Further results on stochastic orderings and aging classes in systems with age replacement

Josué M. Corujo (1, 2) , José E Valdés (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Universidad de La Habana [Cuba]

Reliability properties associated to the classic models of systems with age replacement have been a usual topic of research. Most previous works have checked aging properties of the lifetime of the working units using stochastic comparisons between the systems with age replacement at different times. However, from a practical point of view, it would be also interesting to deduce the belonging to aging classes of the lifetime of the system from the aging properties of the lifetime of its working units. The first part of this article deals with this problem. Later, stochastic orderings are established between the two 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 also compared 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 random time. This last case is very interesting for real-life applications. Illustrative examples are also presented.

Mots clés: age replacement; random time replacement; aging classes; stochastic orders; parallel systems

Domaines: Probabilités [math.PR]

Josué M. Corujo, José E Valdés. Further results on stochastic orderings and aging classes in systems with age replacement. Probability in the Engineering and Informational Sciences, 2021. ⟨hal-02894514v3⟩