The deterministic Goodman diagram, which reflects the relationship among the mean stress, the alternating stress and the appropriate strength properties of a material, is commonly used to bring the influence of the nonzero stress ratio of the alternating to the mean stress into consideration. This is important because many mechanical components are subjected to combined stresses. In this paper, three methods are presented to deal with both the scatter of the loading and of the material strength. In the first method, the distributional Goodman and other combined stress failure relationships are obtained and used, based on the normal approximation and the binary synthesis of distributions. In the second method, the distributional Goodman and other combined stress failure relationships are obtained and used to find the state limit function. Then, the first order second moment algorithm is employed to determine the reliability. In the third method, the distributional Goodman diagram is used directly with the stress ratio mean, obtained by Taylor's expansion about the mean vector. A combined bending-torsion load problem is solved as an application of the methods presented here.