Reliability Engineering and System Safety 170 (2018) 64–72 Contents lists available at ScienceDirect Reliability Engineering and System Safety journal homepage: www.elsevier.com/locate/ress Maximization of system reliability with the consideration of component sequencing Heungseob Kim Department of Systems Engineering, Republic of Korea Air Force Academy, 635, Danjae-ro, Cheongju, South Korea a r t i c l e i n f o Keywords: Redundancy allocation problem (RAP) Cold-standby Component sequencing Structured Markov chain Matrix-analytic method a b s t r a c t This article deals with the optimal reliability design for a system with heterogeneous components, i.e., redundancy allocation problem with mixed components (RAPMC). Furthermore, it is confirmed that the component sequence affects the reliability of a cold-standby system with an imperfect fault detector/switch, and the optimal order depends on the mission time of the system, the reliabilities of a switch and components. Thus, the suggested RAPMC includes a new decision variable for the optimal component order. The usefulness of the RAPMC has been demonstrated by comparing the optimal system reliabilities by it and other RAPs in a well-known example. That is, under the same constraints on system specifications such as cost and weight, it recommended the system configuration with higher reliability than the previous version of RAPs. Finally, introducing the notion of the optimal component sequence for cold-standby subsystems results in a meaningful improvement in the system reliability. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction Standby redundancy is one of the structure design techniques to en- hance the reliability and lifetime of a system. For that reason, it has been employed in many fielded systems such as manufacturing and commu- nicating systems, nuclear plant, aircraft control, space exploration and satellite systems. Furthermore, many realistic systems have been de- signed with dissimilar, yet functionally similar, components in parallel. For example, airplanes often involve an electronic gyroscope as primary and a secondary mechanical gyroscope [1]. In an emergency power sys- tem set in hospitals, scientific laboratories, data centers, telecommuni- cation equipment and ships, a primary electric power supply is differ- ent from standby power systems such as generators, batteries. In wire- less sensor networks for various applications such as medical services, battlefield operations, crisis response, disaster relief and environmen- tal monitoring, the sensors can be allocated to roads, vehicles, hospi- tals, buildings, people [2]. Thus, even the same sensors have different time-to-failure (TTF) distributions due to differences in their operating conditions. A system with cold-standby redundancy has an operating mecha- nism that when the failure of an operating component is sensed, one of the standbys is activated and stands in for its function. Hence, a device, called a fault detector/switch (abbreviated as a switch), is additionally required. Studies on the reliability model for the system are categorized according to whether the switch functions absolutely or not. For the E-mail addresses: afrotc02@naver.com, heungseob79@gmail.com perfect switching case assuming that it does not fail, Albright and Soni [3] and Robinson and Neuts [4] proposed the reliability models for the systems with identical components having an exponential and phase- type TTF distributions, respectively. Azaron et al. [5] suggested the reli- ability function a parallel system with nonidentical components having m-Erlang TTF distribution. However, in reality, the switch also has the likelihood of failure, and this is called the imperfect switching case. Coit [6] suggested the approximated formula for evaluating the reliability of a parallel system with similar standbys that TTF is distributed according to m-Erlang distribution, and it has been widely applied in relevant stud- ies. Kim and Kim [7], which is the most recent study, represented the operating mechanisms of systems with heterogeneous components by structured continuous-time Markov chains (CTMCs), and the TTF distri- butions of the components were assumed to be generalized phase-type distribution (PHD). Though the installation of redundant components enhances the sys- tem reliability, it involves an increase in system cost. Thus, it is promi- nent for the optimal design of the system to accomplish a higher system reliability with limited resources. There have been three aspects of stud- ies on the optimal component allocation, i.e., a redundancy allocation problem (RAP). The most basic viewpoint is to determine the number of redundant components. One of the other aspects is to select the optimal redundancy strategy. In the first RAP proposed by Coit [8], the strategy for each subsystem was determined to be either active or cold-standby redundancy. Finally, it is a RAP that allows the use of non-identical com- https://doi.org/10.1016/j.ress.2017.10.020 Received 12 February 2017; Received in revised form 6 October 2017; Accepted 21 October 2017 Available online 23 October 2017 0951-8320/© 2017 Elsevier Ltd. All rights reserved.