Quality control is a critical component in the life cycle of manufacturing. During mass production, the definition for quality naturally focuses on the variation of a large batch of products. The objective of quality control therefore aims at variation reduction. Thanks to sufficient sample data, statistics-based quality control methods such as statistical process control, acceptance sampling, and design of experiments have been established for quality improvement. Mean and variance estimated from sample data are frequently utilized to characterize quality characteristics.
In contrast to the mass production scenario, additive manufacturing (AM) enables individualized manufacturing of low-volume products with huge varieties and geometric complexity. It is cost-prohibitive to collect sufficient sample data to build credible statistical distributions for quality characterization. Thus the long-established concept process control for mass production cannot be directly adopted for AM. In a cybermanufacturing environment, big data can potentially be aggregated from interconnected AM machines and shared design models. However, the aggregated data can be highly heterogeneous due to variations in product design, materials, AM processes, and process conditions. The independent and identically distributed assumption critical for existing analysis tools is often not satisfied. Furthermore, statistical approaches cannot be applied when no data can be aggregated for new products, materials, or processes not being tried before.
A universal mathematical representation of AM product accuracy, particularly the three-dimensional shape, is currently unavailable. Due to the nature of lay-by-layer fabrication, accuracy of AM built products has often been classified into in-plane (x-y plane) and out-of-plane (z plane) shape deformation. Mathematical description of these two types of accuracy is often inconsistent. Adding to the challenge of accuracy representation is the shape complexity. A shape-dependent representation of product accuracy limits the capability of complexity-free fabrication. Furthermore, accuracy representation shall allow adaptability and extendability of one shape to another. The connection among product shapes has to be established for a universal mathematical accuracy representation.
A typical AM process involves material phase changes, with either liquid, paste, or loose powder selectively solidified into a solid, resulting in shape deformation. The accuracy of an AM-built product can be attributed to many factors, or causes, such as product design, materials, processes, and conditions. Accordingly, establishing causal mechanisms or models relating accuracy to such causes is essential for a unified theory of accuracy prediction and quality control in AM. Novel ideas from modern causal inference can effectively be applied to go beyond previous attempts to solve the fundamental problem of accuracy, which typically involved the daunting task of predicting accuracy from first physical principles. One important idea from modern causal inference is external validity. An analysis of a study, either on experimental or observational data, is said to possess external validity if statistical inferences on causal mechanisms for the study can be extended environments external to that considered in the specific study. External validity is a fundamental concept for the theory of accuracy prediction because AM is inherently concerned with manufacturing one-of-a-kind product shapes. Limitations on available resources constrain data collection for the purposes of quality control. Current predictive models typically fail to address how small samples of data collected on distinct shapes from disparate processes can be used to learn about causal mechanisms for new shapes and environments. Accordingly, they do not effectively achieve unified accuracy prediction for AM. Innovative causal modeling is imperative to the mathematical foundation for matching accuracy to fabrication variations and product performance metrics.
Accuracy of AM built products can be improved through control of AM processes. Three control strategies have been reported to improve geometric accuracy in AM: (i) control process variables based on the observed disturbance of process variables, (ii) control process variables based on the observed product deviation, and (iii) control input product geometry based on the observed product deviation. However, the issue of lack of external validity in causal models fundamentally limits the scope of applying both online and offline control of AM processes. Control model suitable for one group of products may not be applicable to another, needless to mention control models for untried products. There is little study of control optimality and optimal control algorithms for 3D deformation.
Control of the AM process is usually done in an uncertain environment that depends on several time-varying characteristics of production, such as part alterations, and other unknown noise factors. In the current practice, ad hoc or heuristic strategies are widely used for compensation of repeated errors. Optimal control relies on a better understanding of not only the basics of production but also how different products are potentially correlated. The heterogeneous, low-volume AM production process prevents the use of traditional uncertainty quantification based on repeated production of the same products. Thus new uncertainty quantification methods are needed. Uncertainty quantification requires a formal definition of the process in terms of a casual model that has several properties. For the AM process, the model must include observable quantities, have identifiable unknown values and be a function of the shape complexity of the product. Existing models include observable quantities, like the independent and identically distributed model, but do not possess the second and third qualities. Unknown values are often taken from the literature on similar studies or estimated from experimental data, but this introduces another source of uncertainty in the model predictions. To date, no tools exist to construct such a general purpose model for uncertainty quantification.
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