Some new results involving general standby systems

Abstract

SUMMARYThis article presents a stochastic comparison on the total lifetime of the general standby system and a discussion of the optimal allocation of a general standby component in a series system with two independent components. Several examples are also presented to justify the main results, which provide nice generalizations of some existing conclusions in the literature.

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

“…This paper will focus only on the active redundancy. For more on general standby, we refer the reader to Cha et al (2008) and Li et al (2009). Shaked and Shanthikumar (1992) were among the first to study the problem of allocating m active redundancies to a series system with n components in the situation that lifetimes of components and redundancies are independent and identically distributed.…”

On the Allocation of General Standby Redundancy to Series and Parallel Systems

“…Recently, these three kinds of standby redundancy are unified as the so-called general standby model by Cha et al (2008). Afterward, Li et al (2009) further built some stochastic comparison on the entire lifetime of the general standby system and firstly investigate the allocation of one general standby redundancy in series systems. For convenience, unless stated, the term "standby" stands for the general standby from now on.…”

“…Assume that X and Y are independent. According to Li et al (2009), the total lifetime of the general standby system composed of the active component Y and the standby one X is…”

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.…”