Patterns of the Birnbaum importance in linear consecutive-<i>k</i>-out-of-<i>n</i>systems

We propose the consecutive-k r -out-of-n r :F linear zigzag structure and circular polygon structure, which extend the consecutive-k-out-of-n:F system model. By employing the finite Markov chain imbedding approach, we have proven the equations for calculating the reliability of consecutive-k-out-of-n:F system with different patterns given the state of the first and(or) the last component(s). Based on those reliability equations, we provide the rules for obtaining the reliability of the linear zigzag structure and circular polygon structure. Numerical examples are presented as an illustration of our new system model and demonstrate the use of the equations and rules proposed in this paper.Index Terms-Birnbaum importance, circular polygon structure, consecutive-k-out-of-n:F system, finite Markov chain imbedding approach (FMCIA), joint reliability importance (JRI), linear zigzag structure.

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“…For more research on JRI, one can refer to Eryilmaz [15], Zhu et al [45], Armstrong [4], Hagstrom [22], Hong and Lie [23], Yao et al [39] …”

Section: Literature Reviewmentioning

confidence: 99%

Reliability Modeling on Consecutive-<inline-formula> <tex-math notation="LaTeX">$k_r $</tex-math> </inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$n_r $</tex-math> </inline-formula>:F Linear Zigzag Structure and Circular Polygon Structure

et al. 2016

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“…Another interesting future line of work is to study other aspects of consecutive kout-of-n systems when probabilities or dependencies are ill-known, such as for instance importance measures (Zhu et al 2012), multi-state versions of the systems (Radwan et al 2011) or design optimization (Shingyoch et al 2010).…”

Section: Resultsmentioning

confidence: 99%

Reliability Analysis with Ill-Known Probabilities and Dependencies

Destercke

Poss

Sallak

2014

Vulnerability, Uncertainty, and Risk

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In this work, we are interested in estimating the uncertainty that a system will work, given the probabilities that its components will be either failing or working. Usually, this estimation is done by propagating the component uncertainties through a structure function. This problem is well-studied when component probabilities are known and when the component are assumed to be independent. In this paper, we first recall some results obtained when considering that probabilities are unknown and when one either assume component independence or no knowledge about the components dependence. We also explore some structures not studied up to now, such as consecutive k-out-of-n structures.

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“…Yet, the reliability of k-out-of-n systems has been extensively studied (Tian et al (2009), Yun et al (2011), Zhu et al (2012), and Zakaria et al (1992)). De Smidt-Destombes et al (2009) have developed a technique to jointly optimize the spare part stock level, the maintenance initial level and the repair capacity for k-out-of-n systems.…”

Section: Introductionmentioning

confidence: 99%

Periodic inspection frequency and inventory policies for ak-out-of-nsystem

Bjarnason

Taghipour

2015

IIE Transactions

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We investigate maintenance and inventory policy for a k-out-of-n system in which the components' failures are hidden and follow a non-homogeneous Poisson process. Two types of inspections are performed to find failed components: planned periodic inspections and unplanned opportunistic inspections. The latter are performed at system failure times when n-k+1 components are down simultaneously. In all cases, the failed components are either minimally repaired or replaced with spare parts from the inventory. The inventory is replenished either periodically or when the system fails. The periodic orders have a random lead-time, but there is no lead-time for emergency orders, as these are placed at system failure times. The key objective is to develop a method to solve the joint maintenance and inventory problem for systems with considerable number of components, long planning horizon, and large inventory. We construct a simulation model to jointly optimize the periodic inspection interval, the periodic reorder interval, and periodic and emergency order-up-to levels. Because of the large search space, it is infeasible to try all possible combinations of decision variables in a reasonable amount of time. Thus, the simulation model is integrated with a heuristic search algorithm to obtain the optimal solution.

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Patterns of the Birnbaum importance in linear consecutive-k-out-of-nsystems

Cited by 37 publications

References 18 publications

Reliability Modeling on Consecutive-<inline-formula> <tex-math notation="LaTeX">$k_r $</tex-math> </inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$n_r $</tex-math> </inline-formula>:F Linear Zigzag Structure and Circular Polygon Structure

Reliability Modeling on Consecutive-<inline-formula> <tex-math notation="LaTeX">$k_r $</tex-math> </inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$n_r $</tex-math> </inline-formula>:F Linear Zigzag Structure and Circular Polygon Structure

Reliability Analysis with Ill-Known Probabilities and Dependencies

Periodic inspection frequency and inventory policies for ak-out-of-nsystem

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