Probabilistic physics-of-failure models for component reliabilities using Monte Carlo simulation and Weibull analysis: a parametric study

In reliability engineering, component failures are generally classified in one of three ways: (1) early life failures; (2) failures having random onset times; and (3) late life or 'wear out' failures. When the time-distribution of failures of a population of components is analysed in terms of a Weibull distribution, these failure types may be associated with shape parameters β having values <1, ∼1, and >1 respectively. Early life failures are frequently attributed to poor design (e.g. poor materials selection) or problems associated with manufacturing or assembly processes. We describe a methodology for the implementation of physics-of-failure models of component lifetimes in the presence of parameter and model uncertainties. This treats uncertain parameters as random variables described by some appropriate statistical distribution, which may be sampled using Monte Carlo methods. The number of simulations required depends upon the desired accuracy of the predicted lifetime. Provided that the number of sampled variables is relatively small, an accuracy of 1-2% can be obtained using typically 1000 simulations. The resulting collection of times-to-failure are then sorted into ascending order and fitted to a Weibull distribution to obtain a shape factor β and a characteristic life-time η. Examples are given of the results obtained using three different models: (1) the Eyring-Peck (EP) model for corrosion of printed circuit boards; (2) a power-law corrosion growth (PCG) model which represents the progressive deterioration of oil and gas pipelines; and (3) a random shock-loading model of mechanical failure. It is shown that for any specific model the values of the Weibull shape parameters obtained may be strongly dependent on the degree of uncertainty of the underlying input parameters. Both the EP and PCG models can yield a wide range of values of β, from β>1, characteristic of wear-out behaviour, to β<1, characteristic of early-life failure, depending on the degree of dispersion of the uncertain parameters. If there is no uncertainty, a single, sharp value of the component lifetime is predicted, corresponding to the limit β=∞. In contrast, the shock-loading model is inherently random, and its predictions correspond closely to those of a constant hazard rate model, characterized by a value of β close to 1 for all finite degrees of parameter uncertainty. The results are discussed in the context of traditional methods for reliability analysis and conventional views on the nature of early-life failures