On reliability analysis of a multi-state (k+1)-out-of-n:F system with partial failure

  • Nupur Goyal
  • Shubham Amoli
  • Alok Suyal
  • Mangey Ram


In this paper, an idea of reliability measures of complex system has been introduced. The designed system which consists of three repairable subsystems A, B and C connected randomly with each other, the subsystem B is a type of (k+1)-out-of-n:F. The complete system can fail due to the failure of more than k number of units of subsystem B. The whole system is solved with the help of supplementary variable technique, Laplace transformation and birth-death Markov’s law. The generalized expression of the state probabilities, availability, reliability of the system and mean time to failure are derived and investigated the impact of parameter ’s results under various cases graphically. Also, the cost-benefit analysis under the consideration of maintenance cost are possessed.