Dynamic Multilevel Redundancy Allocation Optimization Under Uncertainty

Abstract

System engineers are facing new challenges in designing products due to a variety of reasons: I) as the time between introducing new technologies is getting shorter, the capability of upgrading with new technologies is a key requirement in designing sustainable products. II) To satisfy customers' requirements, products should be adapted to their needs and applications, which may vary from each other, or differ from time to time, such as the changes in working conditions. III) New data about different aspects of products' performance comes to the system on an ongoing basis. Responding to this information and considering the possibility of changing the prior knowledge about the working conditions and the system's performance should be considered in the design phases.Multilevel designs aim to improve the maintenance and replacement process and facilitate redundancy allocation. Components at the same level are replaced and maintained together. For each level, it is possible to consider different choices, and customers can select their combinations based on their needs. This design addresses the aforementioned challenges for high-reliability products. The design can be upgraded with new technologies by replacing old components with new ones at different levels. Moreover, after realizing new information regarding the system's performance and working conditions, the multilevel design enables the possibility of immediate adjustment according to the new information. In addition, multilevel design makes the diagnostic process more efficient and maintenance and replacement actions more economical.Although some methodologies are proposed to allocate redundancy in multilevel systems, they assume all decisions are made at the initial design. They ignore the possibility of responding to future uncertainties by changing the redundancy configuration. Moreover, the redundancy allocation in multilevel series-parallel systems has not been addressed under uncertain conditions.In this study, a multilevel redundancy allocation problem is considered. It is assumed some uncertainties are realized at the time of operation, such as working conditions and workload. Moreover, the system’s configuration at some levels can be updated according to the customers’ needs during the usage. The paper develops a two-stage stochastic model. In stage I, the redundancy allocation is optimally designed at the components’ levels considering the uncertainties. In stage II, after realizing the uncertain parameters, as a response, the customer updates the system redundancy at the defined levels.To deal with the complexity of the proposed model, a genetic algorithm (GA) is developed to find the optimal solution. The results of the static and dynamic stochastic models are compared to show the model’s capability to improve the system's reliability.