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A sensitivity analysis estimates the effect of the change in the uncertain variable parameter on the probability of the structural failure. A novel fuzzy random reliability sensitivity measure of the failure probability is proposed to consider the effect of the epistemic and aleatory uncertainties. The uncertainties of the engineering variables are modeled as fuzzy random variables. Fuzzy quantities are treated using the 𝜆cut approach. In fact, the fuzzy variables are transformed into the interval variables using the 𝜆-cut approach. Genetic approach considers different possible combinations within the search domain (𝜆-cut) and calculates the parameter sensitivities for each of the combinations.