Redundancy allocation problem of a Multi-State system with Binary-State continuous performance level components

•Introducing a new concept for BS-CPL components,•Presenting a modified UGF to calculate the availability of such components,•Performing a RAP for a series–parallel system of subsystems with such components.•Adopting GA, PSO, and TLBO meta-heuristics to solve the provided mathematical model,•Adopting a two-stage algorithm’s parameters tuning for the GA. This paper presents a new single-objective redundancy allocation problem (RAP) for a system with subsystems in a series–parallel configuration. Different types of binary-state components are available for each subsystem, without the choice of component mixing, but the allocated components must be identical. Moreover, the components have a continuous performance level, i.e., their performance level is between zero and their maximum performance level. The presented model aims to maximize the system’s availability by determining the optimum number and type of the allocated components to each subsystem in some constraints, such as the system’s cost and weight. Since the components have continuous performance levels, the performance levels of the subsystems and the system are also continuous. First, the real-time and instantaneous availability of components, subsystems, and systems is modeled and calculated by adopting a modified universal generating function. Then, the mathematical model for the above-mentioned RAP is presented and solved using a Genetic Algorithm (GA), a Particle Swarm Optimization (PSO), and a Teaching-Learning-Based Optimization (TLBO) meta-heuristics. Next, a full enumeration technique is used to validate the performance of the adopted meta-heuristics as well as to validate the presented mathematical model. The results show the superiority of the adopted GA to solve the presented RAP. Finally, sensitivity analyses of the model’s input parameters are conducted using a GA, and the effects of changing the model’s parameters on the system’s availability are investigated.