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

This paper discusses the study of different reliability measures of a complex system composed of two subsystems with controllers connected in a series arrangement, which is an interesting possibility for specific design problems. Subsystem-1 is made up of n units that operate under the policy k-out-of-n: G; policy, whereas subsystem-2 is made up of m units that operate under the r-out-of-m: G; policy. Both subsystems' failure rates are constant and expected to obey an exponential distribution; two types of distributions are permitted to repair: general and Gumbel-Hougaard family copula distributions. During the process the partially failed states are mended via general repair, while the completely failed states are fixed using copula repair. After repair, both subsystems are as good as new. Both subsystems are controlled by a controller, and if the controller fails, the whole system fails. If the operator is dissatisfied with the organization, he/she may purposefully fail the system. The problem is modelled using the supplementary variable technique, Laplace transforms and copula repair. Traditional system reliability measures, such as availability, reliability, and expected profit, are calculated for various arbitrary values of failure and repair parameters.