Reliability assessment of system under a generalized cumulative shock model

2019 ◽  
Vol 234 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Min Gong ◽  
Serkan Eryilmaz ◽  
Min Xie
Keyword(s):  
Reliability Assessment ◽  
Shock Model ◽  
External Shocks ◽  
Phase Type Distribution ◽  
Internal Factors ◽  
Reliability Characteristics ◽  
Shock Models ◽  
The One ◽  
Random Shocks ◽  
Real Practice

Reliability assessment of system suffering from random shocks is attracting a great deal of attention in recent years. Excluding internal factors such as aging and wear-out, external shocks which lead to sudden changes in the system operation environment are also important causes of system failure. Therefore, efficiently modeling the reliability of such system is an important applied problem. A variety of shock models are developed to model the inter-arrival time between shocks and magnitude of shocks. In a cumulative shock model, the system fails when the cumulative magnitude of damage caused by shocks exceed a threshold. Nevertheless, in the existing literatures, only the magnitude is taken into consideration, while the source of shocks is usually neglected. Using the same distribution to model the magnitude of shocks from different sources is too critical in real practice. To this end, considering a system subject to random shocks from various sources with different probabilities, we develop a generalized cumulative shock model in this article. We use phase-type distribution to model the variables, which is highly versatile to be used for modeling quantitative features of random phenomenon. We will discuss the reliability characteristics of such system in some detail and give some clear expressions under the one-dimensional case. Numerical example for illustration is also provided along with a summary.

scholarly journals Reliability assessment of system under a generalized run shock model

2018 ◽  
Vol 55 (4) ◽  
pp. 1249-1260 ◽  
Author(s):  
Min Gong ◽  
Min Xie ◽  
Yaning Yang
Keyword(s):  
Arrival Time ◽  
Reliability Assessment ◽  
State System ◽  
Shock Model ◽  
External Shocks ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Markovian Property ◽  
Phase Type ◽  
Real Practice

Abstract In this paper we are concerned with modelling the reliability of a system subject to external shocks. In a run shock model, the system fails when a sequence of shocks above a threshold arrive in succession. Nevertheless, using a single threshold to measure the severity of a shock is too critical in real practice. To this end, we develop a generalized run shock model with two thresholds. We employ a phase-type distribution to model the damage size and the inter-arrival time of shocks, which is highly versatile and may be used to model many quantitative features of random phenomenon. Furthermore, we use the Markovian property to construct a multi-state system which degrades with the arrival of shocks. We also provide a numerical example to illustrate our results.

Local Strain and Stress Calculation Methods of Irregular Honeycombs Under Dynamic Compression

2016 ◽  
Author(s):  
Jilin Yu ◽  
Peng Wang ◽  
Shenfei Liao ◽  
Zhijun Zheng
Keyword(s):  
Shock Wave ◽  
Wave Speed ◽  
Local Strain ◽  
Cellular Materials ◽  
Shock Model ◽  
Cross Sectional ◽  
One Dimensional ◽  
Loading Direction ◽  
Shock Models ◽  
The One

Several continuum-based shock models have been proposed to understand the dynamic compressive behavior of cellular materials, but they are mainly based on the quasi-static stress–strain relation and thus lack sufficient dynamic stress–strain information. A virtual ‘test’ of irregular honeycombs under constant-velocity compression is carried out using the finite element method. A method based on the optimization of local deformation gradient by using the least square method is employed to calculate the one-dimensional strain distribution in the loading direction of the specimen. Meanwhile, a method based on the cross-sectional engineering stress is developed to obtain the one-dimensional stress distribution in the loading direction. The two typical features of cellular materials under dynamic crushing, namely deformation localization and strength enhancement, can be characterized by the strain and stress distributions, respectively. The results also confirm the existence of plastic shock front propagation in cellular structures under high-velocity impact, from which the shock wave speed can be estimated. The shock wave speed obtained from the local strain field method coincides with that from the cross-sectional stress method. The results of shock wave speed are also compared with those predicted by continuum-based shock models. It is shown that the shock wave speed predicted by the R-PP-L (rate-independent, rigid–perfect plastic–locking) shock model or the R-LHP-L (rate-independent, rigid–linearly hardening plastic–locking) shock model is overestimated, but that predicted by the R-PH (rate-independent, rigid–plastic hardening) shock model is close to those obtained from the local strain and cross-sectional stress calculations using the cell-based finite element model.

