Quantifying resilience for resilience engineering of socio technical systems

Resilience engineering can be defined to comprise originally technical, engineering and natural science approaches to improve the resilience and sustainability of socio technical cyber-physical systems of various complexities with respect to disruptive events. It is argued how this emerging interdisciplinary technical and societal science approach may contribute to civil and societal security research. In this context, the article lists expected benefits of quantifying resilience. Along the resilience engineering definition objectives, it formulates resilience optimization or minimization problems, which can be further detailed, e.g. in terms of resilience chance optimization. The main focus is on four types of approaches to achieve resilience quantification: (1) qualitative/quantitative/analytical resilience assessment processes and frameworks, (2) probabilistic/statistical static expansion approaches, (3) resilience trajectory/propagation/dynamic approaches, and (4) complex system resilience modeling, simulation and analysis. The article comprises for each quantification option its motivation, a top level derivation as well as formal, tabular, schematic or plot-wise representations, as appropriate. For each approach, a list of application examples of methods are given that could implement the resilience quantification. In particular, the article introduces the concepts and notions of resilience expansion order analysis, resilience transition matrix elements, generation of time-dependent resilience response curves, indicators and distributions, resilience barrier, and resilience tunneling or equivalently resilience gap and resilience bridging, as well as resilience quantity probability density.