Reliability Shock Models: A Brief Excursion

Murari Mitra () and Ruhul Ali Khan ()
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Murari Mitra: Indian Institute of Engineering Science and Technology
Ruhul Ali Khan: Indian Institute of Engineering Science and Technology

A chapter in Applied Advanced Analytics, 2021, pp 19-42 from Springer

Abstract: Abstract We attempt to provide a brief introduction to the extensive area of shock model research in reliability theory. Possible connections with application areas such as risk analysis, inventory control and biometry are indicated. Important concepts and tools for proving shock model results such as total positivity and variation diminishing property (VDP) are introduced. Most of the important results concerning nonparametric ageing classes arising from shock models are summarized, and some typical techniques of proof are emphasized. A variety of scenarios with diverse arrival processes such as homogeneous Poisson process, nonhomogeneous Poisson process, stationary and nonstationary pure birth processes are considered. A few interesting results related to cumulative damage models are also discussed.

Keywords: Shock model; Ageing class; Poisson process; Pure birth process; Cumulative damage model; Primary 62N05; Secondary 60K10 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:prbchp:978-981-33-6656-5_3

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DOI: 10.1007/978-981-33-6656-5_3

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