Further results on stochastic orderings and aging classes in systems with age replacement
Corujo, Josué; Valdés, José E. (2021), Further results on stochastic orderings and aging classes in systems with age replacement, Probability in the Engineering and Informational Sciences, p. 1-30. 10.1017/S0269964821000036
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-02894514v2
Journal nameProbability in the Engineering and Informational Sciences
Cambridge University Press
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Valdés, José E.
Facultad de Matematica y Computacion, Universidad de La Habana
Abstract (EN)Reliability properties associated with the classic models of systems with age replacement have been a usual topic of research. Most previous works have checked the aging properties of the lifetime of the working units using stochastic comparisons among the systems with age replacement at different times. However, from a practical point of view, it would also be interesting to deduce to which aging classes the lifetime of the system belongs, making use of the aging properties of the lifetime of its working units. The first part of this article deals with this problem. Further along, stochastic orderings are established between the systems with replacement at the same time using several stochastic comparisons among the lifetimes of their working units. In addition, the lifetimes of two systems with age replacement are compared as well. This is performed assuming stochastic orderings between the number of replacement until failure, and the lifetimes of their working units conditioned to be less or equal than the replacement time. Similar comparisons are accomplished considering two systems with age replacement where the replacements occur at a random time. Illustrative examples are presented throughout the paper.
Subjects / Keywordsage replacement; aging classes; parallel systems; random time replacement; stationary pointwise availability; stochastic orders
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