Geometric-Like Processes: An Overview and Some Reliability Applications

被引:15
作者
Arnold, Richard [1 ]
Chukova, Stefanka [1 ]
Hayakawa, Yu [2 ]
Marshall, Sarah [3 ]
机构
[1] Victoria Univ Wellington, Sch Math & Stat, POB 600, Wellington 6140, New Zealand
[2] Waseda Univ, Sch Int Liberal Studies, Sinjuku Ku, 1-6-1 Nishi Waseda, Tokyo 1698050, Japan
[3] Auckland Univ Technol, Sch Engn Comp & Math Sci, Dept Math Sci, Private Bag 92006, Auckland 1142, New Zealand
关键词
Stochastic processes; Geometric processes; Geometric-like processes; Reliability; Warranty analysis; PROCESS REPAIR-MODEL; WARRANTY COST-ANALYSIS; OPTIMAL REPLACEMENT POLICY; SHOCK MAINTENANCE MODEL; STATISTICAL-INFERENCE; DELAYED REPAIR; SYSTEM; RENEWAL; PROCUREMENT;
D O I
10.1016/j.ress.2020.106990
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
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.
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页数:12
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