An Approximate Calculation of Ratio of Normal Variables and Its Application in Analog Circuit Fault Diagnosis

The challenging tolerance problem in fault diagnosis of analog circuit remains unsolved. To diagnose the soft-fault with tolerance effectively, a novel diagnosis approach based on the ratio of normal variables and the slope fault model was proposed. Firstly, the approximate distribution function of the ratio of normal variables was deduced and the basic approximate conditions were given to improve the approximation accuracy. The conditional monotonous and continuous mapping between the ratio of normal variables and the standard normal variable was proved. Based on the aforementioned proved mapping, the estimation formulas of the range of the ratio of normal variables were deduced. Then, the principle of the slope fault model for linear analog circuit was presented. After the contrastive analysis of the typical methods of handling tolerance based on the slope fault model, the ratio of normal variables and the slope fault model were combined and a test-nodes selection algorithm based on the basic approximate conditions of ratio of normal variables was designed, by which the computation can be reduced greatly. Finally, experiments were done to illustrate the proposed approach and demonstrate its effectiveness.