scholarly journals A generalized class of correlated run shock models

2018 ◽  
Vol 6 (1) ◽  
pp. 131-138 ◽  
Author(s):  
Femin Yalcin ◽  
Serkan Eryilmaz ◽  
Ali Riza Bozbulut
Keyword(s):  
Stopping Time ◽  
Random Variables ◽  
Random Variable ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Shock Models ◽  
Phase Type ◽  
Over Time

AbstractIn this paper, a generalized class of run shock models associated with a bivariate sequence {(Xi, Yi)}i≥1 of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X1, X2, ... over time, let the random variables Y1, Y2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = ∑Nt=1 Yt , where N is a stopping time for the sequence {Xi}i≤1 and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {Xi, 1≤i≤ N}. Distributions of T and M are investigated when N has a phase-type distribution.

Failure distributions of shock models

1980 ◽  
Vol 17 (03) ◽  
pp. 745-752 ◽  
Author(s):  
Gary Gottlieb
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Shock Model ◽  
Life Distribution ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Damage Process

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate.

General shock models associated with correlated renewal sequences

1983 ◽  
Vol 20 (3) ◽  
pp. 600-614 ◽  
Author(s):  
J. G. Shanthikumar ◽  
U. Sumita
Keyword(s):  
Limit Theorem ◽  
Renewal Process ◽  
Threshold Level ◽  
Numerical Results ◽  
Shock Model ◽  
Failure Times ◽  
Clearing System ◽  
Shock Models ◽  
Subsequent Interval

In this paper we define and analyze a general shock model associated with a correlated pair (Xn, Yn) of renewal sequences, where the system fails when the magnitude of a shock exceeds (or falls below) a prespecified threshold level. Two models, depending on whether the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length Yn of the subsequent interval until the next shock, are considered. The transform results, an exponential limit theorem, and properties of the associated renewal process of the failure times are obtained. An application in a stochastic clearing system with numerical results is also given.

Teacher Unions

2017 ◽  
Author(s):  
John McCollow
Keyword(s):  
Education Reform ◽  
Global Education ◽  
Alternative Conceptions ◽  
Teacher Unions ◽  
Special Interest Groups ◽  
Internal Factors ◽  
Government Relations ◽  
The Status ◽  
The One ◽  
Future Of Education

Teacher unions (or alternatively “education unions”) are organizations formed to protect and advance the collective interests of teachers and other education workers. What the collective interests of educators entail and how they should be pursued have been and remain active matters for debate within these organizations. Different unions at different times have responded differently to these questions, for example, in relation to the degree to which an industrial versus a professional orientation should be adopted, and the degree to which a wider political and social justice agenda should be embraced. Several ideal-type models of teacher unionism have been identified, as well as various strategic options that these unions might employ. A spirited debate is ongoing about the legitimacy and power of teacher unions. One perspective portrays them as self-interested special interest groups, and another as social movements advocating for public education. The status of teacher unions as stakeholders in educational policymaking is contested, and union–government relations occur across a spectrum of arrangements ranging from those that encourage negotiation to those characterized by confrontation and hostility. Internationally, education unions face significant challenges in the early decades of the 21st century. Neoliberal economic and industrial policies and legislation have eroded the capacity of unions to collectively organize and bargain, and the global education reform movement (GERM) has created a hostile environment for education unions and their members. Despite these challenges, education unions remain among the most important critics of GERM and of global neoliberal social policy generally. The challenges posed and the strategies adopted play out differently across the globe. There is evidence that at least some unions are now prepared to be far more flexible in adopting a “tapestry” of strategies, to examine their internal organization, build alliances, and develop alternative conceptions of the future of education. Researchers, however, have identified certain internal factors in many teacher unions that pose significant obstacles to these tasks. Unions face difficult choices that could lead to marginalization on the one hand or incorporation on the other.

