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Mission-critical applications require that any failure that may lead to erroneous behavior and computation is detected and signaled as soon as possible in order not to jeopardize the entire system. Totally self-checking (TSC) systems are designed to be able to autonomously detect faults when they occur during normal circuit operation. Based on the adopted TSC design strategy and the goal pursued during circuit realization (e.g., area minimization), the circuit, although TSC, may not promptly detect the fault depending on the actual number of input configurations that serve as test vectors for each fault in the network. If such a number is limited, although TSC it may be improbable that the fault is detected once it occurs, causing detection and aliasing problems. The paper presents a design methodology, based on a circuit re-design approach and an evaluation function, for improving a TSC circuit promptness in detecting faults' occurrence, a property we will refer to as TSC quality.