^aDepartment of Mechanical Engineering and Mathematical Sciences, Oxford Brookes University, Wheatley, Oxford, UK

Correspondence: M.T. Todinov, Department of Mechanical Engineering and Mathematical Sciences, Oxford Brookes University, Wheatley Campus, Wheatley, Oxford OX33 1HX, UK. E-mail: mtodinov@brookes.ac.uk

Abstract

A basic principle for risk-based design has been formulated: the larger the losses from failure of a component, the smaller the upper bound of its hazard rate, the larger the required minimum reliability level from the component. A generalized version and analytical expression for this important principle have also been formulated for multiple failure modes. It is argued that the traditional approach based on a risk matrix is suitable only for single failure modes/scenarios. In the case of multiple failure modes (scenarios), the individual risks should be aggregated and compared with the maximum tolerable risk. In this respect, a new method for risk-based design is proposed, based on limiting the probability of system failure below a maximal acceptable level at a minimum total cost (the sum of the cost for building the system and the risk of failure). The essence of the method can be summarized in three steps: developing a system topology with the maximum possible reliability, reducing the resultant system to a system with generic components, for each of which several alternatives exist including non-existence of the component, and a final step involving selecting a set of alternatives limiting the probability of system failure at a minimum total cost. An exact recursive algorithm for determining the set of alternatives for the components is also proposed.