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2024 | OriginalPaper | Chapter

21. Time-Dependent Random Variables and QRM

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Key Topics in This Chapter: Mainly Quantitative

Large parts of risk modelling are concerned with time-independent aspects of risks, or rather, with aspects related to a fixed period. If we want to go beyond that, we must look at random variables that explicitly depend on time. In this chapter, we look at different approaches on how this can be done. Topics include:
  • Straightforward implementation of time dependence.
  • Time-dependent random variables in reliability theory: Time to failure, reliability function, mean time to failure, max time to failure, mean residual lifetime.
  • Control charts.
  • Characteristics of stochastic processes.
  • Poisson processes.
  • Markov processes.
  • Time series.

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Literature
go back to reference Hoyland A, Rausand M (1994) System reliability theory. Wiley Hoyland A, Rausand M (1994) System reliability theory. Wiley
go back to reference Kao EPC (2019) An introduction to stochastic processes. Dover Publications Kao EPC (2019) An introduction to stochastic processes. Dover Publications
go back to reference Medhi J (2020) Stochastic processes. New Age Science Medhi J (2020) Stochastic processes. New Age Science
go back to reference Montgomery DC (2009) Introduction to statistical quality control. Wiley Montgomery DC (2009) Introduction to statistical quality control. Wiley
go back to reference Papoulis A, Pillai SU (2002) Probability, random variables, and stochastic processes. McGraw Hill Papoulis A, Pillai SU (2002) Probability, random variables, and stochastic processes. McGraw Hill
go back to reference Shumway RH, Stoffer DS (2017) Time series analysis and its applications. SpringerCrossRef Shumway RH, Stoffer DS (2017) Time series analysis and its applications. SpringerCrossRef
Metadata
Title
Time-Dependent Random Variables and QRM
Author
Herfried Kohl
Copyright Year
2024
DOI
https://doi.org/10.1007/978-3-031-71272-2_21

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