Reliability, the part of successful convocations of a voluntary fire brigade, is one of the decisive factors of successfulness and quality of a voluntary fire brigade. The unplanned selection and education of firemen show that the unit is not reliable enough. The presented mathematical model serves as a numerical evaluation of reliability. It helps to analyze the causes of eventual weak points and to make effective steps toward their improvement. This method is the first step to a large analysis of quality and reliability of a voluntary fire brigade. The calculations represent a mathematical model that is not fully equivalent to the real situation, but it depicts well enough and is much cheaper to find and test optimal solutions. It is also relatively easy to test the reliability of each voluntary fire brigade (VFB).