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In reliability engineering, redundancy technique is widely applied to ensure a system remain functional over a long period of time. A k-out-of-n system is a typical redundant system with n components. At a minimum, it requires k operational components for the system to work normally [25, 30, 38]. Many reliability models of k-out-of-n systems have been developed, which assume that components work independently [6, 41]. However, many systems are load-sharing, such as micro-engines in a Micro-Electro-Mechanical System (MEMS) [4, 13], common buses in a common bus performance sharing system [40], and gear pair systems in a machines transmission system [37], which makes the assumption of independent components unrealistic [10, 24]. A common feature in a load-sharing system is that the workload is shared equally or unequally by the surviving components, and when a component fails, its load is distributed to the working components [32]. The increased workload on the component strongly affect its degradation rate and failure rate [11], which has been proved by many empirical studies of mechanical systems [7, 26], and battery systems [20]. Therefore, due to load-sharing characteristics, the components are stochastically dependent on each other. Although numerous studies have explored the reliability of loadsharing systems considering the dependence among the components, they ignore the detrimental effects of random shocks on system reliability. Taghipour et al. [25] propose a periodic inspection optimizaHaiyang CHe Shengkui Zeng Jianbin guo

A reliability model for load-sharing k-out-of-n systems subject to soft and hard failures with dependent workload and shock effects