Fuzzy renewal process, fuzzy renewal reward process and their applications

This work extends the work in Zhao and Liu on fuzzy renewal process and renewal reward process from continuous case to more general case. Fuzzy elementary renewal theorem and fuzzy renewal reward theorem are developed and shown how they can be applied to maintenance policies. Three kinds of maintenance policies- fuzzy age replacement policy, fuzzy block replacement policy and fuzzy inspection policy are discussed. The optimality functions studied are the long run expected costs per unit of time. Finally, a hybrid intelligent algorithm is employed to solve the models proposed in maintenance policies and to arrive at optimum policies. A numerical example is enumerated and the result indicates that the algorithm is effective.