Structure function in analysis of multi-state system availability

2018 ◽  
pp. 897-905
Author(s):  
M. Kvassay ◽  
V. Levashenko ◽  
J. Rabcan ◽  
P. Rusnak ◽  
E. Zaitseva
Keyword(s):  
Structure Function ◽  
State System ◽  
System Availability

scholarly journals Methodology for the Assessment of Imprecise Multi-State System Availability

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 150
Author(s):  
Joanna Akrouche ◽  
Mohamed Sallak ◽  
Eric Châtelet ◽  
Fahed Abdallah ◽  
Hiba Hajj Chehade
Keyword(s):  
Markov Chains ◽  
Constraint Propagation ◽  
State System ◽  
Combined Approach ◽  
System Availability ◽  
Contraction Method ◽  
Numerical Examples ◽  
Complex Architectures ◽  
Backward Propagation ◽  
Interval Constraint

Most existing studies of a system’s availability in the presence of epistemic uncertainties assume that the system is binary. In this paper, a new methodology for the estimation of the availability of multi-state systems is developed, taking into consideration epistemic uncertainties. This paper formulates a combined approach, based on continuous Markov chains and interval contraction methods, to address the problem of computing the availability of multi-state systems with imprecise failure and repair rates. The interval constraint propagation method, which we refer to as the forward–backward propagation (FBP) contraction method, allows us to contract the probability intervals, keeping all the values that may be consistent with the set of constraints. This methodology is guaranteed, and several numerical examples of systems with complex architectures are studied.

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.

scholarly journals Availability Analysis of Software Systems with Rejuvenation and Checkpointing

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 846
Author(s):  
Junjun Zheng ◽  
Hiroyuki Okamura ◽  
Tadashi Dohi
Keyword(s):  
Steady State ◽  
Human Error ◽  
System Modeling ◽  
Regenerative Process ◽  
State System ◽  
Software Systems ◽  
System Availability ◽  
Software Rejuvenation ◽  
Availability Analysis ◽  
Availability Model

In software reliability engineering, software-rejuvenation and -checkpointing techniques are widely used for enhancing system reliability and strengthening data protection. In this paper, a stochastic framework composed of a composite stochastic Petri reward net and its resulting non-Markovian availability model is presented to capture the dynamic behavior of an operational software system in which time-based software rejuvenation and checkpointing are both aperiodically conducted. In particular, apart from the software-aging problem that may cause the system to fail, human-error factors (i.e., a system operator’s misoperations) during checkpointing are also considered. To solve the stationary solution of the non-Markovian availability model, which is derived on the basis of the reachability graph of stochastic Petri reward nets and is actually not one of the trivial stochastic models such as the semi-Markov process and the Markov regenerative process, the phase-expansion approach is considered. In numerical experiments, we illustrate steady-state system availability and find optimal software-rejuvenation policies that maximize steady-state system availability. The effects of human-error factors on both steady-state system availability and the optimal software-rejuvenation trigger timing are also evaluated. Numerical results showed that human errors during checkpointing both decreased system availability and brought a significant effect on the optimal rejuvenation-trigger timing, so that it should not be overlooked during system modeling.

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