Applying User Surveys and Accelerated Tests Data to Estimate Reliability of New Consumer Products Using a Discrete Life Distribution Model

Abstract

Assessing the reliability of consumer products that are subject to random discrete damage is critical during their design. Previous studies have approximated a continuous life distribution for consumer products by treating the occurrence (cycles) of accumulating damage as a continuous random variable. However, when the lifetime of a product is only a few damage cycles (e.g., ten drop cycles of a laptop), using a discrete lifetime distribution is more accurate. Using a discrete lifetime distribution is challenging because it contains a summation term with an unknown upper bound, which makes calculating its likelihood function cumbersome. This paper proposes a method to address this issue. First, the upper bound of the summation term is approximated through a gradient descent algorithm and the Maximum Likelihood Estimation method. Then, the upper bound is fixed, and the other parameters of the reliability model are estimated using Bayesian analysis. The paper presents a hypothetical case study that shows that using the discrete model leads to a more accurate estimation of product life when dealing with a small number of cycles.