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This paper uses R6 to examine the effects of correlated input data on estimatesof failure probability. For 100% positive and 100% negative correlation between fracturetoughness and yield stress, the failure probability can be evaluated ‘exactly’ by integratingthe tails of distributions up to points which can be determined. Approximate estimates offailure probability are introduced, and shown to be upper and lower bound estimates for100% negative correlation. The ‘exact’ and approximate estimates of failure probabilityare compared with some Monte Carlo simulations for a flawed plate under membraneloading. For 100% negative correlation, the upper and lower bound estimates are close toeach other when the failure probability is low (~10-5).