Orthogonal minimally aliased response surface (OMARS) designs permit the study of quantitative factors at three levels using an economical number of runs. In these designs, the linear effects of the factors are neither aliased with each other nor with the quadratic effects and the two-factor interactions. Complete catalogs of OMARS designs with up to five factors have been obtained using an enumeration algorithm. However, the algorithm is computationally demanding for designs with many factors and runs. To overcome this issue, we propose a construction method for large OMARS designs that concatenates two definitive screening designs and improves the statistical features of its parent designs. The concatenation employs an algorithm that minimizes the aliasing among the second-order effects using foldover techniques and column permutations for one of the parent designs. We study the properties of the new OMARS designs and compare them with alternative designs in the literature.

Process monitoring is crucial for ensuring the safe and reliable operation of equipment. Current process monitoring techniques often rely on distribution assumptions, such as the Gaussian distribution, which can be challenging to fulfill or justify in real-world applications. Moreover, many processes are influenced by exogenous covariates. While these covariates are not the primary focus of process monitoring, they offer valuable insights for a comprehensive understanding of process variability. To address these issues, we develop a distribution-free monitoring technique for covariate-regulated processes. Specifically, we propose a multivariate adaptive regression splines (MARS)-based quantile regression model. In contrast to traditional MARS techniques that employ a greedy search to include one pair of basis functions at each step, our approach involves incorporating all basis functions initially. This allows us to transform the problem into a linear programming and effectively incorporate constrains to avoid the quantile-crossing issue. Additionally, we introduce a three-level monitoring framework that progresses from monitoring single observations to quantile values and the entire quantile curves. We conduct numerical and real case studies to demonstrate the effectiveness of this technique.

In chemical and engineering sciences, most factors are quantitative, benefiting from investigation at three distinct levels when studying quadratic or non-linear relationships. Consequently, definitive screening designs (DSDs), a class of 3-level foldover designs introduced by Jones and Nachtsheim (2011), have gained prominence over traditional 2-level designs such as fractional factorial and Plackett–Burman designs. This article extends the framework of conference matrix-based DSDs by introducing a new class of circulant weighing matrix-based screening designs, offering greater design flexibility. Like DSDs and the orthogonal minimally aliased response surface (OMARS) designs recently proposed by Núñez Ares and Goos (2020), these new designs preserve orthogonality among main effects and between main and second-order effects (i.e., quadratic effects and two-factor interactions), while ensuring the absence of full aliasing among second-order effects. We refer to these designs as OMARS designs to highlight their ability to support both factor screening and response surface exploration in a single step. We present a comprehensive catalog of 149 new OMARS designs with desirable projection capability, accommodating up to 50 factors.

Many experiments involve various types of input factors, including continuously numerical, discretely numerical, ordinary and categorical variables. Designs with strong space-filling properties are essential for reducing costs and improving efficiency in such experiments. While some existing methods address multiple factor types, they are often limited by sample size constraints or fail to ensure orthogonality in discrete sub-designs. In this article, we propose a novel coverage-based space-filling criterion and introduce a simulated annealing algorithm to generate optimal coverage designs. The proposed criterion accounts for both the space-filling properties of continuous factors and the orthogonality of discrete factors, offering flexibility in run size. Numerical results confirm that the proposed design exhibits the desired properties.

Engineering design is a complex decision making process that depends on multiple design objectives and often requires frequent information exchange between designers and decision makers (DM), such as product managers or users. A common method to facilitate this information exchange and explore the tradespace of different design objectives is through preference elicitation, where DMs are asked to answer a sequence of queries to inquire preference comparisons between multiple design alternatives. In this work, we generalize the ellipsoid method proposed by Sauré and Vielma (2019) to the batch sequential setting, where multiple queries are selected at a time to be provided to the DM when some operational constraints make a fully sequential questionnaire impractical. In our setting, we use D-error as our selection criterion, the minimization of which leads to more precise estimates of the DM’s utility model parameters. We propose approximations of this criterion using linear surrogate models where the predictors are functions of certain summary statistics of the batch design whose effect can be estimated via offline experiments. Based on these approximations, we propose mixed integer programming formulations for constructing batch designs which can be solved in commercial optimization solvers. Our simulation studies show that the proposed methods provide highly D-efficient batch designs when compared to randomly generated designs. In addition, we show that our methods are comparable to a fully adaptive method when the batch size is small. Lastly, we present an example of using our methodology to aid in tradespace exploration for vehicle concept design.

