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Error-tolerance is an innovative technique to address the problem of low yields in nanometer very large scale integrated (VLSI) circuitry, which is the backbone of the system-on-a-chip (SOC) revolution. The basic principle of error-tolerance is that some chips may occasionally produce erroneous outputs, but still provide acceptable performance when used in certain systems. Using these chips in such systems results in an increase in effective yield. In this paper, a fault-oriented test methodology is presented for classifying whether or not a chip is acceptable based on error rate estimation. A sampling method is proposed to estimate error rate associated with each possible fault in the target circuit. According to this information, an approach is developed to identify a list of faults that are acceptable with respect to a specified upper bound on expected error rates of acceptable chips. Furthermore, a test pattern selection method, and an output masking technique are presented to identify tests which detect all of the unacceptable faults, and as few acceptable faults as possible, so as to maximize the effective yield. Experimental results indicate the high effectiveness of the proposed error rate estimation method, and the degree to which yield can be enhanced.