The Reliability of Coherent Systems Subjected to Marshall–Olkin Type Shocks

Bayramoğlu, İsmihan; Ozkut, Murat

doi:10.1109/tr.2014.2338252

Cited by 17 publications

(21 citation statements)

References 25 publications

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“…Two processes impact a single component each while the third one impacts both components simultaneously. This model is fundamental in reliability theory and it remains an important source of inspiration for much research; see, e.g., [4,5,13,18,21,22,36]. In cumulative shock models [25], a shock simultaneously increases some intrinsic characteristics (such as hazard rate, deterioration level, age, etc.)…”

Section: Introductionmentioning

confidence: 99%

A bivariate failure time model with random shocks and mixed effects

Mercier

Pham

2017

Journal of Multivariate Analysis

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International audienceTwo components are considered, which are subject to common external and possibly fatal shocks. The lifetimes of both components are characterized by their hazard rates. Each shock can cause the immediate failure of either one or both components. Otherwise, the hazard rate of each component is increased by a non fatal shock of a random amount, with possible dependence between the simultaneous increments of the two failure rates. An explicit formula is provided for the joint distribution of the bivariate lifetime. Aging and positive dependence properties are described , thereby showing the adequacy of the model as a bivariate failure time model. The influence of the shock model parameters on the bivari-ate lifetime is also studied. Numerical experiments illustrate and complete the study. Moreover, an estimation procedure is suggested in a parametric framework, under a specific observation scheme

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Section: Introductionmentioning

confidence: 99%

A bivariate failure time model with random shocks and mixed effects

Mercier

Pham

2017

Journal of Multivariate Analysis

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“…The new reliability metric integrates the contri- er supplies [10] and printed circuit boards [17], all of which are subject to the 22 influence of epistemic uncertainty. 23 Currently, the belief reliability of a component or a system can only be e-24 valuated from its definition (i.e., based on design margin, aleotory uncertainty 25 and epistemic uncertainty) [35]. In practice, we often need to calculate the 26 belief reliability of a system based on the structure of the system and the be-27 lief reliabilities of its components (referred to as system reliability analysis in 28 conventional reliability theories [31]).…”

mentioning

confidence: 99%

“…In literature, various mathematical theories have been used to describe epistemic developed an approach to calculate the reliability index when both uncertain 23 variables and random variables are considered. Gao and Yao [12] Most existing system reliability analysis methods in uncertainty theory are 28 based on structure functions (e.g., see [23] and [30] the minimal cut sets, which is a strong condition and restricts its application.…”

mentioning

confidence: 99%

“…Gao and Yao [12] Most existing system reliability analysis methods in uncertainty theory are 28 based on structure functions (e.g., see [23] and [30] the minimal cut sets, which is a strong condition and restricts its application.…”

mentioning

confidence: 99%

“…The reason is that 23 belief reliability considers the effect of insufficient knowledge on the estimated 24 reliability, while the probability-based reliability metric implicitly assumes that 1 knowledge is complete. It is the additional uncertainty caused by the insufficient 2 knowledge that reduces our confidence on the reliability estimation.…”

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confidence: 99%

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Uncertainty theory as a basis for belief reliability

Zeng

Kang

Wen

et al. 2018

Information Sciences

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Belief reliability is a newly developed, model-based reliability metric which considers both what we know (expressed as reliability models) and what we don't know (expressed as epistemic uncertainty in the reliability models) about the reliability. In this paper, we show that due to the explicit representation of epistemic uncertainty, belief reliability should not be regarded as a probability measure; rather, it should be treated as an uncertain measure in uncertainty theory. A minimal cut set-based method is developed to calculate the belief reliability of coherent systems. A numerical algorithm is, then, presented for belief reliability analysis based on fault tree models. The results of application show that the developed methods require less computations than the structure function-based method of classical reliability theory.

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Statistical inference for constant‐stress accelerated life tests with dependent competing risks from Marshall‐Olkin bivariate exponential distribution

Bai

Shi

Liu

et al. 2020

Quality & Reliability Eng

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This paper considers a constant‐stress accelerated dependent competing risks model under Type‐II censoring. The dependent structure between competing risks is modeled by a Marshall‐Olkin bivariate exponential distribution, and the accelerated model is described by the power rule model. The point and interval estimation of the model parameters and the reliability function under the normal usage condition at mission time are obtained by using the maximum likelihood estimation method and the bootstrap sampling technique. Moreover, the pivotal quantities based estimation are adopted to estimate the model parameters and the generalized confidence intervals. As a comparison, we also consider the Bayes estimation and the highest posterior density credible intervals for the model parameters based on conjugate priors and importance sampling method, respectively. To illustrate the proposed methodology, a Monte Carlo simulation is used to study the performances of different estimation methods. Finally, a dataset is analyzed for illustrative purpose and a comparison with the original results is also given.

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The Reliability of Coherent Systems Subjected to Marshall–Olkin Type Shocks

Cited by 17 publications

References 25 publications

A bivariate failure time model with random shocks and mixed effects

A bivariate failure time model with random shocks and mixed effects

Uncertainty theory as a basis for belief reliability

Statistical inference for constant‐stress accelerated life tests with dependent competing risks from Marshall‐Olkin bivariate exponential distribution

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