Yicheng Kang

Center for Analytics and Data Science, Miami University

1 Introduction

In recent years, the landscape of industrial manufacturing has been changed drastically by rapid advancements of emerging technologies such as 3D printing, sensing technology, computer vision, robotics and artificial intelligence (AI). As a result, modern manufacturing facilities often are equipped with a large number of sensors, computers and monitors, which routinely generate data in high volume and at high velocity. This data-rich environment has made it possible to deploy advanced analytic techniques at scale, further enhancing the efficiency and effectiveness of the manufacturing operations. Such fully-integrated and collaborative manufacturing systems are referred to as smart factories (National Institute of Standards and Technology), a typical example of Industry 4.0. In this article, we briefly introduce several commonly used analytic models in their relationship to smart manufacturing.

2 Additive Manufacturing (3D Printing)

Additive manufacturing is the conceptual opposite of the traditional manufacturing, in which an object is produced by cutting away at a solid block of material until the final product is complete. Additive manufacturing is a process that takes a digital 3D representation of an object and creates the object by building it one layer at a time. Therefore, it is also known as 3D printing. Since 3D printing is indifferent to the geometries that it is instructed to produce, it largely eliminates the cost of product-specific tooling and equipment, greatly enhancing the speed to market.

We can use the following regression model to describe a product’s geometry.

$w_{ijk} = g(x_i, y_j, z_k) + \varepsilon_{ijk},$

where $g$ is the regression function, $(x_i, y_j, z_k)$ represents the coordinates in a 3D space, and $\varepsilon_{ijk}$ is a random error. Since the product geometry is arbitrary, the regression function $g$ cannot assume any parametric form. In addition, $g$ is often discontinuous. Therefore, jump regression analysis (JRA, Qiu 2005) is the natural framework to analyze 3D printing data. After a product is printed, we often need to ensure that the printed product’s geometry complies with the intended design. To this end, a laser scanner is used to scan the product, with the product fixed at a rotatable holder placed before the scanner. The relative position between the laser scanner and the product can change from product to product, making it difficult to compare their geometries with the intended design. To align the two products’ geometries, we consider the following transformation.

$(x^{(2)}_i, y^{(2)}_j, z^{(2)}_k) = R(x^{(1)}_i, y^{(1)}_j, z^{(1)}_k) + T$,

where the superscripts denote the two geometries, $R$ represents a 3D rotation, and $T$ represents a 3D translation. Estimating $R$ and $T$ is a technique known as 3D image registration (Bhagalia et al. 2009). This technique allows us to meaningfully compare products’ geometries.

3 Internet of Things (IoT)

The fast development of data acquisition technologies has slashed the cost of sensors over the past decade. In the meanwhile, the processing speed of a sensor has increased by multiple folds. This confluence of cost reduction and processing speed increase has made it economically sensible for factories to be installed with a great number of sensors, which continuously produce data streams in big volume. These data are often referred to as high-dimensional data streams (HDDS, Colosimo et al. 2024). Because of their ability to provide granular information about system-wide performance on a real-time basis, HDDS are regarded to possess great potential to improve business decision-making by breaking the informational constraint. However, analyzing HDDS comes with its challenges. Consider, for instance, readings recorded by $N$ sensors (Here $N$ is usually in the tens of thousands) over time: $x_i, i = 1, \ldots, N.$ Each $x_i$ represents a local attribute of the industrial system. To ensure the system is performing stably, each $x_i$ should stay in a normal range. A common practice is to conduct statistical hypothesis testing with each data stream.

$x_i$ is in a normal range vs. $x_i$ is abnormal, $i = 1, \ldots, N.$

With the typical choice of type-I error threshold 5%, $N/20$ data streams would be flagged as abnormal even if the industrial system is working normally. If $N =$10,000, then the number of falsely flagged streams would be 500, This means that the manufacturer would have to examine these 500 local attributes one by one just to confirm that all alarms turn out to be false, resulting in substantial wastes of time and effort. Large-scale statistical inference is the appropriate framework for HDDS analysis. The key idea is to perform the above hypothesis tests with the missed discovery rate (MDR, Shi et al. 2025) constraint:

$\text{MDR} = \frac{\text{the number of missed abnormal attributes}}{\text{the total number of abnormal attributes}} \leq \alpha$,

where $\alpha$ is a small threshold (e.g., 5%). With metrics such as MDR, manufacturers can focus their resources on malfunctioning components and control their risk at a tolerable level.

