In this work, one of the common issues, the robustness of the soft sensors, in development of such predictive models is discussed and the solution is provided. Large random errors, also known as outliers are one inseparable characteristic of data sets which can be caused by various reasons. Robust probabilistic predictive models overcome this problem by appropriate formulation of noise distributions. In this work possible outliers are considered for both input and output data in contrast to the traditional robust algorithms that have focused on output outliers only. Probabilistic principal component analysis based regression is used for the predictive model in this work and Expectation Maximization algorithm is applied to solve a complex robust estimation problem. Finally the performance of the developed robust predictive model is evaluated by simulated and industrial case studies. This work is a generalization to the traditional robust probabilistic principal component analysis based regression modeling work which considered a different type of outliers that occur in the output only. (C) 2017 Elsevier Ltd. All rights reserved.