Exact reliability formula and bounds for general k-out-of-n systems

Koucky, Miroslav

doi:10.1016/s0951-8320(03)00126-1

Cited by 17 publications

(4 citation statements)

References 2 publications

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“…In accordance with Example 1, we consider further an s-out-of-r system with statistically independent and identically distributed response components. In accordance with the work of (Kouckỳ, 2003), we denote by F D ptq " PpT l ď t @l P Dq " ś lPD F T l ptq the probability of joint failure of the components d Ď t1, ..., ru. Consequently, the joint failure time distribution function for a s-out-of-r system is expressed as,…”

Section: Numerical Examplesmentioning

confidence: 99%

Optimal Design of Stress Levels in Accelerated Degradation Testing for Multivariate Linear Degradation Models

Shat¹

2021

Preprint

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In recent years, more attention has been paid prominently to accelerated degradation testing in order to characterize accurate estimation of reliability properties for systems that are designed to work properly for years of even decades. In this paper we propose optimal experimental designs for repeated measures accelerated degradation tests with competing failure modes that correspond to multiple response components. The observation time points are assumed to be fixed and known in advance. The marginal degradation paths are expressed using linear mixed effects models. The optimal design is obtained by minimizing the asymptotic variance of the estimator of some quantile of the failure time distribution at the normal use conditions. Numerical examples are introduced to ensure the robustness of the proposed optimal designs and compare their efficiency with standard experimental designs.

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Section: Numerical Examplesmentioning

confidence: 99%

Optimal Design of Stress Levels in Accelerated Degradation Testing for Multivariate Linear Degradation Models

Shat¹

2021

Preprint

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“…Consecutive F Exact expression for the failure probability [1] Consecutive G Matrix formulation and solution [2] Consecutive F/G Computational algorithm [3] F/G Consider the environmental effects [4] G Computational algorithm [5] F/G Develop a data completion procedure [6] F/G Achieve exact formula and bounds [7] G Computational algorithm [8] F/G Present exact and approximate approach [9] Consecutive F/G Present a heuristic algorithm for replacement policies [10] Consecutive F Present a formula for twodimensional lower bound [11] F Investigate that where to allocate the spares [12] ( )…”

Section: Binarymentioning

confidence: 99%

Real Time Reliability Study of a Model with Increasing Failure Rates

Sharifi

Hashemi

Farahpour

2011

AMM

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This paper deals with a system with elements with one element is the main element and the other elements are the spare parts of the main element. If one element fails, one of the spare parts starts working immediately. The failure rate of non working elements are zero and the failure rate of working element is time dependent as and the failed elements are not repairable. The system works until all elements failed. In the second part of this paper the differential equations between the state of the system are established and by solving this equation the reliability function of the system () is calculated. In the third part, a numerical example solved to determine the parameters of the system. Nomenclature The notations used in this paper are as follows: : Number of elements, : Failure rate of each element at time, : Probability that the system is in state with spare element at time, : Probability that system works at time, : Mean time to failure of the system,

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“…Note that computing the conditional probability that there are k alarms given that a container is a threat or non-threat is not trivial if there is dependence between the sensors, which is likely to hold in practice. Finding these conditional probabilities can be accomplished by computing the reliability of a k-out-of-n reliability system, in which the system yields an alarm response if at least k sensors yield an alarm (Koucky 2003). Define the following parameters.…”

Section: The Container Reliability Knapsack Problemmentioning

confidence: 99%

“…where U (r) = s∈S(r) U(s) (Koucky 2003). Then, the probability that there are exactly k alarms is given by P kA = R (k,n) − R (k+1,n) , k = 0, 1, .…”

Section: The Container Reliability Knapsack Problemmentioning

confidence: 99%

Interdicting nuclear material on cargo containers using knapsack problem models

2009

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This paper introduces a framework for screening cargo containers for nuclear material at security stations throughout the United States using knapsack problem, reliability, and Bayesian probability models. The approach investigates how to define a system alarm given a set of screening devices, and hence, designs and analyzes next-generation security system architectures. Containers that yield a system alarm undergo secondary screening, where more effective and intrusive screening devices are used to further examine containers for nuclear and radiological material. It is assumed that there is a budget for performing secondary screening on containers that yield a system alarm. This paper explores the relationships and tradeoffs between prescreening, secondary screening costs, and the efficacy of radiation detectors. The key contribution of this analysis is that it provides a risk-based framework for determining how to define a system alarm for screening cargo containers given limited screening resources. The analysis suggests that highly accurate prescreening is the most important factor for effective screening, particularly when screening tests are highly dependent, and that moderately accurate prescreening may not be an improvement over treating all cargo containers the same. Moreover, it suggests that screening tests with high true alarm rates may mitigate some of the risk associated with low prescreening intelligence.

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Exact reliability formula and bounds for general k-out-of-n systems

Cited by 17 publications

References 2 publications

Optimal Design of Stress Levels in Accelerated Degradation Testing for Multivariate Linear Degradation Models

Optimal Design of Stress Levels in Accelerated Degradation Testing for Multivariate Linear Degradation Models

Real Time Reliability Study of a Model with Increasing Failure Rates

Interdicting nuclear material on cargo containers using knapsack problem models

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