Exact equations for the reliability and mean time to failure of 1-out-of-n cold-standby system with imperfect switching

Document Type: Original Manuscript


1 Sharif University of Technology

2 Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran



Standby redundancy is a common and fundamental technique for increasing the reliability and availability of various systems. Cold-standby state is one of the most important strategies that are well used in non-repairable systems and plays an important role in mission-critical systems reliability, such as space exploration and satellite systems. In this paper, closed-form equations are derived using the Markov method to calculate the reliability function and the meantime to failure of a 1-out-of-n cold-standby system with non-repairable components under imperfect switching. While it is assumed that the failures of the switch and its associated active components are independent of each other, a constant failure rate is considered for the components and an increasing constant failure rate for the switch as it is used more frequently. In the end, numerical examples are solved for a system with various numbers of components to demonstrate the application of the closed-form equations.

Graphical Abstract

Exact equations for the reliability and mean time to failure of 1-out-of-n cold-standby system with imperfect switching


  • The system involves one active and (n-1) cold standby non-repairable components.
  • An imperfect switch is used.
  • The Markov method is used to calculate system reliability and MTTF.
  • It is shown that the switch plays a more important role in system reliability.


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