MMAPs to model complex multi-state systems with vacation policies in the repair facility

TL;DR

This paper develops a comprehensive Markovian model for complex multi-state repair systems with vacation policies, incorporating preventive maintenance, and provides computational methods for performance evaluation and optimization.

Contribution

It introduces a novel matrix-analytic approach to model multi-state systems with vacations, preventive maintenance, and economic optimization.

Findings

System performance can be optimized with preventive maintenance.

Vacation time distribution affects system reliability and cost.

The model is validated through numerical examples using Matlab and R.

Abstract

Two complex multi-state systems subject to multiple events are built in an algorithmic and computational way by considering phase-type distributions and Markovian arrival processes with marked arrivals. The internal performance of the system is composed of different degradation levels and internal repairable and non-repairable failures can occur. Also, the system is subject to external shocks that may provoke repairable or non-repairable failure. A multiple vacation policy is introduced in the system for the repairperson. Preventive maintenance is included in the system to improve the behaviour. Two types of task may be performed by the repairperson; corrective repair and preventive maintenance. The systems are modelled, the transient and stationary distributions are built and different performance measures are calculated in a matrix-algorithmic form. Cost and rewards are included in the model in a vector matrix way. Several economic measures are worked out and the net reward per unit of time is used to optimize the system. A numerical example shows that the system can be optimized according to the existence of preventive maintenance and the distribution of vacation time. The results have been implemented computationally with Matlab and R (packages: expm, optim).