Redundancy allocation with non-identical component and uncertainty

Redundancy Allocation of Components with Time-Dependent Failure Rates

“…RAP is a problem of NP-hard class [68], and a meta-heuristic algorithm is here developed to search for the optimal solution. The genetic algorithm (GA) is a well-known meta-heuristic method for solving combinatorial optimization problems [69] and, indeed, it has been successfully employed for solving optimization problems in various fields [1,[4][5][6]8,24,30,38,[41][42][43][44][45][46][47]56]. In the following, the deployment of the algorithm for the solution of the proposed RAP is briefly described.…”

“…At each iteration, new offspring are generated by implementation of the crossover and mutation operators. The roulette wheel selection method is used to select the parents [8,40]. In the roulette wheel selection method, selection of the parents occurs based on their fitness function value: in other words, a solution is selected with probability proportional to its fitness function.…”

“…Other aspects come realistically into play in a RAP; these include the objective function, the states of the components and that of the entire system, the type of the components to be allocated to each subsystem, the reparability of the components, and so on. For example, RAPs may be considered with a single objective function, e.g., aiming to maximizing system reliability [1,[3][4][5][6][7][8][9][10][11]27,28,30,31,[35][36][37][39][40][41]44,[46][47][48][53][54][55], minimizing total system cost [12][13][14][15] or maximizing/minimizing other parameters [16,29]. Alternatively, RAPs may consider multi-objective functions [18][19][20][21][22][23][24][25]32,34,38,42,45,50,…”

“…Regarding the components, they might be represented as binary or multi-state. In the binary state representation, the components can only be totally healthy or completely failed [1,[3][4][5][6][7][8][9][10][11][12][13][17][18][19][20][21][22][23][25][26][27][28][29][30][31][32][33][34][35]40,41,[43][44][45][46][47][48]53,55]; in the multi-state, the components might have other states, intermediate between these two [14][15][16]24,[60][61][62][63][64][65]. The type of the components ...…”

“…The type of the components in the subsystems can be characterized from different viewpoints. For instance, allocation of either identical [1,[3][4][5][6][7]12,[18][19][20]35,36,40,45,46,53,54] or non-identical components to each subsystem might be allowed [8][9][10][11][13][14][15][16][17]21,22,25,27,28,33,37,41,44,48,49,62]. Moreover, the components characteristics, including their cost, weight and performance function, might be deterministic or uncertain functions [66].…”