Multi-State System Reliability

Lisnianski, Anatoly; Levitin, Gregory

doi:10.1142/5221

Cited by 570 publications

(168 citation statements)

References 0 publications

Supporting

Mentioning

167

Contrasting

Unclassified

Order By: Relevance

“…We notice that this definition does not coincide with the definition of a maximal lower vector for level 0 (that is, the failure state of the system in our case) given, for example, in [4]. (Note that a maximal lower vector for level 0 is a state x of the system such that the system reaches level 1 (the functioning state) for any state x x, where this notation means that there exists at least one index c such that x c x c .)…”

Section: Cut Sets For Multistate Coherent Systemsmentioning

confidence: 77%

See 1 more Smart Citation

The Downtime Distribution After a Failure of a System with Multistate Independent Components

Pievatolo

2007

J. Appl. Probab.

View full text Add to dashboard Cite

Aven and Jensen (1999) proposed an approximation to the downtime distribution for arbitrary coherent systems with binary and independent repairable components, where each component follows an alternating renewal process. The approximation is based on a mixture of the duration distributions of the cut sets in the system. We extend this approach to coherent systems composed by multistate independent components, where every component follows a semi-Markov process and where we introduce the concept of a minimal cut set in the multistate setting. We test our proposal on a simple power demand-generation system, by comparing the analytic approximation with simulation results, and we find it is accurate when the system is highly available.

show abstract

Section: Cut Sets For Multistate Coherent Systemsmentioning

confidence: 77%

“…From [4] we also borrow an example of a small two-component system describing the joint evolution of generation and demand of electrical power. Component 1 is the power requested, and component 2 is the power generated, both discretized at three levels and forming a Weibull-Markov system.…”

Section: Example 31 (Electrical Power Demand and Generation)mentioning

confidence: 99%

The Downtime Distribution After a Failure of a System with Multistate Independent Components

Pievatolo

2007

J. Appl. Probab.

View full text Add to dashboard Cite

show abstract

“…Previous researches have been focusing on the reliability evaluation of multi-state system recently [2][3][4][5][6]. As time went by, the commonly used evaluation method of multi-state system consists of two algorithms, Analytical algorithm and Monte Carlo simulation [7][8]. Compared with Analytical algorithm, Monte Carlo simulation is more suitable in large-scale system.…”

Section: Introductionmentioning

confidence: 99%

Reliability Evaluation and Selection in Multi-State System

Hu¹,

Liu²,

Hong-jie³

2018

dteees

View full text Add to dashboard Cite

The multi-state system is an essential tool to present engineering system and previous researches have been focusing on the reliability evaluation of multi-state system recently. The Analytical algorithm and Monte Carlo simulation are the major reliability evaluation methods. However, it is inefficient to apply these algorithms to find the optimal multi-state system with greatest reliability in numbers of systems, whose computational time may last for hours. Hence, this paper proposes a new method based on ordinal optimization algorithm and Monte Carlo simulation applied in reliability evaluation. Calculation methods concerning the characteristics of system are defined, which can dramatically and effectively shorten the computational time. An effective and convenient precision and efficiency verification according to the proposed method is illustrated.

show abstract

“…Some of them are Monte Carlo simulation [41,42], stochastic Petri nets [19,21], universal generating function [24,32], Markov models [6,37] and the combinations of the above methods [9]. However, conventional availability analysis methods for repairable multi-state systems are based on the continuous time models.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Availability Assessment for Discrete Time Multi-State System under Minor Failures and Repairs by Using Fuzzy Lz-transform.

Zhang

et al. 2017

EiN

View full text Add to dashboard Cite

Article citation info:on a continuous scale. In such situations, the lifetimes and repair times can be expressed in terms of the number of working and repairing periods (cycles), respectively. Thus, it is essential to construct discrete time reliability models for repairable multi-state systems.The discrete time reliability has drawn continuous attention in both model analysis and problem solution. Bracquemond and Gaudoin [5] presented a good overview of discrete probability distributions used in reliability for modeling discrete lifetimes of non-repairable systems. The discrete time reliability modeling for general binary systems can be found in [4,22,34]. Eryilmaz [14], Guerry [16] and Sadek and Limnios [35], presented the discrete time reliability models for Markov multi-state systems. The discrete time reliability models for semi-Markov multi-state systems were investigated in [1,4,10]. However, most of the reported works mainly focus on the issues of IntroductionThe availability, as a performance measure, is one of the most important indicators for characterizing a repairable system and its components. For repairable multi-state systems with various performance levels, the availability is more meaningful than reliability to measure the effectiveness of the system to satisfy consumer demand.In the past few years, a variety of methods are available in the literature for analyzing the availability of repairable multi-state systems. Some of them are Monte Carlo simulation [41,42], stochastic Petri nets [19,21], universal generating function [24,32], Markov models [6,37] and the combinations of the above methods [9]. However, conventional availability analysis methods for repairable multi-state systems are based on the continuous time models. In some engineering circumstances, it is sometimes impossible or inconvenient to measure the lifetimes and repair times length of some systems (components) HU L, SU P, PENG R, ZHANG Z. Fuzzy Availability Assessment for Discrete Time Multi-State System under Minor Failures and Repairs by Using Fuzzy L z -transform. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2017; 19 (2): 179-190 discrete time systems with the exact reliability data. As stated in Garg [15], the complicated system has the massive fuzzy uncertainty due to which it is difficult to get the exact probability of the events. Thus, it is of large practical value to investigate the availability assessment for discrete time repairable system with fuzzy uncertainty. fuzzy discrete time Markov model with fuzzy transition probability matrix is proposed to analyze the fuzzy state probability of each component at any discrete time. The fuzzy L z -transform of the discrete-state discrete-time fuzzy Markov chain is developed to extend the L z -transform of the discrete-state continuous-time Markov model with crisp sets. Based on the α-cut approach and the fuzzy L z -transform, the dynamic fuzzy availability of the system is computed by using parametric programming technique. To illustrate the proposed method,...

show abstract

Multi-State System Reliability

Cited by 570 publications

References 0 publications

The Downtime Distribution After a Failure of a System with Multistate Independent Components

The Downtime Distribution After a Failure of a System with Multistate Independent Components

Reliability Evaluation and Selection in Multi-State System

Fuzzy Availability Assessment for Discrete Time Multi-State System under Minor Failures and Repairs by Using Fuzzy Lz-transform.

Contact Info

Product

Resources

About