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Parametric fault testing of non-linear analog circuits based on a new mathematical transform is presented. The V-Transform acts on the polynomial expansion of the circuit's function. Its main properties are: 1) to make the polynomial coefficients monotonic, 2) to reduce masking of parametric faults due to process variation, and 3) to increase the sensitivity of polynomial coefficients to the circuit parameter variation, thus enhancing diagnostic resolution. We show that the sensitivity of V-Transform Coefficients (VTC) with respect to circuit parameter variation is up to 3 to 5 times greater than the sensitivity of polynomial coefficients. Fault diagnosis of parametric faults under process variation using VTC is then presented. We also propose a scheme to distinguish between circuit specifications failures due to process variation versus manufacturing defects which manifest as parametric faults. To validate our approach, we apply the test and diagnosis procedures to a benchmark fifth order elliptic filter. We use SPICE program for fault injection, with about 50,000 Monte Carlo simulation runs to demonstrate fault detection-diagnosis under process variation. The test scheme uncovers 95% of all injected single parametric faults whose sizes deviate 5% from the nominal values of circuit components corrected for process variation, while the procedure successfully diagnosed all component faults under ±3σ process variation with 88% confidence level.