Abstract
In recent decades, the redundancy allocation problem (RAP) is becoming an increasingly important tool in the initial stages of planning, designing, and controlling of systems. Moreover, the redundancy allocation problem in multi-state systems (RAP in MSSs) is the extension derived from the traditional redundancy allocation problem in binary-state systems (RAP in BSSs) for practical modeling in real life. However, RAP in MSSs still has some restrictions that components have only two performances: perfect functionality and complete failure. Therefore, this paper formulates a new kind of RAP called repairable redundancy allocation problem in multi-state systems (RRAP in MSSs) so as to break the restrictions and generalize the previous problem. RRAP in MSSs designs are more closed to reality and widespread in many critical systems, such as power systems, transportation systems, and computing systems. Because of this, the computation of MSSs is more complicated than the BSSs’, and it is difficult to use the traditional technique to calculate system reliability. At this point, this research uses the universal generating function (UGF) to find out the whole system states and the corresponding probabilities with algebraic procedure, and then the system reliability is able to calculate. Moreover, RRAP in MSSs is not only an NP-hard problem, but also a nonlinear integer optimization problem. So this paper applies a novel algorithm called simplified swarm optimization (SSO) which is simple but powerful. Finally, the results obtained by SSO have been compared with that obtained from genetic algorithm (GA). Computational results show that the SSO is very competitive and effective in this problem.