This research includes two topics: (1) the modeling of periodic preventive maintenance policies over an infi nite time span for repairable systems with the reduction of the degradation rate after performing an imperfect preventive maintenance (PM) activity; (2) the parameter estimation of failure distribution and the restoration effect of PM from the proposed PM policy for deteriorating systems. The concept of the improvement factor method is applied to measure the restoration effect on the degradation rate for a system after each PM. An improvement factor is presented as a function of the system's age and the cost of each PM. A periodic PM model is then developed. The optimal PM interval and the optimal replacement time for the proposed model can be obtained by minimizing the objective functions of the cost rate through the algorithms provided by this research. An example of using Weibull failure distribution is provided to investigate the proposed model. The method is proposed to estimate the parameters of the failure process and the improvement effect after each PM by analyzing maintenance and failure log data. In this method, a PSO-based method is proposed for automatically constructing a fuzzy system with an appropriate number of rules to approach the identifi ed system. In the PSO-based method, each individual in the population is constructed to determine the number of fuzzy rules and the premise part of the fuzzy system, and then the recursive least-squares method is used to determine the consequent part of the fuzzy system constructed by the corresponding individual. Consequently, an individual corresponds to a fuzzy system. Subsequently, a fi tness function is defi ned to guide the searching procedure to select an appropriate fuzzy system with the desired performance. Finally, two identifi cation problems of nonlinear systems are utilized to illustrate the effectiveness of the proposed method for fuzzy modeling.