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...

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...

Simple models for the failure (mortality) rate change point are considered. The relationship with the mean residual lifetime function change point problem is discussed. It is shown that when the change point is random, the observed failure (mortality) rate can be obtained via a specific mixture...

The notion of repeated minimal repair is analyzed and applied to modeling the lifesaving procedure of organisms. Under certain assumptions the equivalence between demographic lifesaving model and reliability shock model is proved. Both of these models are based on the non-homogeneous Poisson...

The mortality rates are steadily declining with time. The remaining lifetime for e.g. 65 years old person even 20-30 years ago was substantially smaller than nowadays. Therefore, the age correspondence problem for populations in different mortality regimes is of interest. A simple solution,...

Simple series systems of identical components with spare parts are considered. It is shown that the cumulative distribution function of a system failure time tends to a step function as the number of components increases and resources can be shared. An example of ‘continuous resources’ is...

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...