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 reliabil- - ity 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.