Reliability Stress-Strength Modeling Demystified

A stress versus strength analysis is a common technique within the reliability community especially for tasks associated with structural reliability predictions. Often the strength distribution is plotted with the stress distribution and the intersection of these two curves is of interest from a reliability perspective. Within the reliability community, some view this intersecting or joint area under both distributions as the unreliability of the system. This is a subtle misconception since the reliability (or unreliability) is the area under a subsequent distribution known as the convolution of the stress and strength curves. The intersecting area approach and the convolution methodologies will be contrasted throughout this paper utilizing three examples of increasing complexity. The first example will demonstrate both approaches using a mathematically tractable paradigm that is based on uniform distributions. The second example will also execute both approaches and is based on the ubiquitous Gaussian distributions, which possess closed-form solutions. The last example will be based upon a mixture of the Weibull and Gaussian distributions, which prompts the use of Monte Carlo simulation.