Statistical Process Control Approach Research Articles

Analytical Explicit Formulas of Average Run Length of Homogenously Weighted Moving Average Control Chart Based on a MAX Process

Statistical process control (SPC) is used for monitoring and detecting anomalies in processes in the areas of manufacturing, environmental studies, economics, and healthcare, among others. Herein, we introduce an innovative SPC approach via mathematical modeling and report on its application via simulation studies to examine its suitability for monitoring processes involving correlated data running on advanced control charts. Specifically, an approach for detecting small to moderate shifts in the mean of a process running on a homogenously weighted moving average (HWMA) control chart, which is symmetric about the center line with upper and lower control limits, is of particular interest. A mathematical model for the average run length (ARL) of a moving average process with exogenous variables (MAX) focused only on the zero-state performance of the HWMA control chart is derived based on explicit formulas. The performance of our approach was investigated in terms of the ARL, the standard deviation of the run length (SDRL), and the median run length (MRL). Numerical examples are given to illustrate the efficacy of the proposed method. A detailed comparative analysis of our method for processes on HWMA and cumulative sum (CUSUM) control charts was conducted for process mean shifts in many situations. For several values of the design parameters, the performances of these two control charts are also compared in terms of the expected ARL (EARL), expected SDRL (ESDRL), and expected MRL (EMRL). It was found that the performance of the HWMA control chart was superior to that of the CUSUM control chart for several process mean shift sizes. Finally, the applicability of our method on a HWMA control chart is provided based on a real-world economic process.

An Integrated Real-time Monitoring and Statistical Process Control Approach for Coating Process and Product Quality via In-line Optical Coherence Tomography

An Integrated Real-time Monitoring and Statistical Process Control Approach for Coating Process and Product Quality via In-line Optical Coherence Tomography

Real-time detection of mean and variance changes in experience sampling data: A comparison of existing and novel statistical process control approaches.

Retrospective analyses of experience sampling (ESM) data have shown that changes in mean and variance levels may serve as early warning signs of an imminent depression. Detecting such early warning signs prospectively would pave the way for timely intervention and prevention. The exponentially weighted moving average (EWMA) procedure seems a promising method to scan ESM data for the presence of mean changes in real-time. Based on simulation and empirical studies, computing and monitoring day averages using EWMA works particularly well. We therefore expand this idea to the detection of variance changes and propose to use EWMA to prospectively scan for mean changes in day variability statistics (i.e., , , ln( )). When both mean and variance changes are of interest, the multivariate extension of EWMA (MEWMA) can be applied to both the day averages and a day statistic of variability. We evaluate these novel approaches to detecting variance changes by comparing them to EWMA-type procedures that have been specifically developed to detect a combination of mean and variance changes in the raw data: EWMA- , EWMA-ln( ), and EWMA- - . We ran a simulation study to examine the performance of the two approaches in detecting mean, variance, or both types of changes. The results indicate that monitoring day statistics using (M)EWMA works well and outperforms EWMA- and EWMA-ln( ); the performance difference with EWMA- - is smaller but notable. Based on the results, we provide recommendations on which statistic of variability to monitor based on the type of change (i.e., variance increase or decrease) one expects.

