Renewal and nonhomogeneous Poisson processes generated by distributions with periodic failure rate

1993 ◽  
Vol 17 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Stefanka Chukova ◽  
Boyan Dimitrov ◽  
José Garrido
Keyword(s):  
Failure Rate ◽  
Poisson Processes ◽  
Nonhomogeneous Poisson Processes

STOCHASTIC SURVIVAL MODELS WITH EVENTS TRIGGERED BY EXTERNAL SHOCKS

2012 ◽  
Vol 26 (2) ◽  
pp. 183-195 ◽  
Author(s):  
Ji Hwan Cha ◽  
Maxim Finkelstein
Keyword(s):  
Failure Rate ◽  
Rate Function ◽  
Poisson Processes ◽  
Survival Models ◽  
Failure Rate Function ◽  
Limiting Behavior ◽  
Wear Process ◽  
Shock Models ◽  
Nonhomogeneous Poisson Processes ◽  
Rate Functions

In most conventional settings, the events caused by an external shock are initiated at the moments of its occurrence. In this paper, we study the new classes of shock models: (i) When each shock from a nonhomogeneous Poisson processes can trigger a failure of a system not immediately, as in classical extreme shock models, but with delay of some random time. (ii) When each shock from a nonhomogeneous Poisson processes results not in an ‘immediate’ increment of wear, as in classical accumulated wear models, but triggers its own increasing wear process. The wear from different shocks is accumulated and the failure of a system occurs when it reaches a given boundary. We derive the corresponding survival and failure rate functions. Furthermore, we study the limiting behavior of the failure rate function where it is applicable.

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