B10 value using weibull vs by hand

[vnigam]

In order to understand the sofware, I entered some hypothetical failure time and got a weibull fit. I run the analysis using lower 1 sided, and 2 sided CBs. The parameters I got for the sample is beta=2.2670, Eta=36.6997. With this decided to estimate the B10 life for the given data. By hand I get:

(-Ln(0.9))=exp(-(t/36.6997)^2.2670
Solving this I get t=13.600 where as the QCP gives me 11.7474

I see a similar gap in the upper nad lower band calculations based on the upper and lower band parameters.

Can you please explain?

Thanks

[Pantelis]

The equation [(-Ln(0.9))=exp(-(t/36.6997)^2.2670], as given in your post is wrong..

Note the following derivation starting with reliability equation for a 2P Weibull...
If
R=exp(-(T/h)^b)
then
ln(R)=-(T/h)^b
-ln(R)=(T/h)^b
solving for T yields
T=((-(ln(R))^(1/b))*h)
which then gives you T=13.6 as given by the software for the parameter set you provided.

Now did you reverse 11.7 and 13.6 in your post (i.e. you computed 11.7 and got 13.6 from the software) … Because you do get 13.6 both from the software and the correct equation?

I have no idea how you are computing the upper and lower bounds, thusly I cannot comment on this. In other words the above equation does not look at bounds, but provides the B10 value based on the parameters only. The equations to compute bounds are by no means trivial. See http://www.weibull.com/LifeDataWeb/confidence_bounds_for_the_weibull_distribution.htm

Hope this helped.

[vnigam]

I am sorry for the mess up! I used the same equation you have used in your response. The times match by hand Vs the QCP. Thanks again!

I am evaluating the Weibull++ Version 7 free trial so I could not save the hypothetical data I had a couple of days ago.

I ran the analysis again using, time=10,20,30,40,50
The analysis is set at MLE, SRM, FM and K-M
Confidence: Both 1-sided CB at 90% I am estimating B10 time

The lower CB of Beta= 1.4287, Eta=26.1010
The Upper CB of Beta=3.6826, Eta=44.1406

The Weibull fit parameters are: Beta=2.2938, Eta=33.9428

The B10 life : Lower (software)=6.9833 Vs 5.402 by hand (using the equation you have used)

The B10 life : Upper (software)=23.189 Vs 23.9579 (by hand)

Summary of Hand Calculations:
Lower B10:

((-Ln(0.9))^(1/1.4287))*26.1010=5.402

Upper B10:

((-Ln(0.9))^(1/3.6826))*44.1406=23.9579

Can you explain please?

VN

[Pantelis]

Yes I can explain..

Basicly you can't use the equation and plug in the values of the parameters at a confidence interval... its more complicated than that. See the sectioin mentioned in the prior email as to how to do it by hand. In other words the way you are trying to compute the conf. for BX is incorrect.

[vnigam]

I am not computing the confidence the Upper nad Lower Confidence of the the parameters as it is already calculated using the selected method built in the Weibull ++ software (as per the procedure highlighted in the link). I am just trying to verify the B10 life lower confidence time for the given data.

If what I am doing is incorrect what is the significant of the upper and Lower parameter values for the fit? What does it help me estimate?

I will greatly appreciate your insight in this.

Thanks

[Pantelis]

Well, like any metrics the intervals of the parameters give you an insight as to what the uncertainty is for the parameters... This is useful in many practical applications, including acclerated testing.. i.e. is there a sig diff in the value of beta, prior bayesian beta etc. Now to compute the conf on a metric i.e. B10 the conf on the parameters do factor in, but not in the way you are trying to do it. Basicly and if you looked at the section I pointed to earlier the computation looks at the parameters .. var beta and var of eta but also looks at their cov .. a metric that you are missing in your equation. Hope this helps.

P.

Please do take the time to study the ref I gave you... It should explain what you are looking for and save me from retyping that section here.

[vnigam]

I greatly appreciate your time. I shall try and go through the link material again!

Last thing I would like to do is to put you under any inconvenience.

Thanks