Related papers: Generalized Shock Model Based On The Frequency of …
We propose a generalized extreme shock model with a possibly increasing failure threshold. While standard models assume that the crucial threshold for the system may only decrease over time, because of weakening shocks and obsolescence, we…
In this paper we study the distributional properties of a vector of lifetimes in which each lifetime is modeled as the first arrival time between an idiosyncratic shock and a common systemic shock. Despite unlike the classical…
The distribution of waiting times until the occurrence of a critical event is a crucial statistical problem across several disciplines in Science. In this work we present a statistical model in which a relevant quantity X accumulates until…
In this paper, a new reliability model has been developed for a single system degrading stochastically which experiences soft and hard failure. Soft failure occurs when the physical deterioration level of the system is greater than a…
The present study supposes a single unit and investigates cumulative damage and catastrophic failure models for the unit, in situations where the interarrival times between the shocks, and the magnitudes of the shocks, involve two different…
This paper examines the lifetime distributions of circular $k$-out-of-$n$: G balanced systems operating in a shock environment, providing a unified framework for both discrete- and continuous-time perspectives. The system remains…
A system is considered, which is subject to external and possibly fatal shocks, with dependence between the fatality of a shock and the system age. Apart from these shocks, the system suffers from competing soft and sudden failures, where…
We present a general prediction scheme of failure times based on updating continuously with time the probability for failure of the global system, conditioned on the information revealed on the pre-existing idiosyncratic realization of the…
Scaling analysis reveals striking regularities in earthquake occurrence. The time between any one earthquake and that following it is random, but it is described by the same universal-probability distribution for any spatial region and…
A new class of probabilistic models for cascading failure propagation in interconnected systems is proposed. The models take into account important characteristics of real systems that are not considered in existing generic approaches.…
External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical…
We consider a competing risks model, in which system failures are due to one out of two mutually exclusive causes, formulated within the framework of shock models driven by bivariate Poisson process. We obtain the failure densities and the…
We propose a simple theory for the ``universal'' scaling law previously reported for the distributions of waiting times between earthquakes. It is based on a largely used benchmark model of seismicity, which just assumes no difference in…
In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $\delta$, the so called refraction period. This prevents the optimal exercise times…
We consider a network consisting of $n$ components (links or nodes) and assume that the network has two states, up and down. We further suppose that the network is subject to shocks that appear according to a counting process and that each…
Strengthening of materials and preventing abrupt fracture are really challenging jobs in the field of engineering and material science. Such problems can be resolved by using composite materials. In this work, we have studied the fracture…
Collapse and reverse to collapse explosion transition in self-gravitating systems are studied by molecular dynamics simulations. A microcanonical ensemble of point particles confined to a spherical box is considered; the particles interact…
We introduce a class of continuous-time bivariate phase-type distributions for modeling dependencies from common shocks. The construction uses continuous-time Markov processes that evolve identically until an internal common-shock event,…
Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show…
We show that the failure time $\tau_f$ in fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder $\delta$ and the stress release range $R$ in the system. For $R$ beyond a…