Weibull Bayesian

[Temanag]

hello!

when I want to use weibull bayesian I must enter the beta distribution`s name and its parameter. - for example -lognormal distribution
when I click OK (Calculate) what happens?

the data are analysed also with the lognormal distribution?????
hm, I don`t know, but after klicking OK (Calculate) I see the same lognormal distribution parameters.

I don`t really understand this.
Can you help me?

Tnaks

[Tarik El-Azzouzi]

When using the Weibull-Bayesian distribution you are required to specify a distribution that describes your prior knowledge about the beta parameter. That distribution, along with the data and the Weibull failure distribution assumption is used to obtain the posterior pdf.

Once you enter the prior distribtuion and calculate you will see on the right side the distribution you entered and the value of the median value of the posterior distribution of beta. This by itself doesn't tell you or help you much. You should use the QCP to calculate various reliability metrics or using the plotting feature to obtain reliability related plots.

If you are interested in the theory behind this type of analysis, I suggest you read the material presented in the following links:
http://www.weibull.com/LifeDataWeb/bayesian_statistics.htm
http://www.weibull.com/LifeDataWeb/weibull-bayesian_analysis.htm

[Temanag]

When I analyse my data with Weibull Bayesian (using the parameter of b-prior distribution)
with weibull++ I can

1)plot the data with confidence bounds and so on...
2)make calculations with QCP

But where are the parameter of the distribution when I use Weibull Bayesian? Are they the same parameter when I don`t use Weibull Bayesian?

I know that the effect of using Weibull Bayesian is that the confidence bounds of the distribution are not so wide in compare to the confidence bounds when I don`t use the Weibull Bayesian.
I think that not only the confidence bounds change but also the form of the probability distribution change=>that means the parameter of the distribution are not the same, is that right?

[Tarik El-Azzouzi]

The Weibull distribution is defined in Equation (45) in http://www.weibull.com/LifeDataWeb/weibull-bayesian_analysis.htm. We can't talk about the Weibull-Bayesian in the same 'way' we talk about regular distributions, it's not simply defined with a straightforward function of some parameters, as you see in Equation (45), there are distributions of beta and eta embedded in its definition, so we don’t have just one value of beta and one value of eta to estimate and report. When you use the Weibull-Bayesian, the “shape” of the distribution is different from the parameters you would normally obtain if you use a regular Weibull distribution, that's because the regular Weibull distribution only uses the data to come up with the distribution, while the Weibull-Bayesian uses the data AND the prior distribution that describes your prior knowledge about the beta parameter.

By the way you can obtain Bayesian bounds without having to use the Weibull-Bayesian. Use the Weibll-Bayesian only when you have prior info about beta. The Bayesian bounds methods can be used with regular distributions (you have to the use the Maximum Likelihood Estimation (MLE) method as the parameter estimation method if you want to use the Bayesian bounds method)