Active-Redundancy Allocation in Systems

Abstract

An effective way of improving the reliability of a system is the allocation of active redundancy. Let 1 X , 2 X be independent lifetimes of the components 1 C and 2 C , respectively, which form a series system. Let denoteX is the lifetime of a redundancy (say S ) independent of 1 X and 2 X . That is C is preferred to 2 C for redundancy. In this paper we use the same criterion of Singh and Misra (1994) and we investigate the allocation of one active redundancy when it differs depending on the component with which it is to be allocated. We find sufficient conditions for the optimization which depend on the components and redundancies probability distributions. We also compare the allocation of two active redundancies (say 1 S and 2 S ) in two different ways, that is, 1 S with 1 C and 2 S with 2 C and viceversa. For this case the hazard rate order plays an important role. We obtain results for the allocation of more than two active redundancies to a kout-of-n systems. Note: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accesible. Keywords

Allocation Policies of Redundancies in Two-Parallel-Series and Two-Series-Parallel Systems

“…The problem of how and where to allocate redundancies to the components has been extensively studied in the reliability literature. For example, Boland et al [4] and Shaked and Shanthikumar [22] studied the allocation problem for series and parallel systems using the stochastic order as a criterion for comparison, whereas Singh and Misra [24] and Romera et al [21] used the precedence order. Valdés and Zequeira [27] and more recently Li et al [16] also provided optimal allocation but using the hazard rate order and the increasing concave order, respectively.…”

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

“…For the hot standby redundancy, Boland et al (1988) showed that Romera et al (2004) further proved that…”

“…In the past two decades, many authors conducted comparison on lifetimes of a system under various feasible allocations so as to get the best or better configuation. Readers may refer to Boland et al (1988Boland et al ( , 1992, Singh and Misra (1994), She and Pecht (1992), Boland (1997), Valdés and Zequeira (2003), Romera et al (2004), Li and Hu (2008), and Li et al (2011), etc., for researching results in this line. In general, three types of standby redundancy are usually discussed in literature, namely, cold standby, hot standby, and warm standby.…”

“…Both the hot and cold standby redundant systems have been investigated in literature. For example, Boland et al (1988Boland et al ( , 1992, She and Pecht (1992), Singh and Misra (1994), Valdés and Zequeira (2003), Romera et al (2004), Li and Hu (2008), etc. Recently, these three kinds of standby redundancy are unified as the so-called general standby model by Cha et al (2008).…”

On the optimal allocation of active redundancies in series system

“…Afterward, Singh and Misra (1994) made some further studies along this line. Recently, Romera et al (2004), Zequeira (2003, 2006) and Li and Hu (2008) made further efforts to enrich those existing results in the literature.…”