Stochastic order for redundancy allocations in series and parallel systems

Abstract

The problem of where to allocate a redundant component in a system in order to optimize the lifetime of a system is an important problem in reliability theory which also poses many interesting questions in mathematical statistics. We consider both active redundancy and standby redundancy, and investigate the problem of where to allocate a spare in a system in order to stochastically optimize the lifetime of the resulting system. Extensive results are obtained in particular for series and parallel systems.

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 Stochastic Comparisons for Load-Sharing Series and Parallel Systems

“…We want to obtain the best allocation strategy that maximizes reliability of our system. Similar and more general settings for systems without load sharing are widely studied in the literature (see, e.g., Boland et al [2], Brito et al [3], Misra and Misra [15], Misra et al ([16], [17]), Romera et al [19], Valdéz and Zequeira ( [24], [25])) However, to the best of our knowledge, there are no relevant results in the literature for the load sharing systems with arbitrary distributions of component's lifetimes. The obtained in this paper results have a clear intuitive meaning similar to the case of 'ordinary' redundancy (without load sharing).…”

“…The problem of optimal allocations of redundant components was addressed in numerous publications (cf. Boland et al [2], Brito et al [3], Misra and Misra [15], Misra et al ([16], [17]), Romera et al [19], Valdéz and Zequeira ( [24], [25]), Hazra and Nanda ( [7], [8]), Cha et al [4], Li et al [12], Yun and Cha ([28], [29]) to name a few). The specific case of redundancy, i.e., load sharing, had attracted much less attention (see, for example, Kapur and Lamberson [9], Keccecioglu [10], Scheuer [20], Shechner [23], Lin et al [13], Yinghui and Jing [27], Wang et al [26], Shao and Lamberson [22], Liu [14] and the references therein).…”

Some new results involving general standby systems

“…This issue has been studied in the past decades through conducting a stochastic comparison on lifetimes of a system with various redundancy allocations. For more on this line of research, readers may refer to [1][2][3][4][5][6][7].…”