A fault diagnostic system of a vehicle includes an error module, a proportional integral (PI) module, and a fault module. The error module determines an error based on a difference between a sample of a signal generated by an exhaust gas oxygen sensor and a target value of the sample. The PI module determines a proportional correction based on the error, determines an integral correction based on the error, and determines a fueling correction based on the proportional and integral corrections. The fault module selectively diagnoses a fault based on the integral correction and the fueling correction.