The usage of Statistical Process Control (SPC) in Industry 4.0 conditions

Purpose: The purpose of this publication is to present the usage of Statistical Process Control (SPC) approach in Industry 4.0 conditions. Design/methodology/approach: Critical literature analysis. Analysis of international literature from main databases and polish literature and legal acts connecting with researched topic. Findings: The integration of Statistical Process Control (SPC) with Industry 4.0 signifies a transformative shift in quality management, elevating SPC from a conventional monitoring tool to a proactive force in contemporary manufacturing. Originally employed for ensuring consistent quality through process monitoring, SPC's role has been redefined in the Industry 4.0 era, utilizing data analytics, real-time monitoring, and connectivity to offer a comprehensive understanding of the manufacturing ecosystem. Enabled by the Internet of Things (IoT), SPC gains real-time insights into production processes, crucial for swift anomaly identification and issue resolution. Advanced analytics and artificial intelligence enhance SPC's predictive capabilities, enabling proactive measures to maintain product quality. This publication underscores the significance of SPC in Industry 4.0 conditions, emphasizing its roots in statistical principles, systematic process control, and the distinction between common and special cause variations. The integration of SPC with Industry 4.0 and Quality 4.0 leverages technologies for enhanced quality management, emphasizing real-time data monitoring and collaborative, data-driven approaches. While Table 2 outlines specific aspects of SPC integration, highlighting its versatility, Table 3 enumerates the advantages, emphasizing improved visibility and predictive quality management. However, challenges such as data security concerns and technology integration complexity, outlined in Table 4, necessitate strategic solutions. In conclusion, this integration represents a pivotal advancement, positioning SPC as an indispensable asset for organizations seeking quality excellence, operational efficiency, and resilience in the dynamic landscape of modern manufacturing. Originality/Value: Detailed analysis of all subjects related to the problems connected with the usage of Statistical process Control in Industry 4.0 conditions. Keywords: Industry 4.0; Quality 4.0, quality management; quality methods, SPC, Statistical Process Control. Category of the paper: literature review.

Multisource and temporal variability in Portuguese hospital administrative datasets: Data quality implications

BackgroundUnexpected variability across healthcare datasets may indicate data quality issues and thereby affect the credibility of these data for reutilization. No gold-standard reference dataset or methods for variability assessment are usually available for these datasets. In this study, we aim to describe the process of discovering data quality implications by applying a set of methods for assessing variability between sources and over time in a large hospital database. MethodsWe described and applied a set of multisource and temporal variability assessment methods in a large Portuguese hospitalization database, in which variation in condition-specific hospitalization ratios derived from clinically coded data were assessed between hospitals (sources) and over time. We identified condition-specific admissions using the Clinical Classification Software (CCS), developed by the Agency of Health Care Research and Quality. A Statistical Process Control (SPC) approach based on funnel plots of condition-specific standardized hospitalization ratios (SHR) was used to assess multisource variability, whereas temporal heat maps and Information-Geometric Temporal (IGT) plots were used to assess temporal variability by displaying temporal abrupt changes in data distributions. Results were presented for the 15 most common inpatient conditions (CCS) in Portugal. Main findingsFunnel plot assessment allowed the detection of several outlying hospitals whose SHRs were much lower or higher than expected. Adjusting SHR for hospital characteristics, beyond age and sex, considerably affected the degree of multisource variability for most diseases. Overall, probability distributions changed over time for most diseases, although heterogeneously. Abrupt temporal changes in data distributions for acute myocardial infarction and congestive heart failure coincided with the periods comprising the transition to the International Classification of Diseases, 10th revision, Clinical Modification, whereas changes in the Diagnosis-Related Groups software seem to have driven changes in data distributions for both acute myocardial infarction and liveborn admissions. The analysis of heat maps also allowed the detection of several discontinuities at hospital level over time, in some cases also coinciding with the aforementioned factors. ConclusionsThis paper described the successful application of a set of reproducible, generalizable and systematic methods for variability assessment, including visualization tools that can be useful for detecting abnormal patterns in healthcare data, also addressing some limitations of common approaches. The presented method for multisource variability assessment is based on SPC, which is an advantage considering the lack of gold standard for such process. Properly controlling for hospital characteristics and differences in case-mix for estimating SHR is critical for isolating data quality-related variability among data sources. The use of IGT plots provides an advantage over common methods for temporal variability assessment due its suitability for multitype and multimodal data, which are common characteristics of healthcare data. The novelty of this work is the use of a set of methods to discover new data quality insights in healthcare data.

