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Reliability Shock Models: A Brief Excursion

In: Applied Advanced Analytics

Author

Listed:
  • Murari Mitra

    (Indian Institute of Engineering Science and Technology)

  • Ruhul Ali Khan

    (Indian Institute of Engineering Science and Technology)

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.

Suggested Citation

  • Murari Mitra & Ruhul Ali Khan, 2021. "Reliability Shock Models: A Brief Excursion," Springer Proceedings in Business and Economics, in: Arnab Kumar Laha (ed.), Applied Advanced Analytics, pages 19-42, Springer.
    • Handle: RePEc:spr:prbchp:978-981-33-6656-5_3
    DOI: 10.1007/978-981-33-6656-5_3
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