Metrics for Evaluating Survivability in Dynamic Multi-Attribute Tradespace Exploration

Abstract

Survivability engineering is critical for minimizing the impact of disturbances to the operation of space systems. To improve the evaluation of survivability during conceptual design, metrics are proposed for the assessment of survivability as a dynamic, continuous, and path-dependent system property. Two of these metrics, time-weighted average utility loss and threshold availability, are then incorporated into a tradespace study on the survivability of future space tug vehicles to orbital debris. A value-based design approach, Dynamic Multi-Attribute Tradespace Exploration, is taken to evaluate survivability based on the relationship between stochastic space tug utility trajectories and changing stakeholder expectations across nominal and disturbed environmental states. Results of the tradespace study show that moderate levels of bumper shielding and access to an on-orbit servicing infrastructure benefit space tugs with large exposed cross-sectional areas while active collision avoidance only delivers value to extremely risk-averse decision makers. Timeweighted average utility loss and threshold availability are found to be discriminating metrics for navigating survivability tradespaces of thousands of design alternatives. Nomenclature A T= threshold availability CS = campaign-level survivability ∆V = change in velocity F(t) = failure likelihood as a function of time MoME = measure of mission effectiveness MTAT = mean time above critical value threshold MTBF = mean time between repair MTTR = mean time to repair P K = probability of kill P K|E = probability of kill for multiple-shot engagement P K|SS = probability of kill from single-shot P S = probability of survival P S|E = probability of survival for multiple-shot engagement P H = probability of hit (susceptibility) P K|H = probability of kill given hit (vulnerability) R(t) = reliability as a function of time T dl = time of design life T r = permitted recovery time U ¯ L = time-weighted average utility loss from design utility, U 0 Ū t = time-weighted average utility U(t) = utility delivery over time; multi-attribute utility trajectory V e = emergency value threshold V(t) = value delivery over time V x = required value threshold

Building the tower without climbing it: Progress in engineering systems

“…In particular, Multi‐Attribute Tradespace Exploration (MATE) has succeeded in combining standard multiattribute utility theory with early‐stage system design in a manner that can assist decision makers to explore the consequences of architectural decisions. Furthermore, this approach has made some progress on incorporating some ilities into design . Thus, researchers inspired by the rational approach have made some progress formalizing early design decisions, even beginning to address the challenges outlined by ES scholars.…”

Resilience in engineered resilient systems

“…This will allow for generation of metrics of interest (MOI) trajectories, necessary for the calculation of resilience metrics. 37 Such modeling includes consideration of perturbation to system, e.g., enumeration of potentials, approach, encounter, contact, and impact (as imposed state change), as well as consideration of system to perturbation, e.g., detection of perturbations, susceptibility, vulnerability, and recoverability (as executed state change/resistance).…”

A Practical Method for Tradespace Exploration of Systems of Systems

“…Methods used for SoS attribute combination at the medium level may involve time-weighted averaging, such as the concept of time-weighted average utility. 13 The highest level of attribute combination is required when multiple SoS components deliver performance relating to the same SoS attribute simultaneously. In this case, fusion of the attributes at a more detailed level than just averaging is required.…”