A system according to the principles of the present disclosure includes an error count module and a sensor diagnostic module. The error count module increases an error count when an actual air/fuel ratio generated by an oxygen sensor monitoring an exhaust system of an engine is different than a desired air/fuel ratio. The error count module selectively adjusts a rate at which the error count is increased based on an ambient temperature. The sensor diagnostic module diagnoses a fault in the oxygen sensor when the error count is greater than a first predetermined count.