A probabilistic-based component design methodology is developed for a solid oxide fuel cell (SOFC) stack. This method takes into account the randomness in SOFC material properties as well as the stresses arising from different manufacturing and operating conditions. The purpose of this work is to provide the SOFC designers a design methodology so that the desired level of component reliability can be achieved with deterministic design functions using an equivalent safety factor to account for the uncertainties in material properties and structural stresses. Multiphysics-based finite element analyses were used to predict the electrochemical and thermal mechanical responses of SOFC stacks with different geometric variations and under different operating conditions. Failures in the anode and the seal were used as design examples. The predicted maximum principal stresses in the anode and the seal were compared with the experimentally determined strength characteristics for the anode and the seal, respectively. Component failure probabilities for the current design were then calculated under different operating conditions. It was found that anode failure probability is very low under all conditions examined. The seal failure probability is relatively high, particularly for high fuel utilization rate under low average cell temperature. Next, the procedures for calculating the equivalent safety factors for the anode and seal were demonstrated so that a uniform failure probability of the anode and seal can be achieved. Analysis procedures were also included for non-normal distributed random variables so that more realistic distributions of strength and stress can be analyzed using the proposed design methodology.