R-script to compute a candidate to optimal replacement policy in the problem of minimal repairs allocation for systems with homogeneous components

Abstract

The minimal repairs are a reasonable tool in many practical systems. Under this assumption a failed component is replaced by another one whose reliability is the same as that of the component just before the failure (i.e. a used component with the same age). A natural problem arises when we have a fixed number of repairs m and we need to decide (in advance) in which components (among n available) should be allocated these repairs. The Optimum_Seeker.R file is an R-script which provides, in the case of identically distributed components, a candidate to optimal replacement policy, if it exists, in terms of the usual stochastic order. Furthermore, this script provides a graphical representation of the distortion functions associated to: the system without repairing (in black), all possible strategies (in blue) and the optimal strategy suggested by the algorithm (in red).