Analysis of an k-out-of-n:G system with redundant dependency and repair equipment procurement

This paper studies an k-out-of-n:G system with redundant dependency and repair equipment procurement lead time where the operating times and repair times of components follow exponential distributions and phase-type distributions,respectively.When one component breaks down,it is repaired by a repair equipment.The repair equipment may fail during the repair period and the following repair is not‘as good as new’.After a number of repairs,it is replaced by a new one.The new spare repair equipment for replacement is only available by an order,and the procurement lead time for delivering follows a phase-type distribution.Moreover,in the multi-component system,the redundant dependency is taken into account.Applying the matrix-analytical method,the system availability,the rate of occurrence of failures of the system,the expected number of broken components,the availability and the rate of occurrence of failures of the repair equipment are derived.Finally,numerical examples are given to show these theoretical results.