A practical application of statistical process control to evaluate the performance rate of academic programmes: implications and suggestions

PurposeThis study aims to properly and objectively assess the students’ study progress in bachelor programmes by applying statistical process control (SPC). Specifically, the authors focused their analysis on the variation in performance rates in business studies courses taught at a Spanish University.Design/methodology/approachA qualitative methodology was used, using an action-based case study developed in a public university. Previous research and theoretical issues related to quality indicators of the training programmes were discussed, followed by the application of SPC to assess these outputs.FindingsThe evaluation of the performance rate of the courses that comprised the training programs through the SPC revealed significant differences with respect to the evaluations obtained through traditional evaluation procedures. Similarly, the results show differences in the control parameters (central line and control interval), depending on the adopted approach (by programmes, by academic year and by department).Research limitations/implicationsThis study has inherent limitations linked to both the methodology and selection of data sources.Practical implicationsThe SPC approach provides a framework to properly and objectively assess the quality indicators involved in quality assurance processes in higher education.Originality/valueThis paper contributes to the discourse on the importance of a robust and effective assessment of quality indicators of the academic curriculum in the higher education context through the application of quality control tools such as SPC.

Prediction Control Charts: A New and Flexible Artificial Intelligence-Based Statistical Process Control Approach

Prediction Control Charts: A New and Flexible Artificial Intelligence-Based Statistical Process Control Approach

Managing Shiga Toxin-Producing E. coli Using Statistical Process Control Charts for Routine Health and Production Monitoring in Pig Farming.

Oedema disease (ED) caused by Shiga-toxin-producing E. coli in pigs is a serious life-threatening disease, particularly among weaned piglets. When a preventive protocol is adopted in a specific farm, interpretation of effectiveness is often complicated in field conditions due to natural or “common cause” variation. For this reason, in this study a Statistical process control (SPC) approach was used to retrospectively evaluate the application of an ED preventive protocol (lower protein diet, ad-libitum fiber, vaccination at 5 days of age) in an infected commercial piglets' weaning site. The analysis was established over a 9-years period (n = 75 consecutive batches; 1,800 weaners per batch) using mortality for each batch as the key parameter of health and production; the statistics and the control limits (mean ± 3-fold sd; UCL, upper control limit; LCL, lower control limit) were based on data from the first 28 batches (Period 1) before the onset of the first ED clinical signs. The charts allowed the detection of defined out of control batches (i.e., with mortality out of the intervention limits) from batch 29 ongoing, exploring a Period 2 (unstable production and ED clinical signs; 36 batches) and a Period 3 (application of the ED preventive protocol; 11 batches). Mortality evaluation using SPC revealed a production system defined under-control (mean moving range bar = 1,34%; UCL = 4,37%; LCL = 0%) during Period 1. During Period 2, charts lost the state of statistical control, as showed by several signals of special cause variation due to the ED outbreak. Period 3 was characterized again by a state of statistical control, where no signals of special cause variation was showed. In conclusion, the retrospective application of SPC charts in the present study was able to confirm the efficacy of an ED preventive protocol in reducing mortality in a piglets' weaning site. SPC charting is suggested as an useful tool to provide insights into relationships between health, managerial, and welfare decision and some selected iceberg parameters in livestock.

Deep learning for multivariate statistical in-process control in discrete manufacturing: A case study in a sheet metal forming process

Detecting abnormal conditions in manufacturing processes is a crucial task to avoid unplanned downtimes and prevent quality issues. The increasing amount of available high-frequency process data combined with advances in the field of deep autoencoder-based monitoring offers huge potential in enhancing the performance of existing Multivariate Statistical Process Control approaches. We investigate the application of deep auto encoder-based monitoring approaches and experiment with the reconstruction error and the latent representation of the input data to compute Hotelling’s T2 and Squared Prediction Error monitoring statistics. The investigated approaches are validated using a real-world sheet metal forming process and show promising results.