scholarly journals Reliability modeling for competing failure systems with instant-shift hard failure threshold

2018 ◽  
Vol 42 (4) ◽  
pp. 457-467 ◽  
Author(s):  
Jingyi Liu ◽  
Yugang Zhang ◽  
Bifeng Song
Keyword(s):  
Sensitivity Analysis ◽  
System Reliability ◽  
Reliability Model ◽  
External Shocks ◽  
Reliability Modeling ◽  
Soft Failure ◽  
Random Shock ◽  
Hard Failure ◽  
Engineering Practices ◽  
Random Shocks

Many researchers have modeled systems under multiple dependent competing failure processes (MDCFP) in recent years. Typically, those failure processes consist of degradation (soft failure) and random shock (hard failure). In previous papers the threshold of hard failure has been a fixed value, which does not reflect engineering practices. Threshold refers to the ability to resist external random shocks, which shifts with time as the system is used. Thus, this paper establishes a model for MDCFP with instant-shift hard threshold. The hard failure threshold changes with time instantaneously, and it is also influenced by external shocks. This paper also presents a system reliability model. The effectiveness of the presented model is demonstrated by a reliability analysis of the micro-engine at Sandia National Laboratories. In addition, a sensitivity analysis is performed for specific parameters.

The Decline of the Agrarian Economy in Palestine under Roman Rule

2006 ◽  
Vol 49 (3) ◽  
pp. 285-328 ◽  
Author(s):  
Moshe Gil
Keyword(s):  
The Other ◽  
Considerable Part ◽  
Internal Factors ◽  
Agrarian Economy ◽  
The One ◽  
Inheritance Laws

AbstractFive main problems constitute the background for the decline of Palestine's agrarian economy under the Romans. A considerable part of the land was held by the Roman state, a situation that became more extensive than can be documented under previous regimes. Taxation, as described in talmudic sources, pressed heavily on the cultivators. Usury, a matter contrary to sacrosanct ancient prescriptions, was burdening the agrarian population by stratagems and cover-ups. Expropriation became frequent and there were instances of flight of both owners and sharecroppers. Finally, marriage and inheritance laws and customs brought about a far-reaching parceling of estates. It is shown that the decline was caused not only by Roman oppression, but also by internal factors, which together caused urbanization on the one hand, and emigration on the other. Cinq problèmes principaux constituent l'arrière-plan pour le déclin de l'économie agraire de la Palestine sous les Romains. Une partie considérable de la terre a été tenue par l'état romain, une situation qui est devenue plus étendue que peut être documentée sous des régimes précédents. L'imposition, comme décrite dans des sources talmudiques, oppressait fortement sur les cultivateurs. L'usure, qui contredit les prescriptions antiques sacro-saintes, accablait la population agraire par des stratagèmes et dissimulations. L'expropriation est devenue fréquente et il y avait des exemples de fuite des propriétaires et des métayers. Finalement, le mariage et les lois et coutumes de l'héritage ont produit un morcellement excessif des domaines. Y est montré que le déclin a été produit non seulement par l'oppression romaine, mais également par des facteurs internes, qui ensemble ont causé l'urbanisation d'une part, et l'émigration de l'autre.

Semi-Markov shock models with additive damage

1986 ◽  
Vol 18 (3) ◽  
pp. 772-790 ◽  
Author(s):  
M. J. M. Posner ◽  
D. Zuckerman
Keyword(s):  
Sufficient Conditions ◽  
Control Limit ◽  
Shock Model ◽  
Markov Modelling ◽  
Shock Models ◽  
Replacement Model ◽  
Computational Aspects ◽  
Replacement Problem

We examine a replacement model for a semi-Markov shock model with additive damage. Sufficient conditions are given for the optimality of control limit policies. The paper generalizes and unifies previous research in the area.In addition, we investigate in detail the practical modelling and computational aspects of the replacement problem using a semi-Markov modelling structure.

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