Correlated Quality Characteristics Research Articles

Multivariate HPLC system assessment and optimization for traditional Chinese medicine: a case study of Gastrodia elata.

The development of HPLC analytical methods for traditional Chinese medicine is intricate and time-consuming, influenced by factors such as column wear, solvent purity, and instrumental settings. A comprehensive evaluation of the HPLC system is crucial to mitigate potential variability and ensure the reliability of data. This is especially important given the complex and synergistic nature of the chemical components in traditional Chinese medicine, necessitating a multivariate measurement system analysis (MSA) to assess multiple correlated quality characteristics effectively. This study introduced a multivariate MSA method based on weighted principal components (WPC) to evaluate the HPLC system for the determination of metabolites in Gastrodia elata. By integrating multiple principal components and assigning weights according to their eigenvalues, the WPC method significantly enhanced both accuracy and robustness. It demonstrated a repeatability and reproducibility (% R&R) of 26.43% and a number of distinct categories (ndc) index of 5, confirming the system's acceptability. A full factorial experimental design was employed to identify key performance factors, leading to the recommendation to use five reference solutions for the standard curve and to triple sample preparations for improved precision and accuracy. Monte Carlo simulations confirmed the reliability of the system, showing % R&R and ndc values that follow a normal distribution, ranging from 19% to 22% and 6.07 to 7.38, respectively. Chromatographic conditions were optimized using a Box-Behnken experimental design. Subsequent validation experiments verified the method's high accuracy and reliability, with all relative standard deviation values for analytical precision, repeatability, and stability below 5%. The method also exhibited high recovery rates, exceeding 91% across three concentration levels, with RSD values under 4%. In conclusion, the application of a WPC-based multivariate MSA enabled a detailed evaluation of the HPLC system, ensuring accurate and reliable measurement of quality attributes. This method exemplified a scientifically rigorous approach for developing analytical methods in traditional Chinese medicine, enhancing both precision and reliability.

Process monitoring for covariance matrices with latent structures

The monitoring of process variability is generally achieved by prompt detection of changes in the covariance matrix of multiple correlated quality characteristics. In the literature, there have been many approaches successfully developed for this purpose. Notably, in many chemical processes or some with a special or symmetric structure, involved high-dimensional data are strongly linearly correlated, so that they can be regarded to be determined by a number of low-dimensional latent variables, and hence, have a small intrinsic dimension. In this sense, the observed high-dimensional data have actually a latent structure, formed by latent variables and sensor errors. If such a latent structure can be fully exploited, more efficient monitoring of covariance matrices can be achieved. To this end, this article refines the structure of covariance matrices and develops a series of charting statistics, which are able to efficiently detect shifts in the covariance matrices of latent variables and of sensor errors. Based on the sensitivity analysis of the proposed charting statistics, we provide their choices, as well as a diagnostic scheme to determine the source of shifts. Monte Carlo simulations have demonstrated their superiority over existing alternatives in detecting covariance matrix shifts in latent variables or in sensor errors.

A data-driven monitoring scheme for multivariate multimodal data

Multivariate multimodal data, obtained from complex processes with multiple correlated quality characteristics and multiple operating modes, are commonly used in many applications. Online monitoring of multivariate multimodal data has been receiving increasing attention because timely detection of process problems is important. However, existing statistical process monitoring methods are often inadequate for addressing the challenges of multivariate multimodal data monitoring. For example, they may require the process data to be unimodal or identically distributed or may assume the information regarding the multimodal processes to be known a priori. Therefore, a data-driven monitoring scheme is proposed in this paper. First, the Dirichlet process Gaussian mixture model is adopted, which can depend entirely on data characteristics and automatically cluster the data without any prior knowledge. On this basis, an exponentially weighted moving average scheme is then constructed by incorporating the negative log-likelihood statistic. Using thorough simulations and a real example, we analyse and compare the performance of the model estimation and online monitoring for detecting various out-of-control scenarios. Extensive results show that our proposed monitoring scheme is sensitive to not only model parameter shifts but also model order changes. Moreover, the proposed scheme generally performs better and more robustly than existing methods.

A non-linear mixed model approach for detecting outlying profiles

In parametric non-linear profile modeling, it is crucial to map the impact of model parameters to a single metric. According to the profile monitoring literature, using multivariate T statistic to monitor the stability of the parameters simultaneously is a common approach. However, this approach only focuses on the estimated parameters of the non-linear model and treats them as separate but correlated quality characteristics of the process. Consequently, they do not take full advantage of the model structure. To address this limitation, we propose a procedure to monitor profiles based on a non-linear mixed model that considers the proper variance-covariance structure. Our proposed method is based on the concept of externally studentized residuals to test whether a given profile significantly deviates from the other profiles in the non-linear mixed model. The results show that our control chart is effective and appears to perform better than the T chart.

