Three-step concept (TSC) in modeling microelectronics reliability (MR): Boltzmann–Arrhenius–Zhurkov (BAZ) probabilistic physics-of-failure equation sandwiched between two statistical models

Abstract

When encountering a particular reliability problem at the design, fabrication, testing, or an operation stage of a product’s life, and considering the use of predictive modeling to assess the seriousness and the likely consequences of the a detected failure, one has to choose whether a statistical, or a physics-of-failure-based, or a suitable combination of these two major modeling tools should be employed to address the problem of interest and to decide on how to proceed. A three-step concept (TSC) is suggested as a possible way to go in such a situation. The classical statistical Bayes’ formula can be used at the first step in this concept as a technical diagnostics tool. Its objective is to identify, on the probabilistic basis, the faulty (malfunctioning) device(s) from the obtained signals (“symptoms of faults”). The recently suggested physics-of-failure-based Boltzmann–Arrhenius–Zhurkov’s (BAZ) model and particularly the multi-parametric BAZ model can be employed at the second step to assess the remaining useful life (RUL) of the faulty device(s). If the RUL is still long enough, no action might be needed; if it is not, corrective restoration action becomes necessary. In any event, after the first two steps are carried out, the device is put back into operation (testing), provided that the assessed probability of its continuing failure-free operation is found to be satisfactory. If the operational failure nonetheless occurs, the third, technical diagnostics step should be undertaken to update reliability. Statistical beta-distribution, in which the probability of failure is treated as a random variable, is suggested to be used at this step. While various statistical methods and approaches, including Bayes’ formula and beta-distribution, are well known and widely used in numerous applications for many decades, the BAZ model was introduced in the microelectronics reliability (MR) area only several years ago. Its attributes are addressed and discussed therefore in some detail. The suggested concept is illustrated by a numerical example geared to the use of the prognostics-and-health-monitoring (PHM) effort in actual operation, such as, e.g., en-route flight mission.