Preventive replacement/maintenance program development and evaluation for multi-unit systems with economic dependency: Stochastic modeling and simulation study

The focus of this research was the maintenance decision problem for multi-unit systems with economic dependency. In the research, an opportunistic maintenance policy generally applicable to the economic dependency problem was proposed for developing optimal maintenance schedule.; The system's failure-repair process under such a policy was characterized by two failure modes. The first mode was determined by the failure distribution of the unit under evaluation. The second mode was determined by the conditional failure probability of the remaining units in the system.; In order to better understand and describe the second failure mode for general multi-unit system, the parameter "expected replacement rate" (ERR) was derived from renewal theory, and its asymptotic property was used to approximate the distribution of the second failure mode as exponential. Because the resulting distribution was exponential, the failure-repair process of each unit was approximated as renewal process.; Based on renewal theory, the optimal maintenance schedule problem for multi-unit systems was solved by developing a probabilistic model. This model can accommodate different joint replacement strategies specified by maintenance policy. A robust solution algorithm was developed and coded in FORTRAN to solve the non-linear multi-variate decision model.; Three cost boundary measurements were proposed to evaluate potential cost savings due to the implementation of the different maintenance strategies. Three example problems with different system parameters were systematically studied in order to demonstrate the effectiveness of the model and solution algorithm. In addition, seven maintenance policies were applied to each of the three examples for comparison. A consistent rank order was found for the different maintenance policies based on cost minimization, and the proposed maintenance policy was shown to be the most effective one.; The optimal solutions from the analytical models were tested and verified by simulation. Random variate generation was found to be a possible error source in validating simulation results. This problem was addressed by comparing the simulation results to the results from simple but "error-free" analytical models.; The simulation results confirmed the rank order of maintenance policies obtained from the analytical results. Simulation results also showed that the optimality of the analytical solutions was better than that predicted by the approximated OM analytical models. This indicates that the analytical approach developed in this research is generally applicable and is effective in developing the optimal maintenance program.