Software failures caused by data race bugs have always been major concerns in parallel and distributed systems, despite significant efforts spent in software testing. Due to their nondeterministic and hard-to-reproduce features, when evaluating systems’ operational reliability, a rather long period of experimental execution time is expected to be spent on observing failures caused by data race conditions. To address this problem, in this paper, we make two contributions. First, this paper proposes stress testing with influencing factors, in which the system runs under certain workloads for a long time with controlled stress conditions to accelerate the occurrence of data race failures. Second, it explores and formulates mathematical relationship models between data races’ statistical characteristics of time to failure (TTF) or mean TTF (MTTF) and the influencing factors. Such relationship models are used for TTF/MTTF extrapolation under different operational conditions and are essential to reduce systems’ reliability evaluation time. The proposed method is empirically evaluated on six applications suffering from failures caused by real-world data race bugs. Through analysis of the experimental results, we obtain several important findings: First, the reduction in the manifestation time to data race failures achieved by controlling the influencing factors is statistically significant. Second, Power model is the best-fitting model of the relationship between the MTTF and the influencing factors. Third, Power Weibull distribution is the best-fitting probability distribution between the TTF and the influencing factors. Finally, the TTF/MTTF can be accurately estimated with the approach proposed in this paper.