Journal of Mathematics and Statistics

A Complex Multi-State System with Vacations in the Repair

Juan Eloy Ruiz-Castro

DOI : 10.3844/jmssp.2019.225.232

Journal of Mathematics and Statistics

Volume 15, 2019

Pages 225-232


A complex multi-state system subject to wear failure and given preventive maintenance is considered. Various internal levels of degradation are assumed. The repair facility is composed of a repairperson, who may take one or more vacations during the period considered. A policy is established for the repairperson’s vacation time. Two types of task may be performed by the repairperson: corrective repair and preventive maintenance. All embedded times in the system are phase type distributed. The transient and stationary distributions are determined and several reliability measures are developed in a matrix-algorithmic form. Costs and rewards are included in the model. The results are implemented computationally with Matlab. A numerical example shows that the distribution of vacation time can be optimised according to the net reward established.


© 2019 Juan Eloy Ruiz-Castro. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.