The task of allocating failure rates to components within a complex repairable system is executed early in a product development process in order to set reliability targets for those components. This allocation process is often accomplished versus more than one constraint, for instance to achieve an overall system-level failure rate, λsys, and to achieve an overall system life cycle unplanned maintenance cost (LCUMC) target. Presumably, there exists an optimum component allocation solution that would most effectively meet those goals, while minimizing risk to the ultimate product. In this context, risk is defined as the probability that some subset of the components will not achieve their allocation targets, and the impact, in the form of higher λsys, higher maintenance costs and lower customer satisfaction, of those higher component failure rates. However, with only λsys and LCUMC as constraints, finding such an optimum solution is difficult. Both λsys and LCUMC move together when evaluating different solutions—as a component’s failure rate allocation is reduced, it’s expected LCUMC is proportionally reduced. This affords no opportunity for trading one criterion versus the other. Additionally, this is a multi-dimensional, multi-criteria (MDMC) optimization problem for a complex system; each component’s failure rate is one variable that may be adjusted to find the best solution. To address the first difficulty, it is proposed that a third metric, the System Total Reliability Risk (STRR), be considered to facilitate such an optimization solution. The STRR is a measure of the aggregate product reliability risk inherent in the allocation solution chosen—the probability that the overall allocation solution might not be achievable and the potential impact of that miss. It is roughly a measure of the degree of difficulty to achieving the proposed component failure rate allocations, given that different types of components in a particular service generally have a limit to the best failure rate that can be achieved in practice. Employing a measure such as STRR offers the needed optimization countering force to allow for finding an allocation solution that meets the λsys and LCUMC targets, while reducing product reliability risks by selecting an allocation solution that may be easiest to achieve in practice. Addressing the second difficulty (finding an optimum solution to the MDMC problem) is accomplished through genetic algorithm-based techniques, where those algorithms search for an allocation solution with the highest degree of “fitness”. Fitness is measured as a function of the three constraints of the problem −λsys, system LCUMC, and STRR. The practical utility of such an approach is that it finds an allocation solution which minimizes the STRR, while still meeting the customer-driven reliability targets for λsys and LCUMC.
Investigation of component failure rates for pulsed versus steady state tokamak operation
