Failure-Free Testing

Related to the Upper Probability of Failure (UPF) method for One Shot devices, failure-free (zero failure) testing offers relatively simple methods for calculations of sample size and the lower confidence limit on reliability.

Application

From the Certified Reliability Engineering Primer by the Quality Council of Indiana:

"When performing an acceptance test on one shot devices, or testing if devices work in a given application, zero failure testing can provide the information on reliability levels at a given level of confidence. This allows for determining the appropriate sample size to meet both reliability and confidence requirements.

Failure free testing is most appropriate when one has a high confidence that the item(s) meet the requirements."

Sample Size Calculation

Example: If an experimenter wishes to know if the reliability of their device design is at least 99% with 95% confidence, they would need to test 298 devices with no failures.

• An alternate interpretation of the confidence level: If we were to randomly sample 1000 groups of n = 298 devices from a large population of these devices, we would expect the interval estimate for the sample reliability to include the true population reliability in at least 950 of these groups.

Lower Confidence Limit on Reliability Calculation

Where alpha = (1 - confidence level)

Example: If an experimenter tests a random sample of 30 devices with zero failures, the lower 90% confidence level of reliability is 92.6%.