Uncertain Age-Dependant Renewal Process

The performance of deterioration systems can be improved through the adoption of suitable maintenance policies. The traditional renewal process focus on the uncertainty of stochastic, but in many practical systems, the fuzziness is also important. In this thesis, the fuzzy uncertainty is studied, and three uncertainty maintenance models are provided.One of the most popular maintenance policies is the age-dependent replacement policy. Considered the uncertainty of fuzzy, the fuzzy age-dependent replacement policy is studied in which the lifetimes of components are treated as fuzzy variables. In a practical system the fuzziness and randomness are often mixed up with each other. Thus, both of the two uncertainties should be considered simultaneously. The fuzzy random age-dependent replacement policy and random fuzzy age-dependent replacement policy are also studied here, and the concept of long-run expected cost per unit time is provided.In order to get the best solution of the age-dependent replacement policy and minimize the long-run expected cost per unit time, three programming models are established. The simulation techniques for estimating the expected value of fuzzy, fuzzy random and random variable is developed. Furthermore, the simultaneous perturbation stochastic approximation (SPSA) algorithm based on simulation is designed to get the optimal solution of the proposed models.At the end of this thesis, the numerical examples are enumerated, and solved through the proposed algorithm. The results illustrate the effectiveness of the models and algorithm.