Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually this property is observed asymptotically as time tends to infinity , which is due to the fact that a mixture failure rate is ‘bent down’, as the weakest populations are dying out...

A bivariate competing risks problem is considered for a rather general class of survival models. The lifetime distribution of each component is indexed by a frailty parameter. Under the assumption of conditional independence of components the correlated frailty model is considered. The explicit...

Burn-in is a widely used engineering method which is adopted to eliminate defective items before they are shipped to customers or put into the field operation. In the studies of burn-in, the assumption of bathtub shaped failure rate function is usually employed and optimal burn-in procedures are...

Mixtures of distributions are usually effectively used for modeling heterogeneity. It is well known that mixtures of DFR distributions are always DFR. On the other hand, mixtures of IFR distributions can decrease, at least in some intervals of time. As IFR distributions often model lifetimes...

An impact of environment on mortality, similar to survival analysis, is often modeled by the proportional hazards model, which assumes the corresponding comparison with a baseline environment. This model describes the memory-less property, when the mortality rate at a given instant of time...

A system subject to a point process of shocks is considered. Shocks occur in accordance with a nonhomogeneous Poisson process. Different criterions of system failures are discussed in a homogeneous case. Two natural settings are analyzed. Heterogeneity is modeled by an unobserved univariate...

Some stochastic approaches to biological aging modeling are studied. We assume that an organism acquires a random resource at birth. Death occurs when the accumulated dam-age (wear) exceeds this initial value, modeled by the discrete or continuous random vari-ables. Another source of death of an...

Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually this property can be observed asymptotically as time tends to infinity. This is due to the fact that the mixture failure rate is ‘bent down’ compared with the corresponding...

If aging is understood as some process of damage accumulation, it does not necessarily lead to increasing mortality rates. Within the framework of a suggested generalization of the Strehler-Mildwan (1960) model, we show that even for models with monotonically increasing degradation, the...

Statistical analysis of data on the longest living humans leaves room for speculation whether the human force of mortality is actually leveling o®. Based on this uncertainty, we study a mixture failure model, introduced by Finkelstein and Esaulova (2006) that generalizes, among others, the...