Manufacturing systems are usually nonlinear, nonstationary, highly corrupted with outliers, and oftentimes constrained by physical laws. Modeling and approximation of their underly- ing response surface functions are extremely challenging. Bayesian optimization is a great statistical tool, based on Bayes rule, used to optimize and model these expensive-to-evaluate functions. Bayesian optimization comprises of two important components namely, a sur- rogate model often the Gaussian process and an acquisition function often the expected improvement. The Gaussian process, known for its outstanding modeling and uncertainty quantification capabilities, is used to represent the underlying response surface function, while the expected improvement is used to select the next point to be evaluated by trading- off exploitation and exploration. Although Bayesian optimization has been extensively used in optimizing unknown and expensive-to-evaluate functions and in hyperparameter tuning of deep learning models, mod- eling highly outlier-corrupted, nonstationary, and stress-induced response surface functions hinder the use of conventional Bayesian optimization models in manufacturing systems. To overcome these limitations, we propose a series of systematic methodologies to improve Bayesian optimization for engineering design and quality control of manufacturing systems. Specifically, the contributions of this dissertation can be summarized as follows. 1. A novel asymmetric robust kernel function, called AEN-RBF, is proposed to model highly outlier-corrupted functions. Two new hyperparameters are introduced to im- prove the flexibility and robustness of the Gaussian process model. 2. A nonstationary surrogate model that utilizes deep multi-layer Gaussian processes, called MGP-CBO, is developed to improve the modeling of complex anisotropic con- strained nonstationary functions. 3. A Stress-Aware Optimal Actuator Placement framework is designed to model and op- timize stress-induced nonlinear constrained functions. Through extensive evaluations, the proposed methodologies have shown outstanding and significant improvements when compared to state-of-the-art models. Although these pro- posed methodologies have been applied to certain manufacturing systems, they can be easily adapted to other broad ranges of problems. / Doctor of Philosophy / Modeling advanced manufacturing systems, such as engineering design and quality moni- toring and control, is extremely challenging. The underlying response surface functions of these manufacturing systems are often nonlinear, nonstationary, and expensive-to-evaluate. Bayesian optimization, a statistical modeling approach based on Bayes rule, is used to rep- resent and model those complex (i.e., black-box) objective functions. A Bayesian optimiza- tion model consists of a surrogate model, often the Gaussian process, and an acquisition function, often the expected improvement. Conventional Bayesian optimization models do not accurately represent non-stationary and outlier-corrupted functions. To overcome these limitations, we propose a new asymmetric robust kernel function to improve the model- ing capabilities of the Gaussian process model in process quality control through improved defect detection and classification. We also propose a non-stationary surrogate model to improve the performance of Bayesian optimization in aerospace process design problems. Finally, we develop a new optimization framework that models and optimizes stress-induced constrained aerospace manufacturing systems correctly. Our extensive experiments show significant improvements of these three proposed models when compared to state-of-the-art methodologies.