Pareto efficient correlated multi-response optimisation by considering customer satisfaction

The capability of a manufacturer in satisfying the customer's requirements is an important issue in the current competitive market. Since customers consider several correlated quality characteristics for selecting a product, designing the process variables to meet the required specification limits of the quality characteristics is essential. Furthermore, to attain the most satisfactory solution, a decision maker's preference information should be incorporated into the optimisation procedure. This study suggests a posterior preference articulation approach based on NSGA-II and MOPSO, which is capable to increase customer satisfaction by generating non-dominated solutions within conformance region. The proposed method takes also into account the location and dispersion effects along with the correlation of among quality characteristics as well as the relative importance of them. To demonstrate the applicability of the approach, a computational analysis on two case studies is performed. Results confirm superiority of the suggested method in comparison with the existing posterior approaches.

Two‐phase multivariate supplier selection for symmetric specification region and correlated quality characteristics

AbstractAmong different yardsticks of assessing a supplier's performance and comparing the same with other competing suppliers, quality is often considered as one of the most important criteria. The problem becomes even more complicated for multivariate processes having more than one correlated quality characteristics. Unfortunately, very few research work has been carried out in literature, to compare performances of two suppliers having multivariate processes with correlated quality characteristics and symmetric specification region. In the present article, a two‐phase hypothesis testing‐based supplier selection process using multivariate process capability indices (MPCIs) called and is proposed to address this issue. While measures potential capability of a multivariate process, measures its actual capability. The proposed method is easy to implement in practice and hence is suitable for practical applications. A real‐life example and a simulated example are discussed to supplement the theory developed in this article.

Integrated Quality, Maintenance and Production model for multivariate processes: A Bayesian Approach

In the era of modern manufacturing, automated inspection systems can facilitate online product quality assessment, generating data that can be used not only in a process control context but for equipment maintenance purposes, as well. The challenge is to develop appropriate tools to efficiently exploit the collected data by transforming them into optimal decisions that add value to the monitoring process. To this end, this paper proposes a Bayesian model that jointly optimises the interrelated process aspects of production, maintenance, and quality in modern manufacturing environments. The process output is characterised by multiple correlated quality characteristics and subject to multiple quality shifts and failures. Optimal real-time decisions are made based on a cost optimisation criterion. Finally, a numerical investigation is conducted to evaluate the performance of the proposed data-driven and widely applicable tool for contemporary processes.

Joint optimisation of production run length and maintenance policy for an imperfect process with multiple correlated quality characteristics

Joint optimisation of production run length and maintenance policy for an imperfect process with multiple correlated quality characteristics

Joint optimisation of production run length and maintenance policy for an imperfect process with multiple correlated quality characteristics

Joint optimisation of production run length and maintenance policy for an imperfect process with multiple correlated quality characteristics

THEORETICAL AND EXPERIMENTAL INVESTIGATION OF ESTIMATING CHANGE POINT IN MULTIVARIATE PROCESSES VIA SIMULTANEOUS COVARIANCE MATRIX AND MEAN VECTOR

The identification of change points in statistical process control (SPC) data is the critical criterion for multivariate techniques when output is out-of-control condition. Therefore, monitoring all independent variables is essential and demands targeted attention to avoid errors at the systems control stage. However, estimating change-point in multivariate control charts is the main problem when these correlated quality characteristics monitor together. Therefore, we proposed a combination of an ensemble learning-based model of artificial neural networks with support vector machines to monitor process mean vector and covariance matrix shifts simultaneously to estimate the change point in a multivariable system. The performance of the final model indicated an estimated changing point with one sample over 6,000 simulated cases with a probability of 98 percent, which is a significantly high accuracy rating. Finding suggests the outcome of the project confirms that the proposed model can provide a precise estimating the change point by monitoring the mean vector and the covariance matrix simultaneously and, helps to identify those variable(s) responsible for an out-of-control condition. For further validation of the model, the performance of the proposed model has been compared with previous reported which confirms a better performance of the proposed model. Finally, the model was applied to monitor the performance of the solar hydrogen production system and the model identify the variables which have negative effects on the performance of the system.

