A Diffusion Method for Reliability Prediction

Elements of the theory of diffusion processes are utilized to develop methods for predicting the reliability and the moments of the time to first failure of systems that have nonconstant failure rates and exhibit degradation failure. Specifically, systems characterizable by k independent parameters are considered, each of which independently exhibits degradation failure. The methods presented for obtaining a probabilistic description of such systems rest on the assumption that the time behavior of each of the system parameters can be characterized by a Brownian process (a special type of diffusion process). The methods then allow predictions of reliability and the moments of the time to first failure to be made from data taken early in life tests. In particular, the first moment is the mean time to first failure of the system.