On some stochastic properties of lives lived and left in non-stationary populations.

First, we revisit the "life lived equals life left" property for stationary populations and discuss it from a more general perspective. Specifically, we show that identically distributed random age and the remaining lifetime in stationary populations have the same distribution as the equilibrium distribution of the renewal theory. Then we consider specific non-stationary populations that are closed to migration and have a constant birth rate.

Optimal Abort Rules for Multiattempt Missions.

Many real-world systems use mission aborts to enhance their survivability. Specifically, a mission can be aborted when a certain malfunction condition is met and a risk of a system loss in the case of a mission continuation becomes too high. Usually, the rescue or recovery procedure is initiated upon the mission abort.

Optimal Mission Abort Policy for Systems Operating in a Random Environment.

Many real-world critical systems, e.g., aircrafts, manned space flight systems, and submarines, utilize mission aborts to enhance their survivability.

Justifying the Gompertz curve of mortality via the generalized Polya process of shocks.

A new probabilistic model of aging that can be applied to organisms is suggested and analyzed. Organisms are subject to shocks that follow the generalized Polya process (GPP), which has been recently introduced and characterized in the literature. Distinct from the nonhomogeneous Poisson process that has been widely used in applications, the important feature of this process is the dependence of its future behavior on the number of previous events (shocks).

On some mortality rate processes and mortality deceleration with age.

A specific mortality rate process governed by the non-homogeneous Poisson process of point events is considered and its properties are studied. This process can describe the damage accumulation in organisms experiencing external shocks and define its survival characteristics. It is shown that, although the sample paths of the unconditional mortality rate process are monotonically increasing, the population mortality rate can decrease with age and, under certain assumptions, even tend to zero.

Lifesaving, delayed deaths and cure in mortality modeling.

We generalize the lifesaving model to the case when the probability of lifesaving depends on the number of lifesavings in the past. We also suggest a new approach to analyzing the shape of mortality rates based on considering delays in deaths (and possible cure afterwards) which results in the decline of mortality rates. The derived lifetime distribution and the corresponding mortality rate can be used for a more flexible statistical analysis of mortality data.

On ordered subpopulations and population mortality at advanced ages.

We consider hazard (mortality) rates in heterogeneous populations consisting of ordered (in the defined stochastic sense) subpopulations. This setting can be interpreted via the fixed frailty models with one or more frailty parameters. The shape of the hazard rate is of main interest in this paper.

Admissible mixing distributions for a general class of mixture survival models with known asymptotics.

Statistical analysis of data on the longest living humans leaves room for speculation whether the human force of mortality is actually leveling off. Based on this uncertainty, we study a mixture failure model, introduced by Finkelstein and Esaulova (2006) that generalizes, among others, the proportional hazards and accelerated failure time models. In this paper we first, extend the Abelian theorem of these authors to mixing distributions, whose densities are functions of regular variation.

On the 'rate of aging' in heterogeneous populations.

It is well known that the rate of aging is constant for populations described by the Gompertz law of mortality. However, this is true only when a population is homogeneous. In this note, we consider the multiplicative frailty model with the baseline distribution that follows the Gompertz law and study the impact of heterogeneity on the rate of aging in this population.

Aging: damage accumulation versus increasing mortality rate.

If aging is understood as some process of damage accumulation, it does not necessarily lead to increasing mortality rate. Within the framework of a suggested generalization of the Strehler-Mildwan (1960) [B.L.