On optimal operational sequence of components in a warm standby system

Abstract

We consider an open problem of obtaining the optimal operational sequence for the 1-out-of-n system with warm standby. Using the virtual age concept and the cumulative exposure model, we show that the components should be activated in accordance with the increasing sequence of their lifetimes. Lifetimes of the components and the system are compared with respect to the stochastic precedence order and its generalization. Only specific cases of this optimal problem were considered in the literature previously.

Allocations of cold standbys to series and parallel systems with dependent components

“…Moreover, the failure rate of an inactive warm standby is less than its actual failure rate, and then it is switched to the active state immediately after the failure of the original component and its failure rate will increase. Interested readers may refer to the works of Yun and Cha, Hazra and Nanda, Finkelstein et al, and Hadipour et al for more detailed discussions. For all of these three types of standbys, the system performance under different allocation policies can be effectively evaluated via stochastic comparisons in terms of various stochastic orders.…”

Rejoinder to “Virtual age, is it real?”

“…Soyer provides an interesting connection of the age correspondence and virtual age concepts to the notion of hazard potential (Singpurwalla 14 ). We will interpret it in Section 3 in a slightly different way using the relevant description for degrading items (see Finkelstein et al 15 for more details).…”

“…The value of R is an intrinsic property of a manufactured item, whereas the rate of wear w ( t ) defines the ‘depletion’ of R in a given environment 15 . The larger rate corresponds to the severer environment, whereas w ( t ) = 1 can be often considered as a baseline one.…”

Generalization of the Pairwise Stochastic Precedence Order to the Sequence of Random Variables

“…The problem is to find the optimal activation sequence that maximizes the lifetime of the system in a suitable probabilistic sense. This open (for a general case) problem was solved in Finkelstein et al [7], where it was proved that if the lifetimes of the components are ordered in the SSP sense, then this sequence of activation (starting with the shortest lifetime) results in a system's lifetime that is larger than a lifetime of a warm standby system for any other sequence of activation in the SP order sense (see also Zhai et al [12]).…”