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.
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Acknowledgements
The authors are indebted to Professor Arnab K. Laha for his constant encouragement in making this article a reality and to Mr. Dhrubasish Bhattacharyya for some helpful discussions during the preparation of this manuscript.
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Mitra, M., Khan, R.A. (2021). Reliability Shock Models: A Brief Excursion. In: Laha, A.K. (eds) Applied Advanced Analytics. Springer Proceedings in Business and Economics. Springer, Singapore. https://doi.org/10.1007/978-981-33-6656-5_3
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DOI: https://doi.org/10.1007/978-981-33-6656-5_3
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