Component choice for managing risk in engineered systems with generalized risk/cost functions

Abstract The constrained optimization of resource allocation to minimize the probability of failure of an engineered system relies on a probabilistic risk analysis of that system, and on ‘risk/cost functions’. These functions describe, for each possible improvement of the system's robustness, the corresponding gain of reliability given the considered component or management factor to be upgraded. These improvements can include, for example, the choice of components of different robustness levels (at different costs), addition of redundancies, or changes in operating and maintenance procedures. The optimization model is generally constrained by a maximum budget, a schedule deadline, or a maximum number of qualified personnel. A key question is thus the nature of the risk/cost function linking the costs involved and the corresponding failure-risk reduction. Most of the methods proposed in the past have relied on continuous, convex risk/cost functions reflecting decreasing marginal returns. In reality, the risk/cost functions can be simple step functions (e.g. a discrete choice among possible components), discontinuous functions characterized by continuous segments between points of discontinuity (e.g. a discrete choice among components that can be of continuously increasing levels of robustness), or continuous functions (e.g. exponentially decreasing failure risk with added resources). This paper describes a general method for the optimization of the robustness of a complex engineered system in which all three risk/cost function types may be relevant. We illustrate the method with a satellite design problem. We conclude with a discussion of the complexity of the resolution of this general type of optimization problem given the number and the types of variables involved.