ORIGINAL ARTICLE Reliability optimization with high and low level redundancies in interval environment via genetic algorithm Laxminarayan Sahoo • Asoke Kumar Bhunia • Dilip Roy Received: 15 May 2013 / Revised: 23 September 2013 Ó The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2013 Abstract This paper deals with redundancy allocation problem in interval environment that maximizes the overall system reliability subject to the given resource constraints and also minimizes the overall system cost subject to the given resources including an additional constraint on sys- tem reliability. Here, the reliability of each component is assumed as interval valued and the cost coefficients as well as the amount of resources are imprecise and interval valued. These types of problems have been formulated as an interval valued nonlinear integer programming problem. In this paper, we have formulated two types of redundancy, viz. component level redundancy known as low-level redundancy and the system level redundancy known as high-level redundancy. These problems have been trans- formed as an unconstrained optimization problem using penalty function technique and solved using genetic algo- rithm. Finally, two numerical examples (one for low-level redundancy and another for high-level redundancy) have been solved and the computational results have been compared. Keywords Genetic algorithm  Interval environment  Low-level redundancy  High-level redundancy  Reliability optimization 1 Introduction Development of modern technological system design depends on the selection of components and configurations to meet the functional requirements as well as performance specifications. For a system with known cost, reliability, weight, volume and other system parameters, the corre- sponding design problem becomes a combinatorial opti- mization problem. The best known reliability design problem of this type is referred as the redundancy alloca- tion problem. The basic objective of redundancy allocation problem is to find the number of redundant components that either maximize the system reliability or minimize the system cost under several resource constraints. Redun- dancy allocation problem is basically a nonlinear integer programming problem. Most of these problems can not be solved by direct/indirect or mixed search methods due to discrete search space. According to Chern (1992), redun- dancy allocation problem with multiple constraints is quite often hard to find feasible solutions. This redundancy allocation problem is NP-hard and it has been well dis- cussed in Tillman et al. (1977) and Kuo and Prasad (2000). Earlier, several deterministic methods like heuristic meth- ods (Nakagawa and Nakashima 1977; Kim and Yum 1993; Kuo et al. 1978; Aggarwal and Gupta 2005; Ha and Kuo 2006), reduced gradient method (Hwang et al. 1979), branch and bound method (Kuo et al. 1987; Tillman et al. 1977; Sun and Li 2002; Sung and Cho 1999), integer programming (Misra and Sharma 1991), dynamic L. Sahoo (&) Department of Mathematics, Raniganj Girls’ College, Raniganj 713358, India e-mail: lxsahoo@gmail.com A. K. Bhunia Department of Mathematics, The University of Burdwan, Burdwan 713104, India e-mail: bhuniaak@rediffmail.com D. Roy Centre for Management Studies, The University of Burdwan, Burdwan 713104, India e-mail: dr.diliproy@gmail.com 123 Int J Syst Assur Eng Manag DOI 10.1007/s13198-013-0199-9