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Most of the real world systems are subject to online deterioration resulting in higher production cost, lower product quality and missed schedules. Thus the study of optimal repair, replacement and warranty strategies assumes a special significance. The objective of the present thesis is to propose and analyze a new class of models for deteriorating systems. Amongst the many approaches to model deteriorating system, shock models by virtue of their tractability and applicability to diverse areas has attracted the attention of modelers. Traditional shock models view system failure as a first passage problem of the cumulative damage process to cross a threshold. This thesis proposes a new class of shock models in which system failure is dependent on the frequency of shocks and explicitly obtains the various statistical characteristics of system failure. The thesis presents several optimal replacement problems of deteriorating systems within the ambit of the proposed class of models and explicitly obtains the optimal replacement times and the associated cost. The procedures are illustrated with numerical examples.