Constrained (k, d)-out-of-n systems

Abstract

Two new coherent system reliability models, which generalise k-out-of-n:F and consecutive k-out-of-n:G systems, are proposed and explicit formulae for the reliabilities of these systems are derived when the components are independent and identical and when they are Markov dependent. Our method of deriving reliability functions is based on the use of classical combinatorial arguments. These extensions consider an additional constraint on the number of working components between successive failures. More explicitly, in addition to the working conditions of k-out-of-n:F and consecutive k-out-of-n:G systems there must be at least d consecutive working components between any of two successive failures. This type of consideration might be useful in some situations including the analysis of constrained binary sequences arising in communications systems, and particular infrared detecting systems.

Keywords:

• k-out-of-n system
• consecutive k-out-of-n system
• Markov dependent components
• reliability
• stochastic systems

Acknowledgements

The authors would like to express gratitude to the referees for a thorough review and valuable comments that led to improvements in this article. Partial financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) for the second author is acknowledged.