Many industrial systems demand equipment with high levels of reliability. Companies and academia have been developing, over the years, mathematical methods and advancing engineering techniques to assist in the maintenance of active and reliable systems. There are different optimization problems in this context, highlighting (1) the redundancy allocation problem (RAP), (2) the reliability allocation problem, and (3) the reliability-redundancy allocation problem (RRAP). Multiple, frequently conflicting objectives are included in system reliability design challenges. Yet, a few are universal, such as maximizing reliability and minimizing costs. Many solving methods have already been applied to these problems, e.g., dynamic, linear, integer, and nonlinear programming, as well as classical metaheuristics based on evolutionary algorithms, such as the Genetic Algorithm (GA). Either way, these methods are modeled according to the specificities of the systems. However, these approaches can be very computationally expensive depending on the problem instances. Meanwhile, quantum computing has gained ground for combinatorial optimization problems. The problems are usually remodeled into the Quadratic Unconstrained Binary Optimization (QUBO) form and are optimized using quantum methods such as the Quantum Approximate Optimization Algorithm (QAOA). It is expected that problems with a high level of complexity can be solved more efficiently using these new methods than classical ones. Optimization methods have attempted to improve their efficiency by adding quantum concepts, as is the case of Quantum-inspired Evolutionary Algorithms (QEA). The QEA has a better diversity and convergence rate compared to other EAs because it uses qubit representation instead of numerical, binary, or symbolic representations. In this context, this paper aims to develop a systematic review of the literature through keyword filtering, article reading, and bibliometric analysis on the application of purely quantum and quantum-inspired methods in system reliability optimization problems, specifically in RAP, the reliability allocation problem, and the RRAP. Our goal is to identify quantum-based techniques’ advantages, limitations, and potential in such a context and suggest a research plan based on the observed literature gaps. |