TY - JOUR
T1 - Geometric-Like Processes
T2 - An Overview and Some Reliability Applications
AU - Arnold, Richard
AU - Chukova, Stefanka
AU - Hayakawa, Yu
AU - Marshall, Sarah
N1 - Funding Information:
This research was supported by the following grants: 1. JSPS KAKENHI Grant-in-Aid for Scientific Research (C) Grant Number 18K04621 2. WIAS Visiting Scholars 2018, Waseda University 3. FY2018 Grant Program for Promotion of International Joint Research, Waseda University 4. Grant for Special Research Projects (2018K-383), Waseda University 5. Fulbright New Zealand: Fulbright Scholar Award 2018 6. AUT SECMS Contestable Conference Grant, 2019
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/9
Y1 - 2020/9
N2 - The geometric process (GP) can be used to model the occurrence of events, which have an underlying monotonic trend. This type of trend can be observed in many practical problems in reliability, in particular in the recurrent failures of repairable systems. There are also common areas of everyday life, such as epidemiology, business, and health, where such trends in inter-event times can be observed. In order to provide greater flexibility in modelling phenomena and situations involving monotonic trends, a variety of extensions of the geometric process have been proposed. This paper provides an overview of geometric and the related geometric-like processes (GLP). We include a brief review of the geometric process and some basic definitions, facts and references for geometric-like processes. Some of their applications to areas such as maintenance, reliability, warranty analysis and others, along with appropriate references, are also outlined. Finally, we list a number of open research questions related to GLP.
AB - The geometric process (GP) can be used to model the occurrence of events, which have an underlying monotonic trend. This type of trend can be observed in many practical problems in reliability, in particular in the recurrent failures of repairable systems. There are also common areas of everyday life, such as epidemiology, business, and health, where such trends in inter-event times can be observed. In order to provide greater flexibility in modelling phenomena and situations involving monotonic trends, a variety of extensions of the geometric process have been proposed. This paper provides an overview of geometric and the related geometric-like processes (GLP). We include a brief review of the geometric process and some basic definitions, facts and references for geometric-like processes. Some of their applications to areas such as maintenance, reliability, warranty analysis and others, along with appropriate references, are also outlined. Finally, we list a number of open research questions related to GLP.
KW - Geometric processes
KW - Geometric-like processes
KW - Reliability
KW - Stochastic processes
KW - Warranty analysis
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U2 - 10.1016/j.ress.2020.106990
DO - 10.1016/j.ress.2020.106990
M3 - Review article
AN - SCOPUS:85084951997
SN - 0951-8320
VL - 201
JO - Reliability Engineering
JF - Reliability Engineering
M1 - 106990
ER -