Reliability Model for Step-Stress and Variable-Stress Situations

We propose a reliability model for describing the lifetime of devices and materials working under variable stress (i.e., stresses which are a function of time). The model is based on a two-parameter Weibull distribution obtained by retaining the leading term from a series expansion of a general cumulative hazard function. The scale parameter is related to the real-stress time evolution by means of a differential equation which can be integrated. The paper shows that the solution of this differential equation approaches a well defined asymptotic behavior when the time approaches infinity. The proposed model may include the physics involved in the failure criterion, and hence it can be consistent with accelerated life, step-stress, and variable-stress tests. This important property is illustrated by using the proposed reliability model to build statistical distributions for the lifetime of aluminum-alloy electrical wire connections, and thin film cracking in plastic integrated circuits which are stressed by temperature cycling, and thermal shock testing. A final discussion studies how the model allows extending the applicability, for example, by including time and stress thresholds in the failure criterion.