System Failure Identification using Linear Algebra: Application to Cost-Reliability Tradeoffs under Uncertain Preferences

Reaching a system level reliability target is an inverse problem. Component level reliabilities are determined for a required system level reliability. Because this inverse problem does not have a unique solution, one approach is to tradeoff system reliability with cost and to allow the designer to select a design with a target system reliability, using his/her preferences. In this case, the component reliabilities are readily available from the calculation of the reliability-cost tradeoff. To arrive at the set of solutions to be traded off, one encounters two problems. First, the system reliability calculation is based on repeated system simulations where each system state, indicating which components work and which have failed, is tested to determine if it causes system failure, and second, the task of eliciting and encoding the decision maker's preferences is extremely difficult because of uncertainty in modeling the decision maker's preferences. Establishing if a system state leads to system failure is a cumbersome process using existing techniques. The contribution of this paper is in developing a method to streamline this process, using linear algebra. The method is then applied to cost-reliability tradeoff analysis using the method of conservative envelopes. We show how decisions can be made using a modified Pareto front if the decision maker's preference structure is uncertain. Also, reliability allocation can be performed by comparing different designs on the Pareto front based on the worst performance as measured against different candidate utility functions. We demonstrate our approach using a four-joint robot example.