We propose a Built-In Self-Test (BIST) paradigm for analog and mixed-signal (A/M-S) Integrated Circuits (ICs), called symmetry-based BIST (SymBIST). SymBIST exploits inherent symmetries in an A/M-S IC to construct signals that are invariant by default, and subsequently checks those signals against a tolerance window. Violation of invariant properties points to the occurrence of a defect or abnormal operation. SymBIST is designed to serve as a functional safety mechanism. It is reusable ranging from post-manufacturing test, where it targets defect detection, to on-line test in the field of operation, where it targets low-latency detection of transient failures and degradation due to aging. We demonstrate SymBIST on a Successive Approximation Register (SAR) Analog-to-Digital Converter (ADC). SymBIST features high defect coverage, short test time, low overhead, zero performance penalty, and has a fully digital interface making it compatible with modern digital test access mechanisms. Index Terms-Analog and mixed-signal integrated circuit testing, built-in self-test, design-for-test, defect-oriented test, defect simulation, on-line test, concurrent error detection.