Background theory on Reliability

[dcallent]

My company currently uses your product though I have not had the opportunity to do so yet. I was wondering if you can point me to any white papers or background information you might have that explains how you can create a distribution from only two samples or how you can extrapolate reliability from only two stress levels.

Also, it does not appear that your software offers a degree of confidence with its calculations that I can see (I have only seen the graphs that have been output so perhaps the software does offer this information but just not on the graphs). Any help you could offer would be appreciated. Thanks...

[dcallent]

I found a pretty good discussion on some of the theory at http://www.weibull.com/AccelTestWeb/acceltestweb.htm but it does not help me understand the minimum number of samples needed to generate a good distribution (2 samples seems too small).

Also, I was wondering if you might be able to shed some light on what are acceptable methods for overstressing parts and characterizing legitimate failures, specifically when applied to motors. In my experience, I have elevated ambient temperature only and tested at full rated load to provide the stress. It does not seem to me that running the motor significantly above rated loads is a valid means of stress since specs that would never otherwise be exceeded are causing premature failures such as plastic parts melting, etc. instead of allowing wear on bearings etc. to be brought out. Your comments would be appreciated...

[Tarik El-Azzouzi]

A sample size of 2 is very small! Theoretically, if you have 1 factor (stress type) you get results from a sample size of 2 (if you assume an exponential distribution (constant failure rate assumption, i.e., no wearout, infant mortality…etc) or if you can assume a value for the beta parameter of the Weibull distribution or the Std Deviation of the Lognormal distribution. however with such a small sample size your results will be very uncertain (very wide confidence bounds).

When doing accelerated testing, since you are introducing another source of uncertainty (stress), you will normally need much more units to test then regular life testing. Deciding on the best number of units to test and how many stress levels to use for your stress factor and the stress levels is not a simple task. In Wayne Nelson's “Accelerated Testing – Statistical Models, Test Plans, and Data Anlsyses”, Ch6 describes test planning. Meeker and Escobar ‘s “Statistical Methods for Reliability Data” also discusses this topic. There are some specific models, but also some general allocation schemes, such as the
- Optimum Plans—Maximize statistical precision.
- Traditional plans—Equal spacing and allocation; may be inefficient.
- Optimized (best) compromise plans— require at least 3 levels of the accelerating variable (e.g., 20% constrained at middle) and optimize lower level and allocation.
You can visit these links for more details:
http://www.itl.nist.gov/div898/handbook/apr/section3/apr314.htm
http://www.public.iastate.edu/~wqmeeker/stat533stuff/psnups/chapter20_psnup.pdf

When doing accelerated testing, you have to be careful not to over accelerate and make the product fail in a way that is not how it would fail in normal operation (introducing new failure modes) exceeding the spec limits would cause nuisance failures.

ALTA does provide confidence bounds. In the QCP, you can select to show Confidence Bounds. As for plots, you can use the Confidence Bounds option in the Plot Options menu.

[dcallent]

Thanks for the links. Both proved very helpful...