Multivariate Lifetime Distributions
In most reliability analysis, components of a system are assumed to have independent lifetime distributions. However, in many reliability situations, it is more realistic to assume some form of dependence among components. For instance, we may observe the phenomenon that one component’s survival would increase the chance of another component’s survival, which is termed “positive dependence” in reliability. This positive dependence among component life lengths arises from common environmental stress and shocks, from components depending on common sources of power, and so on. Multivariate lifetime distributions are used to describe life length of multicomponent systems, taking component dependence under consideration.