On the general $$\delta $$ δ -shock model

Dheeraj Goyal, Nil Kamal Hazra and Maxim Finkelstein ()
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Dheeraj Goyal: Indian Institute of Technology Jodhpur
Nil Kamal Hazra: Indian Institute of Technology Jodhpur
Maxim Finkelstein: University of the Free State

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 31, issue 4, No 6, 994-1029

Abstract: Abstract The $$\delta $$ δ -shock model is one of the basic shock models which has a wide range of applications in reliability, finance and related fields. In existing literature, it is assumed that the recovery time of a system from the damage induced by a shock is constant as well as the shocks magnitude. However, as technical systems gradually deteriorate with time, it takes more time to recover from this damage, whereas the larger magnitude of a shock also results in the same effect. Therefore, in this paper, we introduce a general $$\delta $$ δ -shock model when the recovery time depends on both the arrival times and the magnitudes of shocks. Moreover, we also consider a more general and flexible shock process, namely, the Poisson generalized gamma process. It includes the homogeneous Poisson process, the non-homogeneous Poisson process, the Pólya process and the generalized Pólya process as the particular cases. For the defined survival model, we derive the relationships for the survival function and the mean lifetime and study some relevant stochastic properties. As an application, an example of the corresponding optimal replacement policy is discussed.

Keywords: Reliability; $$\delta $$ δ -shock model; Poisson generalized gamma process; Homogeneous Poisson process; 60E15; 60K10 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11749-022-00810-5

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