Reliability assessment of a multi-state mixed $$\delta $$ -shock model based on discrete PH distribution

Zebin Hu () and Linmin Hu ()
Additional contact information
Zebin Hu: Yanshan University
Linmin Hu: Yanshan University

Annals of Operations Research, 2025, vol. 353, issue 3, No 2, 885-916

Abstract: Abstract Both the extreme shock model and the $$\delta $$ -shock model have been extensively studied and applied in various fields. Nevertheless, the research of these shock models under discrete-time conditions remains limited. Under discrete-time conditions, this paper develops a multi-state mixed $$\delta $$ -shock model that incorporates both a generalized $$\delta $$ -shock and an extreme shock. The research has the following two main features: on the one hand, the arrival process of the shocks is generalized by assuming that the shock intervals follow a discrete PH distribution; on the other hand, by constructing a discrete-time Markov chain, the discrete PH distribution representations of the lifetime, operating time in perfect state and operating time in inferior state of the system are given, and the expected values and probability mass functions of the corresponding measures of the system are derived through these discrete PH distributions. Additionally, by means of the numerical experiment, the relationship between various measures and parameters of the system is elucidated. The proposed mixed $$\delta $$ -shock model can degenerate into the extreme shock model or the $$\delta $$ -shock model under certain conditions, thereby providing a new perspective and approach for comprehending and utilizing these shock models.

Keywords: Discrete-time; Discrete PH Distribution; Mixed $$\delta $$ -shock Model; Multi-State System; Discrete-Time Markov Chain (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-025-06815-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:353:y:2025:i:3:d:10.1007_s10479-025-06815-1

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-025-06815-1

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().