While the Slope Fault Model method can solve the soft-fault diagnosis problem in linear analog circuit effectively, the challenging tolerance problem is still unsolved. In this paper, a proposed Normal Quotient Distribution approach was combined with the Slope Fault Model to handle the tolerances problem in soft-fault diagnosis for analog circuit. Firstly, the principle of the Slope Fault Model is presented, and the huge computation of traditional Slope Fault Characteristic set was reduced greatly by the elimination of superfluous features. Several typical tolerance handling methods on the ground of the Slope Fault Model were compared. Then, the approximating distribution function of the Slope Fault Characteristic was deduced and sufficient conditions were given to improve the approximation accuracy. The monotonous and continuous mapping between Normal Quotient Distribution and standard normal distribution was proved. Thus the estimation formulas about the ranges of the Slope Fault Characteristic were deduced. After that, a new test-nodes selection algorithm based on the reduced Slope Fault Characteristic ranges set was designed. Finally, two numerical experiments were done to illustrate the proposed approach and demonstrate its effectiveness.