Contents lists available at ScienceDirect Reliability Engineering and System Safety journal homepage: www.elsevier.com/locate/ress Reliability–redundancy allocation problem considering optimal redundancy strategy using parallel genetic algorithm Heungseob Kim a , Pansoo Kim b, ⁎ a Department of Systems Engineering, Korea Air Force Academy, 635, Danjae-ro, Cheongju, South Korea b School of Business Administration, Kyungpook National University, 80, Daehak-ro, Daegu, South Korea ARTICLE INFO Keywords: Reliability optimization Reliability–redundancy allocation problem Parallel genetic algorithm Redundancy strategy Imperfect switching ABSTRACT To maximize the reliability of a system, the traditional reliability–redundancy allocation problem (RRAP) determines the component reliability and level of redundancy for each subsystem. This paper proposes an advanced RRAP that also considers the optimal redundancy strategy, either active or cold standby. In addition, new examples are presented for it. Furthermore, the exact reliability function for a cold standby redundant subsystem with an imperfect detector/switch is suggested, and is expected to replace the previous approximat- ing model that has been used in most related studies. A parallel genetic algorithm for solving the RRAP as a mixed-integer nonlinear programming model is presented, and its performance is compared with those of previous studies by using numerical examples on three benchmark problems. 1. Introduction Reliability is now a matter of greater concern than in the past, because the increasing complexity of modern engineering and service systems has led to a dramatic rise in their susceptibility to faults. Methods to enhance the reliability of a system involve (i) the improve- ment of component reliability, (ii) the installation of redundant components in parallel, (iii) combinations of (i) and (ii), and (iv) component replacement with substitutable components [1,2]. Reliability optimization problems, using the approaches for im- proving the system reliability mentioned above, optimize reliability objective(s), e.g., the maximization of system reliability or minimiza- tion of required resources subject to some design constraints. That is, they suggest design choices to the system design engineers such as for components, redundancy levels, and redundant configuration. Generally, reliability optimization problems are divided into reliability allocation problem, redundancy allocation problem, and reliability– redundancy allocation problem (RRAP). The RRAP is a composite of the other two problems and determines the reliabilities and the redundancy levels of components to maximize system reliability under design constraints such as those for cost, volume, or weight. The design strategies used to improve system reliability by instal- ling redundant components are divided into two main approaches: active and standby redundancy. In an active redundant system, both the primary and secondary components are exposed to operating stresses. Hence, their failure potentials are regarded as equivalent, and secondary components may break before they are employed. A standby system commonly requires additional equipment, called a fault detector/switch, for detecting the failure of a primary component and activating a standby component. The standby redundancy strategies, based on the standby status of the redundant components, are classified as hot, warm, and cold standby. The cold standby of them is most effective to improve system reliability because it is assumed that standby components are completely shielded against operating stresses. In addition, hot or warm standby is mostly suitable for particular systems. Hot standby is chiefly used for uninterruptible or near-uninterruptible systems such as uninterruptible power supplies or network servers and routers. Examples of warm standby systems are power plants, redundant hard disks, and wireless sensors networks, which require the ability to switch to a primary component [3]. Thus, in general systems, either active or cold standby has been mainly considered as the redundancy strategy for improving the reliability of a system, and the advantageous strategy depends on the reliabilities of a fault detector/switch and components, in addition to redundancy levels. However, most studies on reliability optimization have consid- ered only active redundancy as the redundant configuration. One of the research areas regarding RRAP is to develop methods for solving it efficiently because it was determined to be an NP-hard problem in [4]. Recently, numerous studies using meta-heuristics as well as hybrid forms have been reported. These studies include ones employing genetic algorithms (GAs) [5–8], ant colony optimization (ACO) [9,10], simulated annealing (SA) [11], immune algorithms http://dx.doi.org/10.1016/j.ress.2016.10.033 Received 24 February 2016; Received in revised form 29 August 2016; Accepted 30 October 2016 ⁎ Corresponding author. E-mail addresses: heungseob79@gmail.com (H. Kim), pskim@knu.ac.kr (P. Kim). Reliability Engineering and System Safety 159 (2017) 153–160 Available online 10 November 2016 0951-8320/ © 2016 Elsevier Ltd. All rights reserved. MARK