Obsolescence of embedded parts is a serious concern for managers of complex systems where the design life of the system typically exceeds 20 years. Capital asset management teams have been exploring several strategies to mitigate risks associated with Diminishing Manufacturing Sources (DMS) and repeated life extensions of complex systems. Asset management cost and the performance of a system depend heavily on the obsolescence mitigation strategy chosen by the decision maker. We have developed mathematical models that can be used to calculate the impact of various obsolescence mitigation strategies on the Total Cost of Ownership (TCO) of a system. We have used classical multi-arm bandit (MAB), arm-acquiring bandit and restless bandit models to jdentify the best strategy for managing obsolescence in such instances wherein organizations have to deal with continuous technological evolution under uncertainty.