![]() Furthermore, unit 2 whose cumulative damage is x may fail minorly with probability π( x) at the instant of minor failure of unit 1, and requires minimal repair when it fails. ![]() Once cumulative damage of unit 2 reaches a threshold level L, unit 2 will fail, which will also cause unit 1 to fail at the same time, causing a catastrophic failure of the system. Whenever unit 1 suffers a minor failure, it causes some additive damage to unit 2. The occurrence probabilities of shock types depend on the number of shocks since the last replacement. Whenever a type I shock arrives, unit 1 has a minor failure which can be removed through a minimal repair while a type II shock leads to a catastrophic failure of the system. A system including two units experiences to one of two types of shocks. We investigate a bivariate replacement policy for a system under shocks effect.
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