Traditionally design engineers have used the Factor of Safety method for ensuring that designs do not fail in the field. Access to advanced computational tools and resources have made this process obsolete and new methods to introduce higher levels of reliability in an engineering systems are currently being investigated. However, even though high computational resources are available the computational resources required by reliability analysis procedures leave much to be desired. Furthermore, the regression based surrogate modeling techniques fail when there is discontinuity in the design space, caused by failure mechanisms, when the design is required to perform under severe externalities. Hence, in this research we propose efficient Semi-Supervised Learning based surrogate modeling techniques that will enable accurate estimation of a system's response, even under discontinuity. These methods combine the available set of labeled dataset and unlabeled dataset and provide better models than using labeled data alone. Labeled data is expensive to obtain since the responses have to be evaluated whereas unlabeled data is available in plenty, during reliability estimation, since the PDF information of uncertain variables is assumed to be known. This superior performance is gained by combining the efficiency of Probabilistic Neural Networks (PNN) for classification and Expectation-Maximization (EM) algorithm for treating the unlabeled data as labeled data with hidden labels.