Introduction to a Binomial Approach to Accelerated Life Testing

This paper conceptualizes a new binomial damage model in accelerated life testing (ALT), where the relation between damage or life and stress is established using the binomial probability parameter. The model is explicitly designed to account for certain probabilistic occurrences where failure results from discrete (shock-based) stresses during their life, such as the dropping of a handheld device. A relationship between the binomial failure probability parameters at accelerated stress and use-stress levels is created by forming a binomial-based representation of the acceleration factor (AF) based on the ratio between the binomial distribution definition of use and accelerated life. The binomial AF is then related to the life-stress relation by defining appropriate models that account for multiple stress components, from which the life-stress relation can be used to describe accelerated binomial failure probability. Thus, the model parameters of the probabilistic predictive model are then found and estimated through the maximum likelihood estimation (MLE) and Bayesian estimation methods. In a conceptualized case study, an R-based computational tool was developed to demonstrate the new methodology on a selected life-(shock) stress model and two sets of simulated binomial-(shock) stress data for capacitors where temperature and voltage were the stress factors. The case study reveals several findings about the effectiveness of the binomial model application for ALT, including the observation of several correlative trends between the different model parameters as well as the stress levels. Although the case study was successfully tested, it is ultimately the desire to test the new Binomial ALT methodology on physical test data to certify its effectiveness.