A robust multiobjective solution approach for mean-variance optimisation of correlated multiple quality characteristics

PurposeThe primary objective of this study is to propose a robust multiobjective solution search approach for a mean-variance multiple correlated quality characteristics optimisation problem, so-called “multiple response optimisation (MRO) problem”. The solution approach needs to consider response surface (RS) model parameter uncertainties, response uncertainties, process setting sensitivity and response correlation strength to derive the robust solutions iteratively.Design/methodology/approachThis study adopts a new multiobjective solution search approach to determine robust solutions for a typical mean-variance MRO formulation. A fine-tuned, non-dominated sorting genetic algorithm-II (NSGA-II) is used to derive efficient multiobjective solutions for varied mean-variance MRO problems. The iterative search considers RS model uncertainties, process setting uncertainties and response correlation structure to derive efficient fronts. The final solutions are ranked based on two different multi-criteria decision-making (MCDM) techniques.FindingsFive different mean-variance MRO cases are selected from the literature to verify the efficacy of the proposed solution approach. Results derived from the proposed solution approach are compared and contrasted with the best solution(s) derived from other approaches suggested in the literature. Comparative results indicate significant superiorities of the top-ranked predicted robust solutions in nondominated frequency, closeness-to-target and response variabilities.Research limitations/implicationsThe solution approach depends on RS modelling and considers continuous search space.Practical implicationsIn this study, promising robust solutions are expected to be more suitable for implementation than point estimate-based MOO solutions for a real-life MRO problem.Originality/valueNo evidence of earlier research demonstrates the superiority of a MOO-based iterative solution search approach for mean-variance MRO problems by simultaneously considering model uncertainties, response correlation and process setting sensitivity.

A New Robust Multivariate EWMA Dispersion Control Chart for Individual Observations

A multivariate control chart is proposed to detect changes in the process dispersion of multiple correlated quality characteristics. We focus on individual observations, where we monitor the data vector-by-vector rather than in (rational) subgroups. The proposed control chart is developed by applying the logarithm to the diagonal elements of the estimated covariance matrix. Then, this vector is incorporated in an exponentially weighted moving average (EWMA) statistic. This design makes the chart robust to non-normality in the underlying data. We compare the performance of the proposed control chart with popular alternatives. The simulation studies show that the proposed control chart outperforms the existing procedures when there is an overall decrease in the covariance matrix. In addition, the proposed chart is the most robust to changes in the data distribution, where we focus on small deviations which are difficult to detect. Finally, the compared control charts are applied to two case studies.

On the multivariate progressive control chart for effective monitoring of covariance matrix

AbstractWith the development of modern acquisition techniques, data with several correlated quality characteristics are increasingly accessible. Thus, multivariate control charts can be employed to detect changes in the process. This study proposes two multivariate control charts for monitoring process variability (MPVC) using a progressive approach. First, when the process parameters are known, the performance of the MPVC charts is compared with some multivariate dispersion schemes. The results showed that the proposed MPVC charts outperform their counterparts irrespective of the shifts in the process dispersion. The effects of the Phase I estimated covariance matrix on the efficiency of the MPVC charts were also evaluated. The performances of the proposed methods and their counterparts are evaluated by calculating some useful run length properties. An application of the proposed chart is also considered for the monitoring of a carbon fiber tubing process.

Statistical monitoring of the covariance matrix in multivariate processes: A literature review

Monitoring several correlated quality characteristics of a process is common in modern manufacturing and service industries. Although a lot of attention has been paid to monitoring the multivariate process mean, not many control charts are available for monitoring the covariance matrix. This paper presents a comprehensive overview of the literature on control charts for monitoring the covariance matrix in a multivariate statistical process monitoring (MSPM) framework. It classifies the research that has previously appeared in the literature. We highlight the challenging areas for research and provide some directions for future research.

A Kullback‐Leibler information control chart for linear profiles monitoring

AbstractProfile monitoring is referred to as monitoring the functional relationship between the response and explanatory variables. Traditionally, process control charts monitor the mean and/or the variance of a univariate quality characteristic. For several correlated quality characteristics, multivariate process control charts monitor the mean vector and/or the covariance matrix. However, monitoring the functional relationship between variables is sometimes more beneficial. One example is the power output of a Diesel engine and the amount of fuel injected should be related. In this paper, we propose a Kullback‐Leibler information (KLI) control chart for linear profiles monitoring in Phase II. The plotted statistics of the KLI chart are calculated based on a backward procedure. The functional relationship is described by linear regression. The performance of the proposed KLI control chart is compared with those of other existing control charts, especially the Generalized Likelihood Ratio (GLR) chart for both KLI and GLR charts do not require design parameters. The results show that (1) the KLI control chart is better than the GLR control chart in detecting the shift of variance in terms of Average Time to Signal, and (2) if the shift of the regression coefficient is small, the GLR chart outperforms the KLI chart, but if the size of shift is large, the KLI chart outperforms the GLR chart. The plotted statistics of KLI are compared to that of GLR. Their similarity is discussed.

