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The paper concerns the optimal inspection strategies of complex systems subject to block-chain precedence constraints. Supposing a system consists of independent components, and each of which has a known probability of working. The state of each component can be determined by inspecting it for some inspection cost, the true state of the system can be obtained by sequentially inspecting its components. Our aim is to find the optimal inspection strategies that can minimize the expected inspection cost of complex systems which are subject to block-chain precedence constraints, such as series, parallel or -out-of- system, and the optimal inspection rules of the more complex systems can be obtained by these simple systems.