Approximate Reliability Algebra for Architecture Optimization

Abstract

A more recent trend in Systems Engineering is architecture optimization. Evermore complex aircraft systems make it harder and harder to determine, with reasonable time and effort, optimal architectures by traditional trial-and-error trade off studies. This can be alleviated by architecture optimization techniques where System Engineers only defines boundaries for the design space and then an optimization solver finds the optimal solution automatically. If safety and reliability requirements are not considered during automatic architecture generation, given the high impact of safety on systems design, there is a high probability that the optimized architectures are not valid. Therefore, it is critical to model and take into account reliability and safety requirements during Design Space Exploration in early architectural stages.

Traditional reliability calculations are both not denotational and not linear which significantly narrows possible optimization techniques. In this work we suggest a Mixed Integer Linear Programming (MILP) formulation of the reliability calculus with the following features: (1) The order of magnitude of reliability calculations is correct, (2) There exists an explicit theoretical bound on potential “optimism” of the proposed algebra, (3) For a pool of representative benchmark problems the proposed approximation provides highly accurate results compared to the classical reliability calculations. This paper presents an approximate algebra for the safety analysis problem with explicit bounds and provides representative examples of its application.