A registration-free approach for statistical process control of 3D scanned objects via FEM

Recent work in on-line Statistical Process Control (SPC) of manufactured 3-dimensional (3-D) objects has been proposed based on the estimation of the spectrum of the Laplace-Beltrami (LB) operator, a differential operator that encodes the geometrical features of a manifold and is widely used in Machine Learning (i.e., Manifold Learning). The resulting spectra are an intrinsic geometrical feature of each part, and thus can be compared between parts to assess the state of the manufacturing process while avoiding part to part registration (or “part localization”) pre-processing or the need for equal size meshes, characteristics which are required in previous approaches for SPC of 3D parts. The recent spectral SPC methods, however, are limited to monitoring surface data from objects such that the scanned meshes have no boundaries, holes or missing portions. In this paper we extend spectral methods by first considering a more accurate and general estimator of the LB spectrum that is obtained by application of Finite Element Methods (FEM) to the solution of Helmholtz's equation with boundaries. It is shown how the new spectral FEM approach, while it retains the advantages of not requiring part localization/registration or equal size datasets scanned from each part, it provides more accurate spectrum estimates, which results in faster detection of out of control conditions than earlier methods, can be applied to both mesh or volumetric (solid) scans, and furthermore, it is shown how it can be applied to partial scans that result in open meshes (surface or volumetric) with boundaries, increasing the practical applicability of the methods. The present work brings SPC methods closer to contemporary research in Computer Graphics and Manifold Learning. MATLAB code that reproduces the examples of this paper is provided in the supplementary materials.

Statistical Process Control Charts for Monitoring Next-Generation Sequencing and Bioinformatics Turnaround in Precision Medicine Initiatives

PurposePrecision oncology, such as next generation sequencing (NGS) molecular analysis and bioinformatics are used to guide targeted therapies. The laboratory turnaround time (TAT) is a key performance indicator of laboratory performance. This study aims to formally apply statistical process control (SPC) methods such as CUSUM and EWMA to a precision medicine programme to analyze the learning curves of NGS and bioinformatics processes.Patients and MethodsTrends in NGS and bioinformatics TAT were analyzed using simple regression models with TAT as the dependent variable and chronologically-ordered case number as the independent variable. The M-estimator “robust” regression and negative binomial regression were chosen to serve as sensitivity analyses to each other. Next, two popular statistical process control (SPC) approaches which are CUSUM and EWMA were utilized and the CUSUM log-likelihood ratio (LLR) charts were also generated. All statistical analyses were done in Stata version 16.0 (StataCorp), and nominal P < 0.05 was considered to be statistically significant.ResultsA total of 365 patients underwent successful molecular profiling. Both the robust linear model and negative binomial model showed statistically significant reductions in TAT with accumulating experience. The EWMA and CUSUM charts of overall TAT largely corresponded except that the EWMA chart consistently decreased while the CUSUM analyses indicated improvement only after a nadir at the 82nd case. CUSUM analysis found that the bioinformatics team took a lower number of cases (54 cases) to overcome the learning curve compared to the NGS team (85 cases).ConclusionAs NGS and bioinformatics lead precision oncology into the forefront of cancer management, characterizing the TAT of NGS and bioinformatics processes improves the timeliness of data output by potentially spotlighting problems early for rectification, thereby improving care delivery.

Water Particles Monitoring in the Atacama Desert: SPC Approach Based on Proportional Data

Statistical monitoring tools are well established in the literature, creating organizational cultures such as Six Sigma or Total Quality Management. Nevertheless, most of this literature is based on the normality assumption, e.g., based on the law of large numbers, and brings limitations towards truncated processes as open questions in this field. This work was motivated by the register of elements related to the water particles monitoring (relative humidity), an important source of moisture for the Copiapó watershed, and the Atacama region of Chile (the Atacama Desert), and presenting high asymmetry for rates and proportions data. This paper proposes a new control chart for interval data about rates and proportions (symbolic interval data) when they are not results of a Bernoulli process. The unit-Lindley distribution has many interesting properties, such as having only one parameter, from which we develop the unit-Lindley chart for both classical and symbolic data. The performance of the proposed control chart is analyzed using the average run length (ARL), median run length (MRL), and standard deviation of the run length (SDRL) metrics calculated through an extensive Monte Carlo simulation study. Results from the real data applications reveal the tool’s potential to be adopted to estimate the control limits in a Statistical Process Control (SPC) framework.

