A new class of bivariate Lindley distributions based on stress and shock models and some of their reliability properties

Abstract Shock and stress models are used in reliability analysis to describe different kinds of applications. For instance, shock may refer to damage caused to vital organs by illness or environmental causes. On the other hand, stress can relate, for example, to two components that were maintained working independently, and had joint maintenance scheduled at a fixed time. In this context, the presented paper is aimed to introduce a new class of bivariate Lindley distribution of the Marshall–Olkin type to evaluate a 2-component series system’s reliability function. The proposed methodology is based on introducing a latent variable following an Exponential or a Lindley distribution. The obtained results generalize those achieved by using a Marshall–Olkin bivariate Exponential distribution, suggesting a useful way to search for appropriate bivariate lifetime distributions, especially under engineering reliability studies or in other areas of quantitative research.