ABSTRACT
Reliability optimization is of great concern in the study of operations research. The reliability analysis is essential for any reliable system associated with almost all engineering designs, like telecommunication, transport, computer network, aircraft, production plants, etc. Thus, it is the main aim to maximize the reliability of a system under consideration under several restrictions in terms of cost, volume, weight, some natural effects due to weather, or unpredictable phenomena. In this chapter, we consider an n-stage series system with redundant units in parallel with multiple constraints both in crisp and intuitionistic fuzzy environments. The intuitionistic fuzzy model is considered in two ways. In Model 1, only the design parameters are taken as triangular intuitionistic fuzzy number (TIFN) and the model becomes intuitionistic fuzzy nonlinear integer programming problem (IFNIPP), whereas in the Model 2, the design parameters along with the component reliabilities are taken as TIFN and the model is called fully intuitionistic fuzzy nonlinear integer programming problem (FIFNIPP). Thus, the crisp nonlinear integer programming problem is formulated as intuitionistic fuzzy nonlinear integer programming models. For the ease of solution of the problems, these are crispified using the three methods, the Graded Mean Integration Value (GMIV) method, the (α,β)-cut method, and the Ranking function method. Then the problems are solved using real coded genetic algorithm for integer variables. The results obtained by these methods along with that for the crisp model are compared and are presented in tabular form. The sensitivities with respect to the GA parameters are also presented for these models in case of the (α,β)-cut method.
