
Does it tell me and the values of Eta and Beta can vary between the limits covered by the contour (i.e Eta can be between x1 and x2 value where as beta can be between y1 and y2) with say 90% confidence?

If let us say for a test data the contour plot shows beta between 1.6 and 8.00 what do I conclude?

Pravin

[Arai.M]

The contour plot is used for a "visual" hypothesis testing. When comparing different data sets it can help you quickly detect important points. For example, if you were testing design A vs. design B and the contours at 99% CL for these two designs overlap, you would conclude that at 99% CL you fail to reject the hypothesis these are 2 statistically different populations. Another example is when you are doing accelerated testing, an important assumption is that the shape parameter stays constant. So if you were testing at three levels you would expect to be able draw a line across the shape parameter's axis, and to cross the three contour lines at the desired CL. You would also expect that these contours don't overlap, otherwise, you are testing 2 levels that are not statistically different.
Hope this helps!
Arai

[Pravin Kadekodi]

Got you....
I normally use the contour plots while comparing the equal slopes assumptions on acclerated test. But if the analysis is only for a stress level then does it provide me any useful infromation?

Thanks
Pravin

[Tarik El-Azzouzi]

Contour plots are explained in
http://www.weibull.com/LifeDataWeb/likelihood_ratio_confidence_bounds.htm.

They basically give a visual picture about the bounds on the parameters of a distribution for a certain confidence level.

In addition to their use as a way to verify the assumption of a constant shape parameter in accelerated life testing, contour plots can have many applications. Here is a few of them:

1- Contour Plots and Confidence Bounds on Parameters:
http://www.weibull.com/hotwire/issue18/relbasics18.htm
http://www.weibull.com/hotwire/issue19/relbasics19.htm

2- Comparing different data sets (ex. different designs, different suppliers…):
http://www.weibull.com/LifeDataWeb/using_contour_plots.htm

[Pravin Kadekodi]

Can I have a case where the contour plot limits do not match the QCP limits? If so what's the reason?
For eg: the limits shown in the pot are say beta between .1 to .5
and QCP shows the beta between .1 to 2.5

Pravin

[Tarik El-Azzouzi]

Yes there is that possibility.
This is due to the fact that the contour plot uses two degrees of freedom, while the QCP uses one degree of freedom.

read http://www.weibull.com/hotwire/issue19/relbasics19.htm for more info about contour bounds and confidence bounds on parameters

[Temanag]

hello :)

I read the issues about contour plot.
I have an understanding problem with the degree of freedom...

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

"Note that this plot has been generated with degrees of freedom k = 1, as we are only determining bounds on one parameter. The contour plots generated in Weibull++ (http://weibull.reliasoft.com/) are done with degrees of freedom k = 2, for use in comparing both parameters simultaneously."

what does it mean???

[Temanag]

another question...

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

the result :" it can then be concluded that the new design is better at the 90% confidence level"

ok, that means that I can be sure with 90% confidence that the new desing is better then the old design

I ploted the reliabilities of the two designs with 90% confidence level. the confidence borders intersect (new and old design). that means that the new design is not always better (with 90% confidence) then the old!

is that right? if yes, there is a conflict with the result in the issue

[Pantelis]

When using a contour plots - what you are looking at is the probability that the samples came from the same population – e.g. same underlying distribution (more correctly at an X% confidence level you can not conclude that they are from a different underlying population). When looking at the CL on a function, you are looking at the result of that function when evaluated (i.e. reliability at a point in time). An intersection may occur at a given reliability level – and a similar statement can be made about the reliability at that point in time. However, this is not the same as the first statement, thus no contradiction.

[Temanag]

thank you for your answer.
you are right. i tried to compare two fully different things.

the result :" it can then be concluded that the new design is better at the 90% confidence level"

ok, I can say that the old and the new design are different at the 90% confidence level, but why is the new design better?
bacause it`s mean life time is always bigger than the mean life time of the old design?

[Pantelis]

Better is not the best word. What is better?

You should make statements on the facts and not use words such as better. In other words and as an example you can say that the average life of the new is higher than the old design, etc.