A new class of survival distribution for degradation processes subject to shocks

Mei-Ling Ting Lee () and G. A. Whitmore
Additional contact information
Mei-Ling Ting Lee: School of Public Health, University of Maryland
G. A. Whitmore: McGill University

Journal of Statistical Distributions and Applications, 2019, vol. 6, issue 1, 1-24

Abstract: Abstract Many systems experience gradual degradation while simultaneously being exposed to a stream of random shocks of varying magnitudes that eventually cause failure when a shock exceeds the residual strength of the system. In this paper, we present a family of stochastic processes, called shock-degradation processes, that describe this failure mechanism. In our failure model, system strength follows a geometric degradation process. The degradation process itself is any Lévy process, that is, any stochastic process with stationary independent increments. The shock stream is a Fréchet stochastic process, a process derived from the Fréchet extreme-value distribution. Finally, the shock-degradation process is a convolution of the Fréchet shock process and any one of the candidate degradation processes. The system fails at the first occasion when a shock takes system strength across a threshold at zero. The paper presents results for Wiener diffusion processes and gamma processes as examples of Lévy degradation processes. The paper develops key statistical properties of the process model and its survival distribution, including several that are important for its practical application. As the failure mechanism is a first hitting time event, applications that require regression structures fall within the domain of threshold regression methodology.

Keywords: Degradation process; Extreme value; First hitting time; Fréchet process; Lévy process; Shock stream; Stationary independent increments; System strength; Threshold regression (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1186/s40488-019-0095-1 Abstract (text/html)

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:jstada:v:6:y:2019:i:1:d:10.1186_s40488-019-0095-1

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/40488

DOI: 10.1186/s40488-019-0095-1

Access Statistics for this article

Journal of Statistical Distributions and Applications is currently edited by Felix Famoye and Carl Lee

More articles in Journal of Statistical Distributions and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().