## Abstract

I am developing a new branch of reliability theory called evolutionary reliability theory that concerns the evolution of reliability in populations of systems, such as organisms, that evolve. It subsumes the standard reliability theory but has a higher dimension of time, namely, evolutionary time. In reliability theory, failure phenomena are usually classified according to the monotone properties of the hazard rate h(x) = g(x)/R(x), where h is the hazard rate, x is the age at failure, g is the failure density function, and R is the reliability, where R(x) = P(X > x). Following this method of classification, we have three kinds of evolutionary reliability phenomena: failure events that exhibit (1) a decreasing hazard rate, (2) a constant hazard rate, and (3) an increasing hazard rate. An example of (1) is the reliability of biological development—the selection forces that have evolved safeguards, such as redundancy, so that developmental errors are maintained at a tolerable level. An example of (2) is the reliability of the fully developed system as it faces random failure processes, e.g., accidents, disease, and competition, and it thus concerns the evolution of structural and functional redundancy (e.g., two kidneys and two lungs). Category (3) concerns the reliability of the system with respect to wearout (aging) and this is the main subject of this paper.

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