A review of dispersion control charts for multivariate individual observations

A multivariate control chart is designed to monitor process parameters of multiple correlated quality characteristics. Often data on multivariate processes are collected as individual observations, i.e., as vectors one at a time. Various control charts have been proposed in the literature to monitor the covariance matrix of a process when individual observations are collected. In this study, we review the literature on control charts based on individual observations from multivariate continuous processes, where we find 30 relevant articles from the period 1987–2019. We group the articles into five categories. We observe that less research has been done on CUSUM, high-dimensional and non-parametric type control charts for monitoring the process covariance matrix. We describe each proposed method, state their advantages, and limitations. Finally, we give suggestions for future research.

Should observations be grouped for effective monitoring of multivariate process variability?

AbstractA multivariate dispersion control chart monitors changes in the process variability of multiple correlated quality characteristics. In this article, we investigate and compare the performance of charts designed to monitor variability on the basis of individual and grouped multivariate observations. We compare one of the most well‐known methods for monitoring individual observations—a multivariate exponentially weighted mean squared deviation (MEWMS) chart—with various charts based on grouped observations. In addition, we compare charts based on monitoring with overlapping and nonoverlapping subgroups. We recommend using charts based on overlapping subgroups when monitoring with subgroup data. The effect of subgroup size is also investigated. Steady‐state average time to signal is used as the performance measure. We show that monitoring methods based on individual observations are the quickest in detecting sustained shifts in the process variability. We use a simulation study to obtain our results and illustrated these with a case study.

Joint optimisation of double warning T2-Hotelling chart and maintenance policy with multiple assignable causes

ABSTRACTStatistical process monitoring (SPM) and maintenance management as two key tools for process management can create profound economic benefits, particularly when they are coordinated. This paper demonstrates the value of integrating SPM and maintenance by presenting a multi-objective model consisting of both economic and statistical criteria. Furthermore, to more adapt to complex manufacturing systems, the proposed model consists of two features: (1) monitoring several correlated quality characteristics by designing a double warning lines ‘T2-Hotelling’ chart; and (2) considering the probability of occurrence for more than one assignable cause (AC). To show the effectiveness of the proposed integrated model, two comparative studies are conducted. The first one confirms that the integration of SPM and maintenance policy leads to more effective performance in both economic and statistical viewpoints. The latter results demonstrate that the proposed model outperforms the corresponding single objective models.

Robust multivariate control charts based on Birnbaum–Saunders distributions

ABSTRACTMultivariate control charts are powerful and simple visual tools for monitoring the quality of a process. This multivariate monitoring is carried out by considering simultaneously several correlated quality characteristics and by determining whether these characteristics are in control or out of control. In this paper, we propose a robust methodology using multivariate quality control charts for subgroups based on generalized Birnbaum–Saunders distributions and an adapted Hotelling statistic. This methodology is constructed for Phases I and II of control charts. We estimate the corresponding parameters with the maximum likelihood method and use parametric bootstrapping to obtain the distribution of the adapted Hotelling statistic. In addition, we consider the Mahalanobis distance to detect multivariate outliers and use it to assess the adequacy of the distributional assumption. A Monte Carlo simulation study is conducted to evaluate the proposed methodology and to compare it with a standard methodology. This study reports the good performance of our methodology. An illustration with real-world air quality data of Santiago, Chile, is provided. This illustration shows that the methodology is useful for alerting early episodes of extreme air pollution, thus preventing adverse effects on human health.

An integration of NSGA-II and DEA for economic–statistical design of T2-Hotelling control chart with double warning lines

Control charts are the most applicable tools for monitoring the quality of processes. The day-to-day changes in industrial processes and customers’ expectations motivate the process engineers to monitor multiple correlated quality characteristics, simultaneously. Hence, in this paper, the design of a “double warning lines T2-Hotelling” control chart is studied because of the advantages of this multivariate control chart in detecting moderate and small shifts in a process. In this regard, this research aims to optimize a multi-objective economic–statistical design model that considers monitoring costs and statistical features of control chart, concurrently. The non-dominated sorting genetic algorithm II is utilized to obtain a suitable Pareto set for the model. Since it is difficult for the decision makers to select the most efficient solution among the Pareto set, three different methods of data envelopment analysis consisting of Charnes–Cooper–Rhodes model, cross-efficiency technique and aggressive formulation are used to rank the members of Pareto set and to select the most efficient one. Also, in this research the performance of these three methods in discriminating between the efficient solutions is compared to each other. Eventually, a comparative study is conducted to show the better performance of the suggested model in comparison with the corresponding economic design model.