The conducted investigations aimed at developing of the method of marking diagnostic tolerances of the exhaust temperature of a gas turbine observed during engine start-up. The diagnostic tolerances were determined by means of statistical inference by creating the hypothesis about a normal distribution of the start-up exhaust temperature dispersion in the moment of initial operation, which was subsequently verified applying a non-parametric statistical test χ2 of the compliance between the empirical and the assumed normal distribution. A satisfactory convergence of the compared distributions was obtained as the result of a testing of the created hypothesis, which represented the basis for the acceptance of the three-sigma boundaries of diagnostic tolerances for the considered engine control parameter.