Shock models with underlying birth process
Shock models with underlying birth process
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DOI：
10.2307/3212403
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发表时间：
1975-03
影响因子：
1
通讯作者：
M. A-Hameed;F. Proschan
中科院分区：
文献类型：
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作者：
M. A-Hameed;F. Proschan
本文扩展了 Esary、Marshall 和 Proschan (1973) 以及 A-Hameed 和 Proschan (1973) 的结果。我们考虑根据非平稳纯诞生过程，受到一系列随机发生的冲击的设备的寿命分布：给定在 [0, t] 中发生了 k 次冲击，在 (t, t + Δ] 中发生冲击的概率为 λ kλ (t)Δ + o (Δ)。我们表明，在对 λ 进行适当假设的情况下，可以获得各种基本类别的寿命分布（例如故障率不断增加的寿命分布，或具有“新的比使用的更好”属性的寿命分布） k、λ (t) 以及在给定次数的冲击中幸存的概率。
This paper extends results of Esary, Marshall and Proschan (1973) and A-Hameed and Proschan (1973). We consider the life distribution of a device subject to a sequence of shocks occurring randomly in time according to a nonstationary pure birth process: given k shocks have occurred in [0, t], the probability of a shock occurring in (t, t + Δ] is λ kλ (t)Δ + o (Δ). We show that various fundamental classes of life distributions (such as those with increasing failure rate, or those with the ‘new better than used' property, etc.) are obtained under appropriate assumptions on λ k, λ (t), and on the probability of surviving a given number of shocks.