Allocation of redundancies in systems: a general dependency-base framework
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Allocation of redundancies in systems: a general dependency-base framework Hamideh Jeddi1 · Mahdi Doostparast1 Accepted: 9 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Manufacturers and consumers prefer reliable products, or systems in general, since they need to assure that systems work satisfactory for given mission times. The redundancy allocation to original system components is a common technique to improve reliabilities. But, allocation of redundants is not an easy task and must be considered properly with respect to environmental working conditions and possible restrictions such as cost, volume and weight. Therefore, the problem of finding optimal allocations is important and studied extensively in literature. The existing studies usually assume restrictive conditions such as stochastically independent component and spare lifetimes. This article deals with this problem under a general setting in which component and spare lifetimes can be dependent and heterogeneous. Two common policies, called active and standby, are studied in details. Stochastic orders are implemented for comparing various allocation policies. Findings of this article are derived under general conditions and hold for arbitrary dependency structures among lifetimes. Illustrative examples are also given. Keywords Dependence · Redundancy · Reliability · Stochastic orders Mathematics Subject Classification 90B25 · 60E15
1 Introduction Systems are used to do a given task under some environmental working conditions during predefined mission times. System reliability assessments are then essential for engineers in practice; see, e.g. Barlow and Proschan (1975), Meeker and Escobar (1998), Li et al. (2005), Sarkar et al. (2010a), Sarkar et al. (2010b) and Sarkar (2012). Manufacturers and consumers prefer reliable systems and therefore, additional actions are taken for improving
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Mahdi Doostparast [email protected] Hamideh Jeddi [email protected]
1
Department of Statistics, Ferdowsi University of Mashhad, 91775-1159 Mashhad, Iran
123
Annals of Operations Research
system reliabilities. The most common technique is the allocation of spares to original system components subject to existing constraints such as cost, volume and weight. Determination of optimal allocations of spares is then an essential problem. For a demonstrative example, suppose that n locations are designed for planting a specific type of tree. It is desired that after a period of five years all n locations have a healthy tree growing there. There exist also n + k small trees. After the initial planting of n small trees in the n locations, it is decided to distribute (allocate) the “remaining” k small trees, one to each of the n locations. The remaining trees are to be allocated in order to maximize the probability that all the n locations contain at least one healthy tree after five years. In fact, this is a redundancy allocation problem (RAP) for a system with n components and k spares which should be allocated. F
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