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This paper considers a multi-objective reliability-redundancy allocationproblem (MORRAP) of a series-parallel system, where system reliability andsystem cost are to be optimized simultaneously subject to limits on weight,volume, and redundancy level. Precise computation of component reliability isvery difficult as the estimation of a single number for the probabilities andperformance levels are not always possible, because it is affected by manyfactors such as inaccuracy and insufficiency of data, manufacturing process,environment in which the system is running, evaluation done by multipleexperts, etc. To cope with impreciseness, we model component reliabilities asinterval type-2 fuzzy numbers (IT2 FNs), which is more suitable to representuncertainties than usual or type-1 fuzzy numbers. To solve the problem withinterval type-2 fuzzy parameters, we first apply various type-reduction anddefuzzification techniques, and obtain corresponding defuzzified values. Asmaximization of system reliability and minimization of system cost areconflicting to each other, so to obtain compromise solution of the MORRAP withdefuzzified parameters, we apply five different multi-objective optimizationmethods, and then corresponding solutions are analyzed. The problem isillustrated numerically for a real-world MORRAP on pharmaceutical plant, andsolutions are obtained by standard optimization solver LINGO, which is based ongradient-based optimization - Generalized Reduced Gradient (GRG) technique.

A multi-objective reliability-redundancy allocation problem with active redundancy and interval type-2 fuzzy parameters