Geometric-Like Processes: An Overview and Some Reliability Applications

Richard Arnold, Stefanka Chukova, Yu Hayakawa, Sarah Marshall*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

10 Citations (Scopus)


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.

Original languageEnglish
Article number106990
JournalReliability Engineering and System Safety
Publication statusPublished - 2020 Sept


  • Geometric processes
  • Geometric-like processes
  • Reliability
  • Stochastic processes
  • Warranty analysis

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


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