Research Article Open Access

A Complex Multi-State System with Vacations in the Repair

Juan Eloy Ruiz-Castro1
  • 1 University of Granada, Spain


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.

Journal of Mathematics and Statistics
Volume 15 No. 1, 2019, 225-232


Submitted On: 14 July 2019 Published On: 5 September 2019

How to Cite: Ruiz-Castro, J. E. (2019). A Complex Multi-State System with Vacations in the Repair. Journal of Mathematics and Statistics, 15(1), 225-232.

  • 1 Citations



  • Phase-Type Distribution
  • Preventive Maintenance
  • Optimal Vacation Time