Process capability indices are commonly used to summarize a process’s capability based on a single quality characteristic. However, modern production processes usually involve multivariate and often correlated quality characteristics, rendering univariate indices insufficient to fully assess the capability of a process. This has led to the development of multivariate process capability indices (MPCI). Even though various index formulations have been proposed in the literature, they differ greatly in their approach, interpretation and sensitivity to the parameters such as the “non-centeredness” of the process and the number of the quality characteristics as well as their correlation structure. In this Quality Quandaries, we examine a selection of the available MPCI. We then conduct a sensitivity analysis to examine how these indices respond to changes in certain process parameters. Finally, we illustrate these findings using a case study and emphasize the need for careful interpretation when applying MPCI in practice.

Measurement system analysis is often performed in industry to check the quality of a measurement system. When assessing the capability of measurement systems, two key components of measurement error are commonly considered: repeatability and reproducibility. Experimental designs are generally used to quantify these error components, and the resulting investigation is referred to as a Gauge Repeatability and Reproducibility (Gauge R&R) study. Yet another possible source of error that is often overlooked is within-part variability, which can be a significant source of variability in the measurements of parts. Investigation of this error source requires modifications to both the experimental setup and the effects model for quantifying the components of variability. In this study, we analyze the effects of various measurement assessment plans on the Gauge R&R metric when within-part variation is present. Alternative measurement assessment plans and their ANOVA models are proposed. As common geometric forms in manufacturing processes, cylindrical and rectangular prism shaped parts are considered. Using computer simulations of parts having within-part variability, it is shown that neglecting within-part variation can cause misleading conclusions from an MSA study, and as a consequence, practitioners may not recognize the actual performance of their measurement system. Our conclusions are justified by a real world case study for a cylindrical part.

Experimental data plays a crucial role in sequential learning particularly in industrial applications. There have been great advances in both experimental design and analysis methods offering a myriad of choices for the practitioners. Yet in some real-life applications, it is not always possible to follow textbook approaches precisely. In general, but certainly in those circumstances, expert knowledge can be used to support experimental studies to determine more efficient design and analysis approaches to facilitate the learning process. In this Quality Quandaries, we briefly discuss two great articles advocating the use of expert knowledge in model building and present a drug product development study using experimental techniques for sequential learning.

In a previous Quality Quandaries, we discussed the importance of sequential learning through experimental design in industrial applications. In this Quality Quandaries, we follow the earlier discussion with two case studies in drug product development, in which some relatively less known experimental design techniques were used. Our goal is to once again demonstrate the crucial role that experimental design plays not only in scientific learning but also in practice. Furthermore, by (re-)introducing these experimental design techniques, we aim to emphasize the importance of flexibility and adaptability in overcoming limitations in practical applications through an expanded experimental design toolbox.

Industrial data is often available only in an unlabeled form as obtaining the label (the response) for the input data can be a challenging and time-consuming task. This Quality Quandaries provides an overview of active learning-based sampling methods for streamlining the development of classification and regression models in label-scarce environments. A case study on active learning for vision-based industrial inspection is presented. The case study shows how selecting the most informative data points to label can at a fraction of the cost achieve model performances similar to the case where all input data is labeled.

The great advances in sensor technology and automated data collection schemes allow for real-time data collection at high frequencies, often resulting in serial dependence, also known as autocorrelation. The analysis of such data requires specialized models as most standard approaches to modeling and testing cannot properly handle serial dependence. In this Quality Quandaries, we first discuss the classical approach of Autoregressive and Moving Average models from a practical perspective. We then showcase some deep learning counterparts to these models following a similar model evolution. We also present the so-called Transformers, a relatively newer modeling approach and provide a comparative example involving some of the models we cover. Our aim is to offer the readers of this Quality Quandaries a comparative overview of the ever-growing class of models that can handle serially dependent data.

For many data analytics studies, summarizing the “bottom line” with only a few statistics is very tempting. This is often done to simplify communication and maximize the impact of the outcome. On the other hand, failing to consider the efforts behind the calculations of these statistics, or to fully understand the specifics in data collection and the assumptions used to make the inferences can lead to erroneous conclusions and missed improvement opportunities. The prevalent use of capability indices offers a prime example. These unitless measures of the ratio of the range of the engineering specifications to the natural variation in the process offer a very valuable summary of the capability of the processes yet they are all calculated based on a sample of observations and a set of assumptions. Ignoring all these and just focusing on the point estimates can be misleading. In this Quality Quandaries, we discuss some of the conditions and assumptions in the calculation of these indices, and for the violation of the normality assumption, we present two case studies highlighting potentially problematic issues.

In industrial settings, collecting labeled data, i.e., input data with the corresponding output, is often expensive and time-consuming, while unlabeled process data is typically readily available in large quantities. This Quality Quandaries explores Semi-Supervised Learning (SSL) as a method to enhance predictive modeling by utilizing both labeled and unlabeled data. We provide a general discussion of SSL methods and their applicability in industrial environments, where efficient data utilization is critical. To demonstrate the practical utility of SSL, we present three cases: one focusing on regression, employing semi-supervised Autoencoders to extract meaningful features from unlabeled data, and two others on classification through the Label Spreading approach. These examples highlight the potential of SSL techniques to address data limitations and improve predictive performance in industrial applications.