On evaluation of reliability increase in fault-tolerant multiprocessor systems

Abstract

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-n systems, and more
complex ones, including hierarchical systems. An important feature of the proposed approach is that it involves the preliminary
calculation of some additional auxiliary values that do not depend on the reliability parameters of the added processor. Further, the
reliability increase is assessed by substituting these parameter values into basic expressions, 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 complexity of such calculations. In addition, for the simplest cases
considered, k-out-of-n systems with identical processors, a simple expression is proposed for an approximate estimate of the ratio of
failure probabilities of the original and modified systems. The higher 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.