Direct and indirect test procedures are utilized to provide tensile strengths of rock and concrete samples. While the measurements provided by these methods are considered as identical in theory, a difference between the values is recorded in practice. To provide an association between the tensile test methods, a data-driven algorithm for identifying the uncertainty systems has been suggested. This study presents a novel algorithm including two steps: data processing-fusion and simulation. In the first step, both random and systematic error components in the tensile strength testing procedures are fused by uncertainty treatment-based data processing. By this way, instead of some assumptions and descriptive statistics, a data-fusion method is adapted. After that, a Monte Carlo simulation is performed using parametric and nonparametric probability distributions. Thus, a concurrency between the tensile strength procedures including strength values and uncertainty intervals is provided. The case study implemented by a real data set showed that the proposed algorithm has a feature of transparency, flexibility and also accuracy. The density functions used in the simulations do not require being normal while the conventional uncertainty-based data processing, Taylor's ISO-GUM method depends on the normality. In addition, the algorithm does not need specification of coverage factor and it also works without any sensitivity coefficient. The methodology can be recommended to provide an agreement between the tensile strength values of rocks especially with limited number of data.