With the development of data acquisition technologies, huge amounts of data, which are apt to be modeled as functional data, are now generated. In this setting, standard profile monitoring methods aim to assess the stability over time of a completely observed functional quality characteristic. However, in some practical situations, assessing the presence of assignable causes is of great interest even when the functional quality characteristic is not completely observed yet, that is, to monitor the process state in realtime. To this aim, we propose a new method, referred to as functional real-time monitoring (FRTM), that is able to account for both phase and amplitude variation through the following steps: (i) registration, (ii) dimensionality reduction, and (iii) monitoring of a partially observed functional quality characteristic. An extensive Monte Carlo simulation study quantifies the performance of FRTM relative to three competing methods. Finally, a case study addresses the real-time monitoring of household daily electricity demand FRTM is implemented in the R package funcharts, available CRAN.

We introduce ChatSQC, an innovative chatbot system that combines the power of OpenAI’s Large Language Models (LLM) with a specific knowledge base in Statistical Quality Control (SQC). Our research focuses on enhancing LLMs using specific SQC references, shedding light on how data preprocessing parameters and LLM selection impact the quality of generated responses. By illustrating this process, we hope to motivate wider community engagement to refine LLM design and output appraisal techniques. We also highlight potential research opportunities within the SQC domain that can be facilitated by leveraging ChatSQC, thereby broadening the application spectrum of SQC. A primary goal of our work is to provide a template and proof-of-concept on how LLMs can be utilized by our community. To continuously improve ChatSQC, we ask the SQC community to provide feedback, highlight potential issues, request additional features, and/or contribute via pull requests through our public GitHub repository. Additionally, the team will continue to explore adding supplementary reference material that would further improve the contextual understanding of the chatbot. Overall, ChatSQC serves as a testament to the transformative potential of AI within SQC, and we hope it will spur further advancements in the integration of AI in this field.

This document contained a diagram of a control chart.He explained how this control chart could identify assignable causes of variability.By identifying and eliminating these assignable causes, manufacturers could reduce the variability that arose from ongoing arbitrary adjustments to the process that were reactions to non-conforming units being produced.This could reduce the overall variability in the output and significantly improve product quality.This memo came at an important time.Western Electric, the manufacturing arm of the Bell System, was producing telecommunications equipment that would form the backbone of the telephone system in the US.This equipment needed to be as defect-free and reliable as possible, or this enormous business venture could fail.Western Electric successfully adopted Shewhart control charts and the accompanying theory of chance and assignable causes.Shewhart continued to work at Bell Labs until he retired in 1956.He continued to publish technical papers in the Bell System Technical Journal.He authored two books that described his theories in detail: The Economic Control of Quality of Manufactured Product (Van Nostrand 1931) and Statistical Methods from the Viewpoint of Quality Control (US Department of Agriculture Graduate School 1939).Both books are considered classics.With the start of World War II, the US Department of War (as the US Department of Defense was known then) recognized that the huge manufacturing potential of US industry would be instrumental in winning the war.However, it was going to be necessary to convert many of these organizations from producing consumer goods to military products for wartime use.This was further

To successfully determine if a system meets some reliability standard, typically assurance tests are conducted on the full system. This proven approach is extremely effective. However, it can be cost prohibitive when full system tests are expensive. Previous work has incorporated component and subsystem data to supplement the component prior distributions before a full system assurance test. Although this can be helpful, we propose an additional advance of allowing component and subsystem tests as part of the assurance test. We show that by augmenting full system tests with component and subsystem tests, in some cases, we can reduce the cost of the assurance test. For a system that can be decomposed into independent series and parallel parts, the theory works perfectly. In the case where we cannot accurately classify parts using the series or parallel structure, we add a generalization that works for systems that are “almost-series” or “almost-parallel.”

Spatial modeling and monitoring are critical in geometric characterization and quality control of material/product surfaces. With advances in metrology technology, a long-range dependence (LRD) effect has recently been detected in spatial data over different fields. The spatial LRD refers to a type of dependence that decays slowly over the distance with heavy tails and non-summable autocovariances so that the correlation is high among surface measurements across long spatial distances. Physically, the spatial LRD effect can be caused by specific spatial patterns such as certain material textures, surface profiles, or manufacturing defects. In literature, although various Markovian and non-Markovian spatial models have been proposed to study material surfaces, none of them has yet considered the LRD effect, which can lead to inefficient surface characterization and inaccurate surface quality control. To overcome the challenge, in this article, we first propose a novel spatial model that can capture the spatial LRD on material surfaces. Both isotropic and anisotropic scenarios of the model are developed based on the Lévy fractional Brownian random field and the fractional Brownian sheet, respectively. Subsequently, based on the proposed spatial model we develop an LRD-integrated quality control framework to monitor surface quality via generalized likelihood ratio test. Comprehensive simulation studies and a real case study using images of wood surfaces are conducted to validate the proposed approach. Results show that the proposed model that integrates LRD significantly outperforms multiple existing models in anomaly detection, and traditional models mis-detect out-of-control surfaces when the spatial LRD actually presents.