Solution algorithms for a nonhomogeneous multi-component inspection model

Abstract

In this paper, we present three solution algorithms for an established multi-component inspection system model based upon the delay time concept. First, Algorithm 1 is developed for obtaining the system replacement time if the defect arrival process is non-homogeneous. Algorithm 2 is presented as an extension to Algorithm 1 in which the non-constant optimal inspection intervals are also determined. Algorithm 3 is a numerical algorithm for solving an integral equation arising within the model in the case of opportunistic inspection at failures. Finally, an example is given to demonstrate the algorithm set in practice. The proof of the existence and uniqueness of solutions are presented. Scope and purpose Solution algorithms are proposed for an established multi-component system inspection model based upon the delay time concept. The decision variables are the non-constant inspection interval and the system replacement time if the defect arrival process of the system follows a non-homogeneous Poisson process. This is a typical multiple-decision problem with a possible large number of decision variables depending upon the number of inspections which is unknown before the inspection intervals and the system replacement time are determined. The solution to this problem could be NP-hard if a conventional multi-decision solution approach is adopted. The proposed algorithms use the recursive procedure to determine the replacement time and reduce the number of decision variables to one, namely the first inspection interval. The algorithms developed can be used to optimise maintenance performance of a multiple component system subject to a non-homogeneous deterioration process.