Related papers: Asymptotic Mean Time To Failure and Higher Moments…
The Meantime to Failure is a statistic used to determine how much time a system spends to enter one of its absorption states. This statistic can be used in most areas of knowledge. In engineering, for example, can be used as a measure of…
In this paper we show a limit result for the reliability function of a system -- that is, the probability that the whole system is still operational after a certain given time -- when the number of components of the system grows to…
This paper deals with system with $n$ identical elements and one repairing device. While one element working other ones stay in reserve. The distribution of element working and repairing times are supposed to be exponential. Here we obtain…
Many processes must complete in the presence of failures. Different systems respond to task failure in different ways. The system may resume a failed task from the failure point (or a saved checkpoint shortly before the failure point), it…
We study the large-time asymptotic of renewal-reward processes with a heavy-tailed waiting time distribution. It is known that the heavy tail of the distribution produces an extremely slow dynamics, resulting in a singular large deviation…
The time to failure, $T$, of dynamical models of fracture for a hierarchical load-transfer geometry is studied. Using a probabilistic strategy and juxtaposing hierarchical structures of height $n$, we devise an exact method to compute $T$,…
We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of It\^o semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of…
In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Here, we study the limiting behaviour of the mean residual life, and derive an asymptotic expansion which can be used…
This paper considers the problem of approximating the failure frequency of large-scale composite $k$-terminal reliability systems. In such systems, the nodes ($k$ of which are terminals) are connected through components which are subject to…
For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is non-zero for sets of infinite size. This fact could have a profound significance in…
Most theoretical analysis for lifetime distribution explains origins of specific distribution based on independent failure. We develop a unified framework encompassing different lifetime distribution for failure-coupled network systems. We…
Many tasks are subject to failure before completion. Two of the most common failure recovery strategies are restart and checkpointing. Under restart, once a failure occurs, it is restarted from the beginning. Under checkpointing, the task…
This paper shows how the steady-state availability and failure frequency can be calculated in a single pass for very large systems, when the availability is expressed as a product of matrices. We apply the general procedure to…
This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
This paper is focused on survival analysis of electrical components. The main goal of this paper is to develop a method for on-line estimation of the Mean Time To Failure (MTTF) of electrical components under dynamic stress levels. The…
We consider the first exit time of a nonnegative Harris-recurrent Markov process from the interval $[0,A]$ as $A\to\infty$. We provide an alternative method of proof of asymptotic exponentiality of the first exit time (suitably…
Many large-scale software systems demonstrate metastable failures. In this class of failures, a stressor such as a temporary spike in workload causes the system performance to drop and, subsequently, the system performance continues to…
In this paper we study a generalized class of Maxwell-Boltzmann equations which in addition to the usual collision term contains a linear deformation term described by a matrix A. This class of equations arises, for instance, from the…
In this work the asymptotic properties of $Q_t(N)$ ,the probability of the number of renewals ($N$), that occur during time $t$ are explored. While the forms of the distribution at very long times, i.e. $t\to\infty$, are very well known and…