Stochastic analysis of k-out-of-n: G Type of Repairable system in Combination of Subsystems with Controllers and Multi Repair Approach

Document Type : Review Paper


1 Department of Mathematics Yusuf Maitama Sule University, Kano, Nigeria

2 Department of General Requirement, Sur College of Applied Sciences, Sur, Oman


This paper describes the investigation of different reliability measures of a complex system consisting of two subsystems with controllers in a series configuration, which is a useful opportunity for specific design problems. Subsystem-1 consisting n units functioning under the policy k-out-of-n: G; policy, and subsystem-2 has m units and operating under r-out-of-m: G; policy. The system failure rates of both subsystems are constant and assumed to obey an exponential distribution; two types of distribution are allowed to repair: general distribution and Gumbel-Hougaard family copula distribution. The system's partially failed states/ completely failed states are repaired using General/ copula distribution. After repair, the units in both the subsystems are "as good as new." The controller control both subsystems and the failure of controllers brings the subsystem in the complete failed state. The operator may fail the system deliberately if not satisfied with the organization. The system is analyzed employing the supplementary variable technique, and Laplace transforms implications and traditional system reliability measures, such as the system's availability, system reliability, and profit analysis, have been computed for particular values of failure and repair parameters.

Graphical Abstract

Stochastic analysis of k-out-of-n: G Type of Repairable system in Combination of Subsystems with Controllers and Multi Repair Approach


  • Availability of the system has evaluated for two cases Copula repair and General Repair
  • Comparison of both performances for Copula repair and General repair has conclusively elaborated.
  • System reliability of different cases have evaluated, MTTF for system performance is computed.
  • Profit analysis have also computed for the both cases copula repair and general repair. Copula repair is predicted better performance has concluded.


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