Discrete and continuous reliability models for systems with identically distributed correlated components

Fiondella, Lance; Xing, Liudong

doi:10.1016/j.ress.2014.08.004

Cited by 35 publications

(23 citation statements)

References 21 publications

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“…For example, an n component parallel system with correlated but identically distributed Weibull components m = e A parallel system model may be suitable in cases where computations are replicated across multiple processors to achieve fault tolerance between checkpoints. While the illustrations that follow are presented in the context of a two-component parallel system with correlated but identically distributed Weibull components, we note that the general method 31 is applicable to systems and workflows possessing any structure function represented by a reliability block diagram or fault tree.…”

Section: Correlated Identical Componentsmentioning

confidence: 99%

Optimal equidistant checkpointing of fault tolerant systems subject to correlated failure

Jafary

Fiondella

Chang

2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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Checkpointing is a technique to back up work at periodic intervals so that if computation fails, it will not be necessary to restart from the beginning but will instead be able to restart from the latest checkpoint. Performing checkpointing operations requires time. Therefore, it is necessary to consider the tradeoff between the time to perform checkpointing operations and the time saved when computation restarts at a checkpoint. This article presents a method to model the impact of correlated failures on an application that performs a specified amount of computation and implements checkpointing operations at equidistant periods during this computation. We develop a Markov model and superimpose a correlated life distribution. Two cases are considered. The first assumes that reaching a checkpoint resets the failure distribution. The second allows the probability of failure to progress. We illustrate the approach through a series of examples. The results indicate that correlation can negatively impact checkpointing, necessitating more frequent checkpointing and increasing the total time required, but that the approach can still identify the optimal number of equidistant checkpoints, despite this correlation.

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Section: Correlated Identical Componentsmentioning

confidence: 99%

Optimal equidistant checkpointing of fault tolerant systems subject to correlated failure

Jafary

Fiondella

Chang

2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…However, this numerical technique requires the solution of an exponential number (2^N c ) N c -variate integrals because an analytical solution to the multivariate normal distribution does not exist. Thus, the numerical approach is limited to small systems such as the widely used two-out-of-three system [11], where a majority of the components must be reliable for the system to be reliable. Due to these limitations of the numerical generalization, the simulation approach is employed to evaluate the reliability of TCFN.…”

Section: Encoding Correlated Failuresmentioning

confidence: 99%

Simulation approach to estimate the system reliability of a time-based capacitated flow network susceptible to correlated failures

Lin

Fiondella

Chang

2013

Simulation Modelling Practice and Theory

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“…Thus how to describe the dependency among components in a system has been an interesting topic. Various types of dependence, such as Markov dependence [6][7][8], redundant dependence, [9,10], common cause failure [11][12][13], sequencedependent failures (Xing et al [14]), propagated failures with global or selective effect [15,16], correlated failures [17], economic dependence (Zhou et al [18]), and historydependence (Wang and Cui [19]), have been considered.…”

Section: Introductionmentioning

confidence: 99%

Reliability Analysis of 6-Component Star Markov Repairable System with Spatial Dependence

Wang

Yang

Tian

2017

Mathematical Problems in Engineering

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Star repairable systems with spatial dependence consist of a center component and several peripheral components. The peripheral components are arranged around the center component, and the performance of each component depends on its spatial “neighbors.” Vector-Markov process is adapted to describe the performance of the system. The state space and transition rate matrix corresponding to the 6-component star Markov repairable system with spatial dependence are presented via probability analysis method. Several reliability indices, such as the availability, the probabilities of visiting the safety, the degradation, the alert, and the failed state sets, are obtained by Laplace transform method and a numerical example is provided to illustrate the results.

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Discrete and continuous reliability models for systems with identically distributed correlated components

Cited by 35 publications

References 21 publications

Optimal equidistant checkpointing of fault tolerant systems subject to correlated failure

Optimal equidistant checkpointing of fault tolerant systems subject to correlated failure

Simulation approach to estimate the system reliability of a time-based capacitated flow network susceptible to correlated failures

Reliability Analysis of 6-Component Star Markov Repairable System with Spatial Dependence

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