Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Larry Mann


The subject of this research is the prediction of failures in repairable multi-component systems from statistical models that utilize the historical failure data for the systems. Failures occurring in repairable systems are examples of a series of discrete events which occur randomly in a continuum. Such stochastic point processes are analyzed using the statistics of event series. The Crow nonhomogenous Poisson process, NHPP, model is recognized by the reliability community as being one of the best models for repairable systems. The objective of this research is to show that the Crow NHPP model, with its overall failure predictions for a repairable system, can be utilized as a guide for testing the accuracy of a Monte Carlo simulation that utilizes the individual component Weibull distribution parameters to predict system failures. Failure data, from multiple versions of six different mechanical systems, are modelled by Crow's NHPP model. A program is presented that performs an iteration of Crow's equations to obtain the NHPP parameters that are then utilized to develop a failure intensity function for each respective system. Failure predictions are then determined from the mean value function of the NHPP model. The individual component failure data for each system are fitted to Weibull distributions and the resulting distribution function parameters are utilized in the respective Monte Carlo simulations. In each of the six cases a Monte Carlo simulation, based on the Weibull distributions of the major component failure modes, is used to predict the number of failures expected for each system. The Monte Carlo simulation predictions are shown to closely match the Crow nonhomogenous Poisson process predictions for the respective systems. In addition, the Monte Carlo simulations give failure prediction results that can be traced to individual components. The Crow model predicts when the overall system will be down, and then the simulation predicts the number of failures from each of the included components. The simulation can identify a finite number of parts that contribute to the overall system downtime. This information can be used to design an optimum preventive maintenance program or guide research into more reliable components.