Monte Carlo simulations have become very popular in industrial applications as a tool to study variational influences on reliability assessments. The method is appealing because it can be done without any statistical knowledge and produces results that appear very informative. However, in most cases, the information gathered is no more than a complicated transformation of initial guesses because the statistical distributions of the dominating variational influences are unknown. The seemingly informative result may then be highly misleading, in particular, when the user lacks sufficient statistical knowledge. Instead, in cases where the input knowledge of the distributional properties is vague, it may be better to use a reliability method based on the actual knowledge, often not more than second moment characteristics. This can easily be done by using a method, based on variances, covariances, and sensitivity coefficients. Here, a specific problem of fatigue life of a welded structure is studied by (i) a Monte Carlo simulation method and (ii) a second moment method. Both methods are evaluated on a fatigue strain–life approach and use experimental data showing variation in weld geometry and material strength parameters. The two methods are compared and discussed in view of the engineering problem of reliability with respect to fatigue damage.