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.
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.
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.
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.
Zaitseva, E. and Levashenko, V. (2017), "Reliability analysis of multi-state system with application of multiple-valued logic", International Journal of Quality & Reliability Management, Vol. 34 No. 6, pp. 862-878. https://doi.org/10.1108/IJQRM-06-2016-0081
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