Joint Reliability of Two Consecutive-(1, l) or (2, k)-out-of-(2, n): F Type Systems and Its Application in Smart Street Light Deployment

Li, Jingwen; Yi, He; Li, Xiang

doi:10.1007/s11009-023-09984-3

Cited by 7 publications

(3 citation statements)

References 34 publications

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“…Such systems are called non-basic. These include, in particular, systems such as consecutive k-out-of-n [20][21][22][23][24][25][26][27], consecutive k-within-m-out-of-n [28, 29], [30] [41,42], [43,44], kc-out-ofn [38], (r, s)-out-of-(m, n) [45,46], [47], consecutive-krout-of-nr [48] as well as many hierarchical systems [50,51], [52,53].…”

Section: Concepts and Definitionsmentioning

confidence: 99%

On evaluation of reliability increase in fault-tolerant multi processor systems

Romankevich,

Morozov,

Feseniuk

et al. 2024

AAIT

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The work is devoted to the problem of evaluating the reliability increase of a fault-tolerant multiprocessor system by adding an extra processor to the system. It is assumed that the behavior of the modified system in the failure flow, in the case of the extra processor failure, does not differ from the behavior of the original system. The article describes both k-out-of-nsystems, and more complex ones, including hierarchical systems.An important feature of the proposed approach is that it involves the preliminary calculation of someadditionalauxiliaryvalues that do not depend on the reliability parameters of the added processor.Further, the reliability increase is assessed by substituting these parameter values into basicexpressions, which simplifies the selection of the optimal processor from the available set, sufficient to achieve the required level of system reliability, or confirms the impossibility of this.The proposed approach is compatible with any methods of calculating the reliability parameters of fault-tolerant multiprocessor systems but is particularly relevant for methods based on statistical experiments with models of system behavior in the failure flow, in particular, such as GL-models, due to the significant computational complexityof such calculations. In addition, for the simplest cases considered, k-out-of-nsystems with identical processors, a simple expression is proposed for an approximate estimateof the ratio of failure probabilities of the original and modified systems.Thehigher the reliability of the system processors, the higher the accuracy of such an assessment. Examples are given that prove the practical correctness of the proposed approaches.The calculation of the reliability system parameters, as well as auxiliary expressions, was based on conducting statistical experiments with corresponding GL-models.

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Section: Concepts and Definitionsmentioning

confidence: 99%

On evaluation of reliability increase in fault-tolerant multi processor systems

Romankevich,

Morozov,

Feseniuk

et al. 2024

AAIT

View full text Add to dashboard Cite

show abstract

“…The methods of the first group are based on the construction of analytical expressions for calculating the corresponding parameters. Their advantage is the ability to obtain results with high accuracy, but their disadvantage is non-universality: for each type of system, it is often necessary to create a new calculation method [23,24], [25,26], [27,28], [29,30], [31,32], [33,34], [35,36], [37,38], [39,40], [41,42], [43,44], [45,46], [47,48], [49,50], [51,52], [53,54]. The methods of the second group are based on conducting statistical experiments with models of system behavior in the failure flow [55,56], [57].…”

Section: Introductionmentioning

confidence: 99%

On the modification of GL-models by adding edges to a cyclic graph

Romankevich,

Morozov,

Romankevich

et al. 2024

HAIT

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This work suggests a method for constructing GL-models of fault-tolerant multiprocessor systems. These models can be used, in particular, to estimate the reliability parameters of the latter by conducting statistical experiments with models of their behavior in the failure flow.Two cases are considered: the non-basicsystem, unlike the basicsystem, is resistant to somefailures of increased multiplicity, or else, on the contrary, the non-basicsystem is vulnerableto certain failures that do not lead to the failure of the basicsystem. In this case, the condition under which the system’s behavior differs from the baselinecorresponds to a Boolean expression, thatdepends on the values of the elements of the system state vector, which characterizes the states of its processors in the failure flow. According to the method proposed in the article, amodel of such system is built by adding an edge or several edges to the so-called MLE-model, atype of GL-model, thatcan be constructed for any basicsystem and isbased on cyclic graphs. The edge function for this edge is formed based on the aforementioned Boolean expression. The models constructed by the proposed method are also based on cyclic graphs, which, in particular, significantly simplifythe procedure for assessing the connectivityof the last ones. A series of experiments have been conducted to confirm the adequacy of the models (obtained by the proposed method) to the behavior of systems in the failure flow. This work presents examplesthat demonstratethe process of constructing GL-models for non-basicfault-tolerant multiprocessor systemsusingthe proposed method for both of the above cases.

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“…The advantage of such approaches is the relative simplicity of the calculation process itself, as well as the ability to achieve high calculation accuracy. The disadvantage, is the complexity of building these expressions for different types of systems: for each of them, a new calculation method often has to be created [23,26], [27,28], [29,30], [31,32], [33,34], [35,36], [37,38], [39,40], [41,42], [43,44], [45,46], [47,48], [49,50], [51,52], [53,54].…”

Section: Introductionmentioning

confidence: 99%

On the method of building of non-basic GL-models which are formed on combination of edge functions of basic models

Romankevich,

Morozov,

Romankevich

et al. 2024

AAIT

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Thiswork is dedicatedto the problem of building GL-models of behaviorof non-basicfault-tolerant multiprocessor systems in the failure flow. Such models can be used to calculate the reliability parameters of the latter. The system, depending on the fulfillment of certain conditions, is resistant to failures of various multiplicities. These conditions depend only on the states of the system's processors and can be represented by special Boolean expressions. A method ofconstructing GL-models of such systems based on combining expressions of the edge functions of auxiliary basicmodelsis proposed. At the same time, the specific featureof the models that were built by the proposed methodis that they are based on cyclic graphs. This simplifies the process of evaluating their connectivity and also simplifies the analysis of the model's operation. In addition, this allows usingother methods of modifying GL-models if necessary. The method involves usingauxiliary models that have the same number of edges.In order toequalize the number of edges, auxiliary models can be extendedwith additional edges with edge functions of a special type. It is shown that this extensiondoes not change the behavior of the models. In particular, theprocedure oforthogonalization ofthe Boolean expressions is described, which should be carried out if the conditions can be satisfiedsimultaneously. It is shown that the expressions of the edge functions of the obtained GL-models, which can be quite complex, can sometimes be significantly simplified. Numerous experiments have been conducted to confirmthe adequacy of the models (builtby the proposed method) to the behavior of the corresponding systems in the failure flow. Theexample is given to demonstratethe application of the proposed method.The resulting model is analyzed and shown to correspond to the behavior of the system forwhich it was built.

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Joint Reliability of Two Consecutive-(1, l) or (2, k)-out-of-(2, n): F Type Systems and Its Application in Smart Street Light Deployment

Cited by 7 publications

References 34 publications

On evaluation of reliability increase in fault-tolerant multi processor systems

On evaluation of reliability increase in fault-tolerant multi processor systems

On the modification of GL-models by adding edges to a cyclic graph

On the method of building of non-basic GL-models which are formed on combination of edge functions of basic models

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