Generalized delta-shock model via runs

作者：Eryilmaz Serkan^*

来源：Statistics & Probability Letters, 2012, 82(2): 326-331.

DOI：10.1016/j.spl.2011.10.022

• Geometric distribution of order k
• Poisson process
• Runs
• Shock model

According to the delta-shock model, the system fails when the time between two consecutive shocks falls below a fixed threshold delta. This model has a potential application in various fields such as inventory, insurance and system reliability. In this paper, we study run-related generalization of this model such that the system fails when k consecutive interarrival times are less than a threshold delta. The survival function and the mean value of the failure time of the system are explicitly derived for exponentially distributed interarrival times. We also propose a new combined shock model which considers both the magnitudes of successive shocks and the interarrival times.

• 出版日期2012-2