Tolerance limits under normal mixtures: Application to the evaluation of nuclear power plant safety and to the assessment of circular error probable

Upper tolerance limits are derived for (i) a normal mixture distribution, and (ii) for the distribution of the Euclidean norm of a bivariate normal mixture random variable, using asymptotic normality of the MLE and bootstrap calibration. Scenario (i) is used to model the peak cladding temperature (PCT) of nuclear power plants, to assess if the PCT distribution is below a safety threshold of 2200 °F. Scenario (ii) is used to model impact location data on projectiles launched from different locations or systems, and the problem is inference concerning the circular error probable (CEP). Simulation studies show the accuracy of the proposed methodology.