Optimal allocation of active redundancies in -out-of- systems

Optimal Allocation of Active Redundancies to k-out-of-n Systems with Heterogeneous Components

“…. , n) and r 1 + · · · + r n = m. They proved that T s (r), the lifetime of the resulting series system with allocation policy r, has a Schur-concave survival function with respect to r. Afterward, in view of the importance of the hazard rate which describes a system's wear out, Singh and Singh (1997) showed that the failure rate function of T s (r) is Schur convex with respect to the allocation policy r. Recently, Hu and Wang (2009) further investigated the allocation of m active redundancies to a k-out-of-n system where lifetimes of all working…”

On allocating redundancies to k‐out‐of‐ n reliability systems

“…; r n / be an allocation policy with r 1 C Cr n D m; that is, r i redundancies are put in parallel to the ith original component in the system. They showed that the survival function of the resulting system's lifetime with allocation policy r is Schur-concave with respect to r. Further, Singh and Singh [6] established that the hazard rate function of the resulting system's lifetime with allocation policy r is Schur-convex with respect to r. Recently, Hu and Wang [7] studied the allocation of m active redundancies to a k-out-of-n system in the situation that lifetimes of components and redundancies are all i.i.d., and they proved that the lifetime of the resulting k-out-of-n system with allocation policy r has a survival function Schur-concave with respect to r. On the other hand, for m i.i.d. active redundancies allocated to a series system with n independent stochastically ordered components, Misra et al [8] showed that the lifetime of the resulting series system has a survival function Schur-concave with respect to r in f.r 1 ;…”

On matched active redundancy allocation for coherent systems with statistically dependent component lifetimes

“…Subsequent to Boland et al (1992) and Mi (1999), a large amount of research has been conducted along this line. See, for example, Valdés and Zequeira (2003), Romera, Valdés, and Zequeira (2003), Hu and Wang (2009), Li, Zhang, and Wu (2009), Li and Ding (2010, Li, Wu, and Zhang (2013) and Li, Fang, and Mi (2015). On the other hand, some authors have focused on simple coherent systems with independent component lifetimes having some specific distributions, such as exponential distributions.…”