Towards A Unified Definition For Reliability, Survivability And Resilience (I): The Conceptual Framework Inspired By The Handicap Principle And Ecological Stability

Reliability function [R(t) = P(T > t)] (where T is the lifetime or failure time, and P is the probability) serves as the definition of reliability very successfully in the sense that (i) it acts as an excellent pedagogical model; (ii) its fundamental concept, although often extended extensively, still holds in complex real-world reliability analysis. In contrast with reliability analysis, there is not a commonly accepted survivability function that assumes a similar role as the reliability function does in reliability analysis. In this article, I first analyze the challenges of defining such a survivability function that is similar to reliability function, and then argue that by synthesizing the existing definitions developed by leading scholars of survivability research [notably, Ellison et al. (1997), T1A1 group (ANSI T1A1.2, 2001), Knight (2003), Liu & Trivedi (2004), "ResiliNets Project" (ReSterbenz & Hutchinson et al. 2009)], a unified definition for reliability and survivability in the form of a 4-tuple: Survivability = [Resistance, Resilience, Persistence, Failure Counter], with the notion that resistance is equivalent to traditional reliability, is meaningful. Although the 4-tuple definition is much more complex than the reliability function, I argue that it possesses promising potential to become a survivability definition with the two similar properties demonstrated by the traditional reliability function. My arguments are based on two lines of developments: (i) The first three elements of the 4-tuple capture critical aspects of survivability and each of them possesses rigorously defined mathematical models. These models, developed in a series of our previous studies (Ma & Krings 2008a-d, Ma 2008, 2009a-c), when integrated together, form a modeling architecture for performing many real-world reliability and survivability analyses. This contribution from the new 4-tuple definition corresponds to the second property of the traditional reliability function. (ii) The 4-tuple definition is also inspired by two biological theories: the handicap principle that governs the honesty (reliability) of animal communication, and the stability theory of ecological systems. Both theories are examples of nature's versions of 'reliability' and 'survivability'. How nature evolves both reliable and survivable (super reliable) features should be inspirational to the study of engineering reliability and survivability.