A novel statistical method for step-down stress accelerated life tests using PSO and MLE

This paper focuses on the statistical method for the lifetime data from Weibull distribution in step-down-stress accelerated life tests (ALT). The key procedure of the ALT is to get the equivalent testing time of normal stress level from the higher stress, which is very sophisticated to solve with the traditional inverse moment method. This paper brings about a novel method, featuring maximum likelihood estimation (MLE) and particle swarm optimization (PSO) algorithm based iterative optimization. It's assumed the ALT lifetime data meets the Arrhenius equation, leaving the parameters a and b to be solved. First, using the failure data S_k at the highest stress, the Weibull distribution shape parameter m and characteristic life parameter η were obtained via MLE evaluation. Then, a new characteristic life parameter η is set for the next ALT stress level and a pseudo-failure data is generated from the stress corresponding failure data via the acceleration formula, and the new Weibull in and η pair is produced by using the pseudo-failure data. Under the premise that failure mechanism is consistent in ALT, it is deduced that the shape parameter m is consistent at different load stress, thus the iterative process of η optimization can be repeated by optimization the Arrhenius equation parameters a and b using PSO algorithm, till the appropriate distribution parameters are achieved by finding the global optimum value. According to the practical usage of the algorithm in the ALT data, it is proved that the algorithm in this paper is free from the table look-up technique by using GLUE or BLUE, and its accuracy is guaranteed by using the PSO algorithm which could avoid from local optimum.