A bivariate exponentially weighted moving average control chart based on exceedance statistics

The magnificent seven statistical process control (SPC) tools are commonly used to monitor the variation in the process. Control charts are the most efficient and real‐time monitoring tool from the SPC toolkit. A control chart visually differentiates the effect of special or inherent cause variations and indicates the process as out‐of‐control when such a special cause exists. For single occasion problems, simple random sampling (SRS) is used as a sampling design. When the quality of a product is assessed at regular intervals, then modified successive sampling (MSS) is chosen as the preferred sampling mechanism. Hence, this paper intends to propose EWMA‐MSS(S) and CUSUM‐MSS(S) charts under MSS schemes to monitor moderate to small shifts in the location parameter of a process. We presented the performance evaluation of EWMA‐MSS(S) and CUSUM‐MSS(S) charts in terms of run length metrics and compared them with the Shewhart‐MSS(S) control chart. The outcomes show that the EWMA‐MSS(S) perform amazingly well as compared to the Shewhart‐MSS(S) and CUSUM‐MSS(S) control charts. Further, illustration of the proposed charts on the QSAR aquatic toxicity dataset is also used to demonstrate the application of the proposed charts.

The monitoring of processes is a vital mechanism for ensuring that such processes remain safe and under control. The present research aims to solve problems associated with correlated data by applying the Box-Jenkins method integrated with statistical process control (SPC) tools, namely the Shewhart chart, the moving average chart, the cumulative sum (CUSUM) chart, and the exponentially weighted moving-average (EWMA) chart. The efficiency of the four SPC tools was also compared in terms of the false alarm rate (FAR) and the missed detection rate (MDR). The findings indicated that the EWMA chart was the most effective in detecting anomaly, the Shewhart chart and the moving average chart produced high MDR, and the CUSUM chart suffered the highest FAR.

A statistical weld process monitoring system is described. Using data collected while welding, the welding statistical process control (SPC) tool provides weld process quality control by implementing techniques of data trending analysis, tolerance analysis, and sequential analysis. The SPC system computes the mean, standard deviation, and range of each of the parameters sampled by the data collection system. Changes in the mean, standard deviation, and range are displayed using control (or trend) charts. The control chart displays a function of a parameter with respect to the ordering of the weld records (for a single weld) or weld number (for multiple welds). The SPC tool also permits plotting tolerance charts of the mean, standard deviation, and range for each of the sampled parameters. The tolerance chart is plotted versus the record number (or weld number) and consists of a vertical line for each record (or weld number) showing the minimum and maximum value of that parameter for that record (or weld number). The upper control limit (UCL), lower control limit (LCL), and nominal value may also be displayed on the tolerance chart printout. The SPC also performs sequential analysis, which allows the user to examine the process as it goes along, which in turn may permit the user to locate a possible change in the process before it goes out of control. Work directed toward developing an expert interpreter of the voluminous statistical output generated by the SPC is also described.

The multivariate exponentially weighted moving average (MEWMA) control chart, in which the smoothing parameter is a principal diagonal matrix, is established based on the assumption that the samples follow the standard normal distribution to monitor the multivariate quality characteristics. However, monitoring quality characteristics always exists in the whole process. To make the MEWMA control chart more effective, a modified multivariate exponentially weighted moving average control chart, namely practical MEWMA (PEWMA) control chart, is proposed, in which the smoothing coefficient matrix is extended to a full-rank matrix which the smoothing parameter are all not zero. Analysis of both the in-control and out-of-control statistical performance of PEWMA control chart illustrate that the average run length of PEMWA control chart is more superior to the MEWMA. Finally combined with a factory example, a minimisation cost model is constructed based on the Lorenzen-Vance economic model to optimise the parameter combination.

Nonparametric control charts are among the most important tools of statistical process control. Such charts are useful when there is a lack of knowledge about an underlying distribution or its parameters. Most existing nonparametric control charts are used for monitoring location parameters: they may perform poorly when the scale parameters change arbitrarily over time. In this paper, we propose a new nonparametric control chart based on a powerful likelihood ratio test and the exponential weighted moving-average (EWMA) control chart. Its nonparametric property is applied via a consistent series density estimator in the exponential family. The proposed control chart does not require historical reference samples and can be monitored by fixed control limits. The Monte Carlo simulation results show that the proposed control chart performs well in monitoring both mean and variance shifts, especially in monitoring variance or large mean shifts. Furthermore, a real-data example is given to illustrate the effectiveness of the proposed method.

