The determination of mathematical reliability in static structures is still a motivating ยฎeld of research. On one hand, the failure probability values are of greater importance in engineering activities; on the other hand, the determination of this probability remains a time consuming computational task when real problems are examined. To obtain a signiยฎcant value for the failure probability while preserving a reasonable computation cost is therefore an objective to be considered. One of the necessary conditions to reach this target is to design a method to determine the computational error. Knowing the error will then give the capacity to limit the computation time, in particular by avoiding a too accurate probability evaluation. This paper presents a method allowing one to deal with these factors. The RGMR method, presented at the ICASP'7 meeting (July 1995, Paris) was designed to make such an error evaluation possible. Examples of numerical error computations with the RGMR method, particularly when low signiยฎcant variables are eliminated, are given. These new developments are a step towards the goal mentioned above.