On Excess-time Correlated Cumulative Processes

Agrafiotis, G. K.; Tsoukalas, Michail

doi:10.1038/sj/jors/0461010

Cited by 3 publications

(4 citation statements)

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“…In the literature, random shocks are typically modeled by Poisson processes (Li and Pham, 2005), distinguishing two main types, extreme shock and cumulative shock processes (Bai et al, 2006), according to the severity of the damage. The former could directly lead the component to immediate failure (Anderson, 1987), whereas the latter increases the degree of damage in a cumulative way (Agrafiotis and Tsoukalas, 1995). Esary and Marshall (1973) have considered extreme shocks in a component reliability model, whereas Wang et al (2011), Klutke and Yang (2002) and Wortman et al (1994) have modeled the influences of cumulative shocks on a degradation process.…”

Section: Degradation Modelingmentioning

confidence: 99%

Some Challenges and Opportunities in Reliability Engineering

Zio

2016

IEEE Trans. Rel.

180

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Today's fast-pace evolving and digitalizing World is posing new challenges to reliability engineering. On the other hand, the continuous advancement of technical knowledge and the increasing capabilities of monitoring and computing offer opportunities for new developments in reliability engineering. In this paper, I reflect on some of these challenges and opportunities in research and application. The underlying perspective taken stands on:  the belief that the knowledge, information and data (KID) available for the modeling, computations and analyses done in reliability engineering is substantially grown and continue to do so;  the belief that the technical capabilities for reliability engineering have been significantly advanced;  the recognition of the increased complexity of the systems, nowadays more and more made of heterogeneous, highly interconnected elements. In line with this perspective, opportunities and challenges for reliability engineering are discussed in relation to degradation modeling and integration of multi-state and physics-based models therein, accelerated degradation testing, component-, system-and fleet-wide prognostics and health management in evolving environments. The paper is not a review, nor a state of the art work, but rather it offers a vision of reflection on reliability engineering, for consideration and discussion by the interested scientific community. It does not pretend to give the unique view, nor to be complete in the subject discussed and the related literature referenced to.

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Section: Degradation Modelingmentioning

confidence: 99%

Some Challenges and Opportunities in Reliability Engineering

Zio

2016

IEEE Trans. Rel.

180

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“…While in the extreme shock case, shock effects are memoryless and the system breaks down as soon as the magnitude of an individual shock is larger than the threshold. With relations (1) and (2), the so-called cumulative shock process { ( ); ≥ 0} and maximum shock process { ( ); ≥ 0} can be defined by…”

Section: Introductionmentioning

confidence: 99%

“…Due to the important theory value and the broad application areas, shock models remain an academic focus in reliability researches during the last three decades. The main literatures on the two types of shock models include 2 Mathematical Problems in Engineering Agrafiotis and Tsoukalas [1], Bai et al [2], Gut [3,4], Gut and Hüsler [5], Igaki et al [6], Skoulakis [7], Finkelstein and Marais [8], Mercier and Pham [9], Omey and Vesilo [10], Sumita and Zuo [11], Wang et al [12], and others. In these works, various reliability backgrounds are provided, the distributed characteristics of the system lifetime are discussed, and the asymptotic properties of the cumulative and maximum shock processes are investigated.…”

Section: Introductionmentioning

confidence: 99%

Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure

Bai

Chen

Yuan

et al. 2015

Mathematical Problems in Engineering

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This paper considers a more general shock model with insurance and financial risk background, in which the system is subject to two types of shocks called primary shocks and secondary shocks. Each primary shock causes a series of secondary shocks according to some cluster pattern. In reliability applications, a primary shock can represent an issue of insurance policies of an insurer company, and the secondary shocks then denote the relevant insurance claims generated by the policy. We focus on the local cumulative shock process where only a certain number of the most recent primary and secondary shocks are accumulated. This process is a very new topic in the available literature which is more flexible and realistic in modeling some more complex reliability situations such as bankrupt behavior of an insurance company. Based on the theory of infinite divisibility and stable distributions, we establish a central limit theorem for the local cumulative shock process and obtain the conditions for the process to converge to an infinitely divisible distribution or to anα-stable law. Also, by choosing the proper scale parameters, the process converges to a normal distribution.

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“…In the literature, random shocks are typically modeled by Poisson processes (Li & Pham 2005, Nakagawa 2007, Bai et al 2006, Wang & Pham 2012, Esary & Marshall 1973, distinguishing two main types, extreme shock and cumulative shock processes (Bai et al 2006), according to the severities of the damages. The former type could directly lead the component to immediate failure (Gut 1999, Anderson 1987, whereas the latter increases the degree of damage in a cumulative way (Agrafiotis & Tsoukalas 1995, Nakagawa & Kijima 1989.…”

Section: Introductionmentioning

confidence: 99%