Transparent Sequential Learning for Statistical Process Control of Serially Correlated Data

Machine learning methods have been widely used in different applications, including process control and monitoring. For handling statistical process control (SPC) problems, conventional supervised machine learning methods (e.g., artificial neural networks and support vector machines) would have some difficulties. For instance, a training dataset containing both in-control and out-of-control (OC) process observations is required by a supervised machine learning method, but it is rarely available in SPC applications. Furthermore, many machine learning methods work like black boxes. It is often difficult to interpret their learning mechanisms and the resulting decision rules in the context of an application. In the SPC literature, there have been some existing discussions on how to handle the lack of OC observations in the training data, using the one-class classification, artificial contrast, real-time contrast, and some other novel ideas. However, these approaches have their own limitations to handle SPC problems. In this article, we extend the self-starting process monitoring idea that has been employed widely in modern SPC research to a general learning framework for monitoring processes with serially correlated data. Under the new framework, process characteristics to learn are well specified in advance, and process learning is sequential in the sense that the learned process characteristics keep being updated during process monitoring. The learned process characteristics are then incorporated into a control chart for detecting process distributional shift based on all available data by the current observation time. Numerical studies show that process monitoring based on the new learning framework is more reliable and effective than some representative existing machine learning SPC approaches.

Truncated normal distribution-based EWMA control chart for monitoring the process mean in the presence of outliers

In many applications, it is very important to detect outliers during the analysis of normal data. Many existing methods preprocess the data to remove the outliers and then analyse the data accordingly when the data are contaminated by different unexpected outliers; however, it is difficult to use this method for applications where the data must be analysed online. In this article, we present an online monitoring approach for statistical process control (SPC) that is robust with respect to the presence of outliers. The Monte Carlo simulation results show that the proposed control chart is quite robust under the standard normally distributed data and, moreover, the control limit is not be affected by the number and sizes of the outliers. Furthermore, a real data example from a foetal heart rate (FHR) process is used to illustrate an application of our proposed procedure.

An Experimental Evaluation of a Teaching Approach for Statistical Process Control in Computer Courses

In organizations that are seeking a high degree of maturity, it is necessary to achieve a statistical control of software processes and to know their behavior and operational performance. The approach adopted for the research involves reading articles and experience performance reports, practical cases, discussion, the use of games and simulators, practical projects, and reflection by students on the knowledge learned and activities carried out. The evaluation was conducted with undergraduates enrolled in a Computer Science Bachelor's degree programme, who were divided into a control group and an experimental group. At the end, the two groups carried out a practical project to evaluate the learning effectiveness reached by the students. The results of the study suggest that there was a difference in the effectiveness of the learning resulting from the teaching approach and traditional instruction. The authors observed a mean gain of 30.06% in the experimental group, which is evidence of this rise in the learning effectiveness.

An Intrinsic Geometrical Approach for Statistical Process Control of Surface and Manifold Data

We present a new method for statistical process control (SPC) of a discrete part manufacturing system based on intrinsic geometrical properties of the parts, estimated from three-dimensional sensor data. An intrinsic method has the computational advantage of avoiding the difficult part registration problem, necessary in previous SPC approaches of three-dimensional geometrical data, but inadequate if noncontact sensors are used. The approach estimates the spectrum of the Laplace–Beltrami (LB) operator of the scanned parts and uses a multivariate nonparametric control chart for online process control. Our proposal brings SPC closer to computer vision and computer graphics methods aimed to detect large differences in shape (but not in size). However, the SPC problem differs in that small changes in either shape or size of the parts need to be detected, keeping a controllable false alarm rate and without completely filtering noise. An online or “Phase II” method and a scheme for starting up in the absence of prior data (“Phase I”) are presented. Comparison with earlier approaches that require registration shows the LB spectrum method to be more sensitive to rapidly detect small changes in shape and size, including the practical case when the sequence of part datasets is in the form of large, unequal size meshes. A post-alarm diagnostic method to investigate the location of defects on the surface of a part is also presented. While we focus in this article on surface (triangulation) data, the methods can also be applied to point cloud and voxel metrology data.

