In this paper,a δ-shock maintenance model for a deteriorating system is studied.Assume that shocks arrive according to a renewal process,the inter-arrival time of shocks has a log-normal distribution.Whenever an inter-arrival time of shocks is less than a threshold,the system will fail.A replacement policy N is adopted by which the system will be replaced by an identical new one at the time following the Nth failure.Then the long-run average cost per unit time is evaluated and an analytic expression for the optimal replacement policy N~* is given. 研究了一類退化系統的δ沖擊模型.假定沖擊來自于一個具有對數正態分布更新間距的更新過程,當沖擊之間的間距小于一個閾值時,系統就會失效.作者采用更換策略N,即當且僅當系統已經失效N次時用一個全新的系統更換,然后得到了系統長期運行下的平均費用的表達式,并且找到了最優更換策略N*的解析表達式,最后給出了一個數值實例.