Related papers: Reliability modeling and statistical analysis of a…

Accelerated degradation tests are used to provide accurate estimation of lifetime properties of highly reliable products within a relatively short testing time. There data from particular tests at high levels of stress (e.\,g.\ temperature,…

The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…

We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…

We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that…

One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale…

Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…

Successful modeling of degradation performance data is essential for accurate reliability assessment and failure predictions of highly reliable product units. The degradation performance measurements over time are highly heterogeneous. Such…

Accelerated degradation tests are used to provide accurate estimation of lifetime characteristics of highly reliable products within a relatively short testing time. Data from particular tests at high levels of stress (e.g., temperature,…

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…

In recent years, more attention has been paid prominently to accelerated degradation testing in order to characterize accurate estimation of reliability properties for systems that are designed to work properly for years of even decades.…

Financial markets have long since been modeled using stochastic methods such as Brownian motion, and more recently, rough volatility models have been built using fractional Brownian motion. This fractional aspect brings memory into the…

In chemical and manufacturing processes, unit failures due to equipment degradation can lead to process downtime and significant costs. In this context, finding an optimal maintenance strategy to ensure good unit health while avoiding…

We propose a method for the algorithmic quantum simulation of memory effects described by integrodifferential evolution equations. It consists in the systematic use of perturbation theory techniques and a Markovian quantum simulator. Our…

Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the…

Analysis of non-Markovian systems and memory induced phenomena poses an everlasting challenge for physics. As a paradigmatic example we consider a classical Brownian particle of mass $M$ subjected to an external force and exposed to…

With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…

This paper proposes a gamma process for modelling the damage that accumulates over time in the lumber used in structural engineering applications when stress is applied. The model separates the stochastic processes representing features…

Accurate and robust trajectory predictions of road users are needed to enable safe automated driving. To do this, machine learning models are often used, which can show erratic behavior when presented with previously unseen inputs. In this…

We study the consequences of adopting the memory dependent, non-Markovian, physics with the memory-less over-damped approximation usually employed to investigate Brownian particles. Due to the finite correlation time scale associated with…

Understanding degradation is crucial for ensuring the longevity and performance of materials, systems, and organisms. To illustrate the similarities across applications, this article provides a review of data-based method in materials…