Case studies on the use of central statistical monitoring and interventions to optimize data quality in clinical trials

Purpose: QDSS is an analytics-driven centralized monitoring system that uses a Statistical Process Control (SPC) approach with added clinical surveillance. The objective of this study was to review recent cases that arose in the course of Central Statistical Monitoring and intervention to illustrate the nature of the data quality issues that can be observed and corrected using this approach. Methods: SPC charts were generated with upper and lower limits based on the distribution of the data, which is updated as the study progresses. Red signals indicate an “out of control” data point and green signals represent data points that are within the control limits. Cases with red signals that illustrate the full lifecycle of QDSS were chosen to examine the process of signal detection, root cause analysis, intervention, and follow-up. Results: Three cases with “out of control” data points were selected. Data was visualized using SPC charts such as an X-bar control chart. The out of control data points signaled a root-cause analysis to begin. Further examination into related data discrepancies, discussions with study staff, and review of study protocols resulted in the identification of the root cause of the poor data quality, for example, a lack of training for new study staff that entered part way through the study. Based on the root cause, interventions were suggested to the study staff, such as retraining new staff members. After the implementation of the intervention, the data was re-examined to confirm the resolution of the “out of control” data points. Conclusions: Centralized statistical monitoring is an important tool in clinical trials to detect data outliers and anomalies that may have an effect on study outcomes. In all three cases studies were threatened by a data quality risk in their primary or secondary endpoints that were easily corrected. These case studies illustrate the power of QDSS to effectively identify and resolve data aberrancies to increase assay sensitivity.

Bulanık İstatistiksel Proses Kontrol Tekniği İle 19x39x19 cm Bims Hafif Yapı Malzemesi Üretiminin Analizi

Statistical Process Control (SPC) is the most important a math-based tool used by engineers to control non-standard production and to ensure that production outputs are performed at specified quality ranges. However, in cases where conventional SPC is inadequate, fuzzy statistical process control approaches have been developed which enable more precise statistical process control using fuzzy set theory. In this study, fuzzy statistical process control techniques have been used to determine whether a 19x39x19 cm pumice brick, which is a product of a pumice brick factory, with fuzzy observation values is under control of the production process.

Gauge capability studies for high-density data: SPC Phase 0

In manufacturing, advanced measurement systems (e.g., 3D laser scanners) are continually being incorporated into modern quality control (QC) systems to provide high-density (HD) data. A significant amount of research efforts has been placed in the development of QC tools, such as Phase I and II statistical process control (SPC) approaches using HD data. However, the effectiveness of SPC tools highly depends on measurement system adequacy. The study of the quality and adequacy of a measurement system, known as measurement capability or Phase 0 in SPC applications, is a prerequisite to implementing any SPC tool; which has mostly been neglected for HD data. This paper proposes a holistic Gauge study approach for HD data obtained from 3D laser scanners (e.g. point clouds) by using spatial statistics data models. The main objectives of this work are two-fold: 1) Study how to analyse the repeatability and reproducibility of a point cloud and 2) Quantify the uncertainty associated with a point cloud under different factors involved in acquiring point clouds from 3D laser scanners.

Spatial Monitoring of Wafer Map Defect Data Based on 2D Wavelet Spectrum Analysis

Since machine vision systems (MVS) lead to a wide usage of monitoring systems for industrial applications, the research on the statistical process control (SPC) of image data has been promoted as an automated method for early detection and prevention of unusual conditions in manufacturing processes. In this paper, we propose a non-parametric SPC approach based on the 2D wavelet spectrum (WS-SPC) to extract the feature that contains the spatial and directional information of each subspace in an image. Using the 2D discrete wavelet transform and spectrum analysis, the representative statistic, the Hurst index, is calculated, and a single matrix space that consists of estimated statistics is reconstructed into a spatial control area for SPC. When a control limit is determined by the density of statistics, real-time monitoring based on WS-SPC is available for time releasing images. In the application, an analysis of wafer bin maps (WBMs) is conducted at a semiconductor company in Korea in order to evaluate the performance of the suggested approach. The results show that the proposed method is effective in terms of its fast computation speed and spectral monitoring.