Annals of Operations Research

, Volume 212, Issue 1, pp 21–41 | Cite as

Lifetime properties of a cumulative shock model with a cluster structure



This paper studies a generalized cumulative shock model with a cluster shock structure. The system considered is subject to two types of shocks, called primary shocks and secondary shocks, where each primary shock causes a series of secondary shocks. The lifetime behavior of such a system becomes more complicated than that of a classical model with only one class of shocks. Under a non-homogeneous Poisson process of primary shocks, we analyze the lifetime behavior of the system with light-tailed and heavy-tailed distributed secondary shocks. We show some important characteristics of lifetime of this type of system. Our model, as an extension of the classical shock models, has wide applications in maintenance engineering, operations management, and insurance risk assessment.


Cumulative shock model Cluster point process Lifetime Light-tailed distribution Regular-tailed distribution 



This work is supported by the Natural Science Foundation of China 71171103 and 10871086 and the NSERC grant RGPIN197319 of Canada. The authors would like to thank the editor and the anonymous referees for their valuable comments and suggestions and also are grateful to Dr. Zhi Liu and Dr. Yanjun Shi for their help in creating the illustrations.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of ManagementLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.Beedie School of BusinessSimon Fraser UniversityBurnabyCanada
  3. 3.Department of Decision SciencesWestern Washington UniversityBellinghamUSA
  4. 4.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China

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