Estimating proportion of failure

[Fudjie]

Hi,
I am trying to estimate the percentage of population of marbles that would break when dropped from a certain height. Basically what I am trying to do is given x % of marbles breaking from x height, y % of marbles breaking from y height, etc., what is the estimated % of marbles breaking when dropped from z height?
Can Weibull ++ analyze this problem? Of if not, I'd appreciate if you can recommend a method or a book.
Thanks very much.
Fudjie

[Pantelis]

Yes (as per discussion below)

a) Your random variable is the height dropped and the event is “it breaks”. (ref: http://www.weibull.com/LifeDataWeb/basic_statistical_definitions.htm)
b) If it does break then you would treat it as “complete data”; if it does not you treat it as “right-censored”. (ref: http://www.weibull.com/LifeDataWeb/data_classification.htm)
c) Fit a distribution to the data (Lognormal may be a better fit, but try Weibull also).
d) Compute the probability of failure (percent breaking) at any height z.

[Fudjie]

Thanks,
Last but not least, is the free form data sheet one tool I can use for the problem as well? Do you have a real world example that utilized this aproach?
Fudjie

[Pantelis]

It depends on how you perform the experiment.

a) Lets say you are dropping the marbles from different heights (i.e. from 10, 12, 13, 14 etc.). Then the data is the height along -- with if it failed (F) or if it did not (S). You would not use free form data if done this way.

b) Now if you take 20 marbles and drop 10 from 5 ft and 10 from 12 ft, then you could use free form data with the height and the cumulative percent failed at each height (i.e. if 2 failed at 5 ft and 4 at 12 ft then: X1=5, Y1=2/20, X2=12, Y2=6/20).

If you have not done the experiment yet -- I would be partial to (a) instead of the free form data approach.

This is my first marble experience :-)

[db]

I see this is a very old thread, but I thought perhaps if the marble broke you should consider treating it as left-censored - after all, you don't know that if you dropped the same marble from a lower height whether it might also have broken. Then you would have LC for the broken marbles and RC for the unbroken marbles - what Nelson and others call "quantal response data".