4 AI-Based Quality Control

Quality control is of critical importance for manufacturers to ensure that their products meet their quality standards. Traditionally, to achieve the purpose of quality control, human operators are hired to perform visual inspection of the products to check for defects. This human visual inspection approach, however, lacks consistency and objectivity in the sense that human operators are susceptible to fatigue due over time and different operators tend to have different visual perception characteristics. It also severely limits the ability to keep up with high production rates. Consequently, often only a fraction of products are sampled. In contrast, the high degree of automation in smart factories comes with quality monitoring systems which leverages powerful technologies such as computer vision and artificial intelligence. Sensors and cameras unceasingly watch the production lines and capture information about product specifics (e.g., dimension, surface defects and spatial patterns) in real time. After an image of products is captured by a camera, certain computer algorithms will analyze the image and determine whether the product satisfies the quality standards. One way to represent a digital image is via a two-dimensional wavelet transform (Kang 2022). Write an image as $f(x, y)$, where $f(x, y)$ denotes the location of a image pixel. Then $f(x, y)$ can be approximated by the following wavelet expansion.

$f(x, y) = \sum_{b=1}^p \beta_b B_b(x, y)$,

where $\{B_b(x, y): b = 1, \ldots, p \}$ are wavelet basis functions. With this representation, Monitoring the product images is equivalent to monitoring the vector $\{\beta_b: b = 1, \ldots, p \}$. In some cases where the spatial pattern in images can not be adequately described by wavelet functions. Convolutional neural network (CNN, Stevens et al. 2020) are designed to accommodate a wide variety of image patterns. In the quality control setting, a product image is fed to a CNN, which automatically determines whether the product is of good-quality or defective. That is,

$\text{CNN}(f) \rightarrow 0 \text{ if good quality, } \text{ and } 1 \text{ if detective.}$

A major limitation with using CNN in quality control is that its calibration requires a large accumulation of both good-quality and defective products, which may not be available in practice. Techniques such as transfer learning may be helpful in such situations.

5 Concluding Remarks

It is worth noting that we have only mentioned a few technologies involved in smart manufacturing. Other technologies such as advanced robotics, augmented reality, wearable devices and blockchain are all relevant to modern industrial facilities. The use of each of these technologies often requires a different set of analytic techniques. In addition, all these technologies can in combination improve manufacturing operations and management. Therefore, we believe that analytics professionals will have ample opportunities and challenges in this space.

References

Bhagalia, Roshni, Jeffrey A Fessler, and Boklye Kim. 2009. “Accelerated Nonrigid Intensity-Based Image Registration Using Importance Sampling.” IEEE Transactions on Medical Imaging 28 (8): 1208–16.

Colosimo, Bianca M, L Allison Jones-Farmer, Fadel M Megahed, Kamran Paynabar, Chitta Ranjan, and William H Woodall. 2024. “Statistical Process Monitoring from Industry 2.0 to Industry 4.0: Insights into Research and Practice.” Technometrics, 1–24.

Kang, Yicheng. 2022. “Statistical Quality Control Using Image Intelligence: A Sparse Learning Approach.” Naval Research Logistics (NRL) 69 (7): 996–1008.

Qiu, Peihua. 2005. Image Processing and Jump Regression Analysis. John Wiley & Sons.

Shi, Jianqing, Yicheng Kang, Liqiang Pu, and Dongdong Xiang. 2025. “A Unified Framework for High-Dimensional Data Stream Analysis in Fault Diagnosis.” Journal of Quality Technology 57 (1): 35–50.

Stevens, Eli, Luca Antiga, and Thomas Viehmann. 2020. Deep Learning with PyTorch. Manning Publications.