Reliability optimization problem is one of the most important issues in studies about production systems and after-sales services. Nowadays, consumers expect lower-cost products and services with higher reliability, longer life, and better quality. New technologies introduction and their additional costs, including maintenance costs raises reliability analysis as a critical issue in engineering studies. In this manner, most of the studies are aim to improve the reliability of system along with minimal cost and change in the structure of systems. For complex systems which experience multiple dependent failure processes, the dependency among failure processes is a challenging issue in reliability modeling. In this thesis, the redundancy allocation is studied as an approach to increase the reliability of system. It is assumed that system components are subject to competition failure modes. In other words, the process of random shocks and degradation processes are linked together while, the shocks cause changing in degradation rate. In previous works, the impact of shocks and degradation process are studied exclusively in single-component systems.
