‎The performance of a system depends not only on its design and operation but also on the servicing and maintenance of the item during its operational lifetime‎. ‎Thus‎, ‎the repair and maintenance are important issues in the reliability‎. ‎In this paper‎, ‎a repairable k-out-of-n system is considered that starts operating at time 0‎. ‎If the system fails‎, ‎then it undergoes minimal repair and begins to operate again‎. ‎The reliability function‎, ‎hazard rate function‎, ‎mean residual life function and some reliability properties of the system are obtained by using the connection between the concepts of minimal repair and record values‎. ‎Some known stochastic orders are also used to compare the lifetimes and residual lifetimes of two repairable k-out-of-n systems‎. ‎Finally‎, ‎based on the given information about the lifetimes of k-out-of-n systems‎, ‎some prediction intervals for the lifetime of the proposed repairable system are obtained‎.

Redundancy and reduction are two main methods for improving system reliability. In a redundancy method, system reliability can be improved by adding extra components  to some original components of the system. In a reduction method, system reliability increases by reducing the failure rate at all or some components of the system. Using the concept of reliability equivalence factors, this paper investigates equivalence between the reduction and redundancy methods. A closed formula is obtained for computing the survival equivalence factor. This factor determines the amount of reduction in the failure rate of a system component(s) to reach the reliability of the same system when it is improved. The effect of component importance measure is also studied in our derivations.