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Testability is a new and important technology as reliability and maintainability. A lot of literature has discussed the optimal problems of testability in recent years. In Chiu’s paper, a new kind of precedence constraints, parallel-chain precedence constraints, was presented, which is a common constraint in many products and systems. He discussed the optimal inspection strategies to determine the states (good/failed) of some typical reliability systems with parallel-chain precedence constraints. But in reality we encounter more problems with fault-testing models, and how to locate all the failed components with minimal cost is our interest. Suppose that a coherent system has n independent components, each of which has a known prior probability of fault. The true state of each component can be obtained by inspecting it with some cost. This paper discusses the optimal inspection strategies of the coherent system with parallel-chain precedence constraints when the system fails, which can minimize the total expected inspection cost. If the system is known to have failed, there are two situations: one is that the number of the failed components in the system is unknown, which is a common phenomenon; another is that the number of the failed components is known. In addition, the coherent systems concerned in this paper are all typical reliability systems, such as series, parallel, parallel-series, series-parallel and k -out-of- n systems, and all of them are subject to parallel-chain precedence constraints.