Multistate series-parallel mixed redundancy allocation design heuristic

This study describes the use of a heuristic approach for optimizing the multistate series-parallel system (MSPS) design problem. The binary redundancy optimization problem is a classical combinatorial optimization problem. The binary problem formulation assumes a specific number of subsystems are connected in series and for each subsystem there are multiple component types to select from and use in parallel. The problem is then to choose the best system component configuration in order to optimize a figure-of-merit subject to a set of given constraints. Optimization approaches that yield very good or optimal solutions have included genetic algorithms (GA), linear programming , mixed integer programming, dynamic programming, non-linear programming and heuristics. These procedures assume the system functional behavior follows a binary nature. That is, the system can have only two states either working or failed. For some systems, the binary assumption fails to recognize the true nature of the system functional behavior. An incorrect binary state assumption could potentially overestimate system reliability leading to incorrect results and poor system design. Furthermore, the binary approach assumes that the different component types available to provide a defined function contribute to the system performance in equal terms. That is, no difference in the components' system nominal performance exists. However in practice, there are different component versions with known cost and reliability that can yield different system performance; measured as a capacity of system requirement. Recognition of these performance considerations for system configuration is important due to the significant reduction in cost that an optimal system design can yield. Thus, for many design problems a modeling approach that addresses these multi-state performance issues and yields good solutions to the reliability design problem can have an immediate impact in industry. This study considers a series-parallel system where components are binary but different kinds of components have different nominal performance levels and the system is expected to work at different demand levels. Thus, the system can have a range of different performance states, i.e., multistate, depending on the performance levels and the operating state of the components. The study proposes an extension of the heuristic developed by the authors for optimizing a MSPS. This extension addresses system designs allowing heterogeneous mixing of components within a particular subsystem. This is a common design practice in many industries but available techniques can be cumbersome to apply. For the MSPS problem, researchers have developed heuristic approaches, based on GA, to solve the problem of minimizing system cost subject to a reliability or availability constraint. These methods do not guarantee an optimal solution although they have been demonstrated to yield very good results. In this paper, an estimation methodology for the MSPS is presented and a heuristic algorithm is developed. This new approach offers simpler, more efficient analyses. It is unlikely that these methods improve upon the results using the universal generating function/GA approach; however they may be attractive to many practitioners. In this paper, the system is designed as a series-parallel configuration, but the system is not subject to the usual binary structure function formulation because of the components performance considerations. The system is composed of a fixed number of subsystems connected in series to be designed so that its total cost is minimized and reliability is greater than or equal to prescribed levels for different operating time intervals. Different components are available for each subsystem design. Cost, reliability and system performance nominal capacity are known for each component type.