A modified reliability-based design optimization (RBDO) technique was developed and applied to optimal designs of composite patches of a perforated base plate. The modified RBDO technique uses adaptive sampling strategies for the response surface method (RSM) to enhance the computational efficiency of the traditional RSM-based RBDO technique. Optimal design of composite patches was conducted for a perforated base plate using the newly proposed failure criteria which state that two conditions must be satisfied simultaneously for failure to occur. One condition is based on stress magnitude while the second condition is associated with the stress gradient. In other words, the failure criteria suggests that failure is more likely for higher stresses and lower stress gradients. Therefore, the design optimization of the composite patch was conducted to decrease the stress and to increase the stress gradient simultaneously at the edge of the perforated hole of the base plate in order to optimize the probability of failure of the base plate with composite patches.