Minimum Required Analyses for Multiple Failure Mode Detection in Resource-Constrained Reliability Testing

Failure analysis, or forensic analysis of failed circuit elements, is an integral part of reliability assessment for the development of new materials and systems, particularly heterogeneously-integrated systems where multiple underlying failure mechanisms (modes) exist. To detect the presence of more than one failure mechanism, we usually require destructive, expensive tests (autopsies or analyses) on a number of failed units. Developing selective failure analysis strategies in the presence of limitations on time and resources is of the utmost importance. Using mixture and competing-risks models of Weibull distributions, this paper develops a probabilistic method to determine the minimum number of post-failure physical tests (analyses) required to detect the presence of more than one failure mode from the results of accelerated life tests, showing that (i) a successful detection of the presence of two distinct failure modes can be performed with 95% confidence for failure dataset sizes as small as 10 (without requiring exhaustive failure analysis on all units), and (ii) the minimum number of units to be analyzed (on average), expressed as a fraction of the sample size, decays exponentially with a power of the sample size, demonstrating the feasibility of the detection method. Our method can also handle component distributions other than Weibull. Results on three real experimental datasets are presented, along with statistical validation.