article.page.titleprefix Reliability of a mixed 𝜹-shock model with a random change point in shock magnitude distribution and an optimal replacement policy
Date
2023-04
Journal Title
Journal ISSN
Volume Title
Publisher
Reliability Engineering and System Safety
Abstract
A mixed 𝛿-shock model when there is a change in the distribution of the magnitudes of shocks is defined and studied. Such a model which is a combination of the 𝛿-shock model and the extreme shock model with a random change point (studied by Eryilmaz and Kan, 2019), is useful in practice since a sudden change in environmental conditions may cause a larger shock. In particular, the reliability and the mean time to failure of the system are evaluated by assuming that the random change point has a discrete phase-type distribution. Analytical results for eval-uating the reliability function of the system for several joint distributions of the interarrival times and the magnitudes of shocks, are also given. The optimal replacement policy that is based on a control limit is also proposed when the number of shocks until the change point follows geometric distribution. The results are illustrated by numerical examples.
Description
Reliability Engineering and System Safety, https://doi.org/10.1016/j.ress.2022.109080, aUniversity of Piraeus, Department of Statistics and Insurance Science, Piraeus, Greece E-mail: stch@unipi.gr (S. Chadjiconstantinidis), bAtilim University, Department of Industrial Engineering, Ankara, Turkey E-mail: serkan.eryilmaz@atilim.edu.tr (S. Eryilmaz)
Keywords
Mixed -shock model
Citation
https://doi.org/10.1016/j.ress.2022.109080