The present work investigates the reliability optimization problem of the repairable industrial systems by utilizing uncertain, limited, and imprecise data. In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting objectives. Moreover, data collected or available for the systems are vague, ambiguous, qualitative, and imprecise in nature due to various practical constraints and hence create some difficulties in optimizing the design problems. To handle these problems, this work presents an interactive method for solving the fuzzy multiobjective optimization decision-making problem, which can be used for the optimization decision making of the reliability with two or more objectives. Based on the preference of the decision makers toward the objectives, fuzzy multi-objective optimization problem is converted into crisp optimization problem and then solved with evolutionary algorithm. The proposed approach has been applied to the decomposition unit of a urea fertilizer plant situated in the northern part of India producing 1500–2000 metric tons per day. 1. Introduction Reliability in general can be defined as the ability of a system to perform its required functions under stated conditions for a specified period of time. Reliability technology is an important phenomenon and is widely used for increasing the efficiency, risk analysis, production availability studies, and design of industrial systems. The industrial systems run continuously and suffer failure over a period of time which can be brought back in to service by proper repair or replacement. Consequently, it may be extremely difficult, if it is not possible to construct accurate and complete mathematical model for the system in order to access the reliability because of inadequate knowledge about the basic failure events [1, 2]. In highly competitive industrial market, the concept of failure analysis is an unavoidable fact in complex industrial systems. Reliability of such systems not only depends on the reliability of each element of these systems but also depends on occurrence of sequence of failures. Generally, the design problems are always stated in precise mathematical forms. It must be recognized that many practical problems encountered by designers and decision makers would take place in an environment in which the statements might be vague or imprecise. Usually, it is difficult to describe the goals and constraints of such optimization problems by crisp relations through equations
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