New Indices for Measure of Parallel and Series Multi-State System Reliability

2005 ◽  
Author(s):  
Kailash Kapur ◽  
Elena Zaitseva ◽  
Vitaly Levashenko
Keyword(s):  
System Reliability ◽  
Differential Calculus ◽  
Parallel Systems ◽  
State System ◽  
System Component ◽  
Dynamic Reliability ◽  
Reliability Indices ◽  
Multiple Valued Logic ◽  
Technical Systems ◽  
Definition Of

The reliability of multi-state system is analyzed in this paper. In a multi-state system, both the system and its components may experience more than two reliability states. We propose dynamic reliability indices for reliability analysis of this system. Mathematical tools of the multiple-valued logic (the Logical Differential Calculus in particular) are exploited for definition of these indices. These indices estimate the effect on the multi-state system reliability by the state of a system component. We concentrate on series and parallel systems, because these structures are basic for many technical systems and get measures of reliability for the failure and restoration of these systems.

scholarly journals Decomposition and Estimation of Multi-State Systems by Dynamic Reliability Indices

2008 ◽  
Vol 4 (1) ◽  
pp. 353-361
Author(s):  
Zaitseva Elena ◽  
Levashenko Vitaly ◽  
Matiaško Karol
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Parallel Systems ◽  
State System ◽  
Reliability Estimation ◽  
Technical System ◽  
Dynamic Reliability ◽  
Reliability Indices ◽  
Multiple Valued Logic

Decomposition and Estimation of Multi-State Systems by Dynamic Reliability IndicesSome typical configurations of Multi-State System and their mathematical descriptions are considered in paper with relation to Reliability Analysis. Multiple-Valued Logic is applied for these descriptions synthesis and Dynamic Reliability Indices are used for Multi-State System reliability estimation. We concentrate on series and parallel systems, because these structures are basic for most of the technical system. We get measures of reliability for the failure and restoration of this system.

Reliability analysis of multi-state system with application of multiple-valued logic

2017 ◽  
Vol 34 (6) ◽  
pp. 862-878 ◽  
Author(s):  
Elena Zaitseva ◽  
Vitaly Levashenko
Keyword(s):  
Boolean Algebra ◽  
Structure Function ◽  
Reliability Analysis ◽  
Differential Calculus ◽  
Natural Extension ◽  
State System ◽  
System Component ◽  
Critical System ◽  
Content Type ◽  
Multiple Valued Logic

Purpose The purpose of this paper is to develop a new mathematical method for the reliability analysis and evaluation of multi-state system (MSS) reliability that agrees with specifics of such system. It is possible based on the application of multiple-valued logic (MVL) that is a natural extension of Boolean algebra used in reliability analysis. Design/methodology/approach Similar to Boolean algebra, MVL is used for the constriction of the structure function of the investigated system. The interpretation of the structure function of the MSS in terms of MVL allows using mathematical methods and approaches of this logic for the analysis of the structure function. Findings The logical differential calculus is one of mathematical approaches in MVL. The authors develop new method for MSS reliability analysis based on logical differential calculus, in particular direct partial logical derivatives, for the investigation of critical system states (CSSs). The proposed method allows providing the qualitative and quantitative analyses of MSS: the CSS can be defined for all possible changes of any system component or group of components, and probabilities of this state can also be calculated. Originality/value The proposed method permits representing the MSS in the form of a structure function that is interpreted as MVL function and provides the system analyses without special transformation into Boolean interpretation and with acceptable computational complexity.

Bayesian Networks Application in Multi-State System Reliability Analysis

2013 ◽  
Vol 347-350 ◽  
pp. 2590-2595 ◽  
Author(s):  
Sheng Zhai ◽  
Shu Zhong Lin
Keyword(s):  
Bayesian Network ◽  
Reliability Analysis ◽  
System Reliability ◽  
Prior Probability ◽  
State System ◽  
Weak Links ◽  
Uncertain Reasoning ◽  
Reliability Modeling ◽  
Line System ◽  
Reliability Indices

Aiming at the limitations of traditional reliability analysis theory in multi-state system, a method for reliability modeling and assessment of a multi-state system based on Bayesian Network (BN) is proposed with the advantages of uncertain reasoning and describing multi-state of event. Through the case of cell production line system, in this paper we will discuss how to establish and construct a multi-state system model based on Bayesian network, and how to apply the prior probability and posterior probability to do the bidirectional inference analysis, and directly calculate the reliability indices of the system by means of prior probability and Conditional Probability Table (CPT) . Thereby we can do the qualitative and quantitative analysis of the multi-state system reliability, identify the weak links of the system, and achieve assessment of system reliability.

scholarly journals Copula-Based Bayesian Reliability Analysis of a Product of a Probability and a Frequency Model for Parallel Systems When Components Are Dependent

2021 ◽  
Vol 11 (4) ◽  
pp. 1697
Author(s):  
Shi-Woei Lin ◽  
Tapiwa Blessing Matanhire ◽  
Yi-Ting Liu
Keyword(s):  
System Reliability ◽  
Classification Tree ◽  
Parallel Systems ◽  
Reliability Model ◽  
Key Factors ◽  
Frequency Model ◽  
Independent Components ◽  
Aggregate Analysis ◽  
Dependence Assumption ◽  
Disaggregate Analysis

While the dependence assumption among the components is naturally important in evaluating the reliability of a system, studies investigating the issues of aggregation errors in Bayesian reliability analyses have been focused mainly on systems with independent components. This study developed a copula-based Bayesian reliability model to formulate dependency between components of a parallel system and to estimate the failure rate of the system. In particular, we integrated Monte Carlo simulation and classification tree learning to identify key factors that affect the magnitude of errors in the estimation of posterior means of system reliability (for different Bayesian analysis approaches—aggregate analysis, disaggregate analysis, and simplified disaggregate analysis) to provide important guidelines for choosing the most appropriate approach for analyzing a model of products of a probability and a frequency for parallel systems with dependent components.

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