A reliability model for non-isothermal isotropic damages

Abstract

This study introduces a novel lifetime distribution originating from the Neyman Type A distribution. We built a Neyman Type A counting process and developed a survival function. Some statistical properties of the new distribution were presented, such as the resulting humped hazard function and its convergence. An accelerated test model structure with Arrhenius law was specified, and the effects of different accelerating stresses were analyzed. The hazard function implied by the model is inversely proportional to the stress, which results in interesting features and provides an efficient approach to describe the lifespan phenomena of some engineering metals and bulbs under low temperatures. The estimation of parameters of the accelerated model by maximum likelihood, mean time to failure, and expected number of failures are discussed in the numerical experiments.