Real systems face with uncertainty. Two categories are defined for uncertainty: Aleatoric Uncertainty, and Epistemic uncertainty. The first one is unbiased, and often defined in a probabilistic framework. The second is biased, and it is less naturally defined in a probabilistic framework. One goal of uncertainty quantification is to convert epistemic uncertainties to aleatorics, to apply probabilistic analysis. One of the activities done, calibrating a model, is statistical adjustment. Statistical adjustment is defined by the process of calculating auxiliary variables. Model calibration is studied to be done through minimal adjustments. Minimal adjustment is an adjustment procedure that brings the computer model closer to the data by making minimal changes to it. The probabilistic quantification of predicted experimental and computational outcomes with identified and quantified uncertainty is sometimes termed predictive estimation. To forecast accurately and make decisions, this uncertainty must be modeled. In this research, different approaches for modeling and quantifying uncertainty are studied. One approach is engineering approach, which is time consuming and unrealistic, due to its simplifying assumptions. The second is based on data gathering, called statistical approach, which is not correct out of the data range, and lacks physical interpretation. Some researchers compounded these two approaches and de-fined engineering-statistical approach which is more useful, fast, and realistic. Besides, for large scale systems, usual techniques of model solving are inadequate. In such cases, surrogate models are used. Uncertainty quantification consists of four steps: verification, validation, calibration and uncertainty propagation, In this research, a methodology is defined to develop an engineering-statistical model. Then, the methodology is used for solving a real problem. As a case study, Laser Assisted Micro-Machining (LAMM) system is chosen. The problem is studied by some researches, before. So, it is proper to compare the proposed methodology by the previous ones in literature. In continue, the compare is done.