OPTIMAL APPORTIONMENT OF RELIABILITY AND REDUNDANCY IN SERIES SYSTEMS UNDER MULTIPLE OBJECTIVES

A multiobjective reliability apportionment problem for a series system with time-dependent reliability is presented. The resulting mathematical programming formulation determines the optimum level of component reliability and the number of redundant components at each stage. The problem is a multiobjective, nonlinear, mixed-integer mathematical programming problem, subject to several design constraints. Sequential unconstrained minimization techniques in conjunction with heuristic algorithms are used to find an optimum solution. A generalization of the problem in view of inherent vagueness in the objective and the constraint functions results in an ill-structured reliability apportionment problem. This multiobjective fuzzy optimization problem is solved using nonlinear programming. The computational procedure is illustrated through a numerical example. The fuzzy optimization techniques can be useful during initial stages of the conceptual design of engineering systems where the design goals and design constraints have not been clearly identified or stated. These techniques can effectively model the vague and imprecise information in the objective function & constraints to formulate fuzzy goals & constraints. These models can be used efficiently and effectively for decision-making problems in ill-structured situations.