Sample Size Estimate

[Tom Anderson]

[Originally Posted: 9/1/00--Transferred by ReliaSoft Moderator]

For a constant fialure rate regime, one can estimate a defective part per million (DPPM) from chi-square statistics using:

DPPM = [chi-sq{2f+2,1-alpha}*1e6]/(2*N), where f is the number of fails, alpha is a confidence limit and N is the sample size.

For bath tub curves, the above can be applied, but what can one use in the early failure rate portion of the bath tub curve, where failure rate is not constant but continuously decreasing. The above equation might be true as a burn in plan (reducing/eliminating) early failures approaches the constant failure rate portion of the curve.

Thanks for your help and comments ...

tom Anderson (tom325@ti.com)

[Dave Olwell]

[Originally Posted: 9/5/00--Transferred by ReliaSoft Moderator]

What are you trying to do? Determine a sample size to show that you exceed some reliability goal with a specified confidence? That is a difficult question. If a product greatly exceeds the requirement, it only takes a few samples to show it with the required confidence. If it barely exceeds the requirement, it will take many more samples to show it with the required confidence.

If you are trying to estimate a failure rate at a given time (DPPM(t)), that can be done but the sample size again will depend on how accurate you want the estimate to be and whether or not you need to show you exceed some threshold.

Please post your goal, and I'd be glad to try to help you once I understand it.

Best wishes,

Dave Olwell RSPS

[Tom Anderson]

[Orginally Posted: 9/7/00-- Transferred by ReliaSoft Moderator]

The goal is to estimate a DPPM level coming out of a burn in environment of ~1000 DPPM or less. I would assume that at this stage of a product life (integrated circuit) one would have culled out all infant mortality and any residual failures are part of the main population. Allowing for one failure and seeking demonstration of 1000 DPPM or better I am estimating a sample size of approximately 2000 devices for 60% confidence and 4000 devices for a 90% confidence that this would be attained.

The question originated because the equation I am using really assumes a constant failure rate, while the burn in environment in practice is not in that mode until sufficient time has been used to accelerate weak devices to an early failure.