Sample size determination

[claude metzger]

Is there a mean to determine, before starting an accelerated testing campaign, the ideal sample size ?
I have to limit the number of samples, due to important costs...But on the other hand, I would be sure to have some defective parts during the test !
Is there a sttistical method able to determine this sample size, given for example an expected reliability and time life at a certain confidence level ?
I would appreciate your support.
Regards,
claude

[RS Support]

Yes there are (I am assuming you are talking about quantifying reliability with the tests). Having said that let me also point out that what you are asking is NOT trivial.

In standard test design (not accelerated) one optimizes (trades off) between sample size, test duration and accuracy. (See discussions at http://www.weibull.com/LifeDataWeb/test_design.htm and also at http://www.weibull.com/freetools/discuss_simumatic.htm).
The aforementioned methods assume that you have some knowledge as to the expected reliability of the products (i.e. an underlying life distribution).

Now when one goes into accelerated testing, one needs to assume the effect of the stresses on life (i.e. the acceleration factor from stress to stress). Based on that then one also needs to determine at what and how many stress levels to test at (if we assume a constant stress test) -- and each stress level will have an assumed effect on life. In doing this one also needs to be aware that the further one tests from the use conditions the greater the error in the extrapolation. Additionally the more stress levels one tests at the better the results. Taking all of that into account is a complex problem and beyond what one can cover in this forum. There are several papers that address this in the literature.

Now there are some approximations (simplistic/crude methods) one could use. Lets say you are testing at levels A and B and you have made an assumption as to the life of the units under normal conditions (i.e. if you tested 20 for 100 hours then 10 would fail). Then, if A has an AF of 2 and B has an AF of 4 you would expect 50% of the sample tested at A to fail by 50 hrs and 50% of the sample tested at B to fail by 25 hrs. This could also then be extrapolated to different times, thus simple sample allocation could be done this way -- based on the desired test duration. Obviously, you will find out that more units will need to be allocated at the lower stress levels.

I hope this sheds some light…

[Dr. Dave Olwell]

Meeker and Escobar have some rules of thumb in their book, "Statistical Methods for Reliability Data". I recommend them.

[Larry Strouse]

I have been asked where the nonparametric calculations come from in QCP, what is their background, etc. Do they represent a specific distribution?

[Pantelis]

Non-parametric implies no underlying distribution assumption. (see http://www.weibull.com/LifeDataWeb/nonparametric_analysis.htm)

Did you mean the DRT instead of the QCP?
see http://www.weibull.com/LifeDataWeb/test_design.htm