During the course of diagnosing the faults, the time for each testing point to detect the fault may be different. The problem that each testing point can detect once all the fault points that it can detect has been solved. If each testing point can detect only one fault point once, two questions will be discussed. If the sum of all the detection time is required to be minimal, an optimization algorithm is provided；If the maximum detection time is required to be minimal, the problem is proved to be NP-completeness and an approximate algorithm is given. Finally an example is given to explain the algorithms.