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Despite AI’s significant growth, its “black box” nature creates challenges in generating adequate trust. Thus, it is seldom utilized as a standalone unit in high-risk applications. Explainable AI (XAI) has emerged to help with this problem. Designing effectively fast and accurate XAI is still challenging, especially in numerical applications. We propose a novel XAI model named Transparency Relying Upon Statistical Theory (TRUST) for XAI. TRUST XAI models the statistical behavior of the underlying AI’s outputs. Factor analysis is used to transform the input features into a new set of latent variables. We use mutual information to rank these parameters and pick only the most influential ones on the AI’s outputs and call them “representatives” of the classes. Then we use multi-model Gaussian distributions to determine the likelihood of any new sample belonging to each class. The proposed technique is a surrogate model that is not dependent on the type of the underlying AI. TRUST is suitable for any numerical application. Here, we use cybersecurity of the industrial internet of things (IIoT) as an example application. We analyze the performance of the model using three different cybersecurity datasets, including “WUSTLIIoT”, “NSL-KDD”, and “UNSW”. We also show how TRUST is explained to the user. The TRUST XAI provides explanations for new random samples with an average success rate of 98%. Also, the advantages of our model over another popular XAI model, LIME, including performance, speed, and the method of explainability are evaluated.