Dependence in failure times due to environmental factors

In many applications, common factors influence a set of failure (or survival) times of interest. This is, for instance, the case in mortality analysis, where mortality is influenced by socio-economic and health factors, or in the analysis of time-to-failure observations, where the items are functioning under similar conditions. This paper aims to answer the following question: is it true that more positively dependent factors generate more positively dependent outcomes? The analysis is conducted with the help of various stochastic order relations.