A bivariate failure time model with random shocks and mixed effects

The object of the present paper is the study of the joint lifetime of d components subject to a common stressful external environment. Out of the stressing environment, the components are independent and the lifetime of each component is characterized by its failure (hazard) rate function. The impact of the external environment is modelled through an increase in the individual failure rates of the components. The failure rate increments due to the environment increase over time and they are dependent among components. The evolution of the joint failure rate increments is modelled by a non negative multivariate additive process, which include Lévy processes and non-homogeneous compound Poisson processes, hence encompassing several models from the previous literature. A full form expression is provided for the multivariate survival function with respect to the intensity measure of a general additive process, using the construction of an additive process from a Poisson random measure (or Poisson point process). The results are next specialized to Lévy processes and other additive processes (time-scaled Lévy processes, extended Lévy processes and shock models), thus providing simple and easily computable expressions. All results are provided under the assumption that the additive process has bounded variations, but it is possible to relax this assumption by means of approximation procedures, as is shown for the last model of this paper.

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“…This behaviour is coherent with what could be expected in such a context (see e.g. [23]). Example 1 We here consider a Clayton-Lévy copula…”

Section: ⊓ ⊔supporting

confidence: 92%

A general multivariate lifetime model with a multivariate additive process as conditional hazard rate increment process

Mercier

Sangüesa

2022

Metrika

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“…Vaidyanathan et al [33] contribute a bivariate distribution to model lifetime data using the Morgenstern approach and study the reliability properties of the contributed model. Mercier and Pham [34] design a bivariate random shock model and review the reliability of the shock model. Lee et al [35] provide a bivariate distribution using conditional failure rate to model discrete random variable.…”

Section: Introductionmentioning

confidence: 99%

Modeling of System Availability and Bayesian Analysis of Bivariate Distribution

Farooq,

Gul,

Alshanbari

et al. 2023

Symmetry

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To meet the desired standard, it is important to monitor and analyze different engineering processes to obtain the desired output. The bivariate distributions have received a significant amount of attention in recent years due to their ability to describe randomness of natural as well as artificial mechanisms. In this article, a bivariate model is constructed by compounding two independent asymmetric univariate distributions and by using the nesting approach to study the effect of each component on reliability for better understanding. Furthermore, the Bayes analysis of system availability is studied by considering prior parametric variations in the failure time and repair time distributions. Basic statistical characteristics of marginal distribution like mean median and quantile function are discussed. We used inverse Gamma prior to study its frequentist properties by conducting a Monte Carlo Markov Chain (MCMC) sampling scheme.

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“…The current literature continues to propose many extensions and refinements of shock models. In (Mercier and Hai Ha 2017), for example, a bivariate failure model is proposed for which some shocks may be fatal while others are damaging but not fatal. Stochastic processes as models for system degradation have also been studied in depth.…”

Section: Introductionmentioning

confidence: 99%

A new class of survival distribution for degradation processes subject to shocks

Lee

Whitmore

2019

J Stat Distrib App

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Many systems experience gradual degradation while simultaneously being exposed to a stream of random shocks of varying magnitudes that eventually cause failure when a shock exceeds the residual strength of the system. In this paper, we present a family of stochastic processes, called shock-degradation processes, that describe this failure mechanism. In our failure model, system strength follows a geometric degradation process. The degradation process itself is any Lévy process, that is, any stochastic process with stationary independent increments. The shock stream is a Fréchet stochastic process, a process derived from the Fréchet extreme-value distribution. Finally, the shock-degradation process is a convolution of the Fréchet shock process and any one of the candidate degradation processes. The system fails at the first occasion when a shock takes system strength across a threshold at zero. The paper presents results for Wiener diffusion processes and gamma processes as examples of Lévy degradation processes. The paper develops key statistical properties of the process model and its survival distribution, including several that are important for its practical application. As the failure mechanism is a first hitting time event, applications that require regression structures fall within the domain of threshold regression methodology.

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A bivariate failure time model with random shocks and mixed effects

Cited by 10 publications

References 29 publications

A general multivariate lifetime model with a multivariate additive process as conditional hazard rate increment process

A general multivariate lifetime model with a multivariate additive process as conditional hazard rate increment process

Modeling of System Availability and Bayesian Analysis of Bivariate Distribution

A new class of survival distribution for degradation processes subject to shocks

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