we propose to use a mathematical method based on stochastic comparisons of markov chains in order to derive performance indice bounds‎. ‎the main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (fcfs) orbit and general retrial times using the stochastic ordering techniques‎.

The class of new worse/better than used in expectation on average (NWUEA/NBUEA) distributions is proposed. It is defined by the requirement that for each age t a weighted average of mean residual lives be greater/smaller than the life expectancy at birth. The weights are the shares of ages up to t in the steady state stock which results from cohorts whose density is to be classified. The NWUEA ...

Here we propose a new definition of memory distributions in renewal-theoretic framework and study the corresponding notions ageing ordering distributions. Discrete life times are also considered.

In this paper we introduce a four-parameter generalized Weibull distribution. This new distribution has a more general form of failure rate function. It is more general for modeling than six ageing classes of life distributions with appropriate choices of parameter values, so it can display decreasing, increasing, bathtub shaped, unimodal, increasing-decreasing increasing and decreasing-increas...

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 governed by ageing processes, the operation of mixing can dramatically change the pattern of ageing. The...

In this paperwe study the properties of total time on test transforms of ordern and examine their applications in reliability analysis. It is shown that the successive transforms produce either distributions with increasing or bathtub-shaped failure rates or distributions with decreasing or upside bathtub-shaped failure rates. The ageing properties of the baseline distribution is compared with ...

We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indice bounds‎. ‎The main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (FCFS) orbit and general retrial times using the stochastic ordering techniques‎.

Lifespan distributions of populations of quite diverse species such as humans and yeast seem to surprisingly well follow the same empirical Gompertz-Makeham law, which basically predicts an exponential increase of mortality rate with age. This empirical law can for example be grounded in reliability theory when individuals age through the random failure of a number of redundant essential functi...

Failure distributions of components and assemblies are commonly approximated by analytical functions, e.g. by exponential or Weibull distributions. The advantages of this approach are its simplicity and the staightforwardness of the calculations. Another possibility is to describe failure distributions by means of Markov or semiMarkov chains, however several constraints are thereby introduced. ...

BACKGROUND Statistical models of normal ageing brain tissue volumes may support earlier diagnosis of increasingly common, yet still fatal, neurodegenerative diseases. For example, the statistically defined distribution of normal ageing brain tissue volumes may be used as a reference to assess patient volumes. To date, such models were often derived from mean values which were assumed to represe...