In the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications. Communications in Statistics – Simulation and Computation 49(1): 110–120] introduced two types of extreme shock models when the shocks arrive from one of $m\geq 1$ possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of $m$ sources, and shocks continue to arrive from the same source. In this paper, we prove that the lifetime of Model 1 is less than Model 2 in the usual stochastic ordering. We further show that if the inter-arrival times of shocks have increasing failure rate distributions, then the usual stochastic ordering can be generalized to the hazard rate ordering. We study the stochastic behavior of the lifetime of Model 2 with respect to the severity of shocks using the notion of majorization. We apply the new stochastic ordering results to show that the age replacement policy under Model 1 is more costly than Model 2.

在通常的冲击模型中，冲击来自单一来源。Bozbulut 和 Eryilmaz [(2020)。广义极端冲击模型及其应用。统计通信 – 模拟与计算 49 (1): 110–120] 当冲击来自$m\geq 1$可能来源之一时，引入了两种类型的极端冲击模型。在模型 1 中，冲击随着时间的推移从不同的来源到达。在模型 2 中，最初，冲击随机来自$m$之一源，并且冲击继续来自同一个源。在本文中，我们证明了在通常的随机排序中模型 1 的寿命小于模型 2。我们进一步表明，如果冲击的到达时间具有递增的故障率分布，那么通常的随机排序可以推广到危险率排序。我们使用主化概念研究模型 2 生命周期相对于冲击严重程度的随机行为。我们应用新的随机排序结果表明模型 1 下的年龄替代政策比模型 2 的成本更高。