A control chart is a tool for statistical process control (SPC) used to determine variations in manufacturing processes resulting from common or assignable causes. The presence of unnatural patterns in control charts is an indication that the process has been influenced by assignable causes, and corrective actions must be taken. However, the assumption of uncorrelated or independent observations is not suitable for all of the characteristics pertaining to a product. This study presents a method with which to improve the accuracy of pattern recognition in control charts, through the autocorrelation of product characteristics. Particularly, we developed an artificial algorithm-based machine learning model to recognize unnatural patterns and processes in AR(1) simultaneously. The proposed method integrates an artificial immune system and support vector machine within a recognition system. This study evaluated the accuracy with which four patterns could be recognized. The four patterns include trends, sudden shifts, cyclic patterns, and normal patterns. Identifying unnatural patterns can greatly narrow the range of possible causes that must be investigated, thereby speeding up the diagnostic processes. Key words: Pattern recognition, artificial immune algorithm, support vector machine, autocorrelation.

The implementation of Statistical Quality Control (SQC) has been tracked in various areas, such as agriculture, environment, industry, and health services. The employment of SQC methodologies is frequently employed for monitoring and identification of process irregularities across various fields. This research proposes and implements a novel SQC methodology in agricultural areas. A control chart is one of the SQC tools that facilitates real-time monitoring of multiple activities, including agricultural yield, industrial yield, and hospital outcomes. Advanced control charts with symmetrical data are being subjected to the new SQC method, which is suitable for this purpose. This research aims to develop a novel hybrid exponentially weighted moving average control chart for detecting the coefficient of variation (CV) using a repetitive sampling method called the HEWMARS-CV control chart. It is an effective tool for monitoring the mean and variance of a process simultaneously. The HEWMARS-CV control chart used the repetitive sampling scheme to generate two pairs of control limits to enhance the performance of the control chart. The proposed control chart is compared with the classical HEWMA and Shewhart control charts regarding the average run length (ARL) when the data has a normal distribution. The Monte Carlo simulation method is utilized to approximate the ARL values of the proposed control charts to determine their performance. The proposed control chart detects small shifts in CV values more effectively than the existing control chart. An illustrative application related to monitor the wheat yield at Rothamsted Experimental Station in Great Britain is also incorporated to demonstrate the efficiency of the proposed control chart. The efficiency of the proposed HEWMARS-CV control chart on the real data shows that the proposed control chart can detect a shift in the CV of the process, and it is superior to the existing control chart in terms of the average run length.

According to the Diagnosis Related Groups (DRGs) policy initiated in Taiwan in 2010, hospital payments within a given diagnosis group should be fixed, making it critical for hospitals to monitor growth of medical care costs. This study investigates how to monitor the cost of unusual factors on single vessel percutaneous transluminal coronary angioplasty (PTCA) and attempts to build a surveillance mechanism for DRGs medical care expenses. This investigation sampled objects from the National Health Insurance Database of Taiwan during 2010. This study analyzed variation in fees of single vessel PTCA in selected medical centers, and chose inpatients over 17 years old as objects for study. This study used two nonparametric control charts, Nonparametric Shewhart control chart and Nonparametric Exponentially Weighted Moving Average control chart, contributing further to constructing the mechanism for surveying medical care expenses. The selected medical center underwent construction changes, and medical expenses rose gradually increased following August 2010. The selected medical center thus had good fiscal control of single vessel PTCA surgery, and the medical expenses for most cases were lower than the standardized payment rate of National Health Insurance. This study used a Nonparametric Shewhart control chart to analyze monthly medical costs and identify unusual months. This approach was suitable for monitoring large changes in process. This study also used the Nonparametric Exponentially Weighted Moving Average control chart to estimate the current data and long-term trend data to reduce Nonparametric Shewhart control chart error, because this could not be achieved by analyzing past long-term trends. Nonparametric Exponentially Weighted Moving Average control chart had better detection of small process changes and achieved early awareness of gradual financial losses. This study used two nonparametric control charts to build the surveillance mechanism for DRGs. This study provided effective information to medical providers seeking to maintain health care quality and obtain sufficient profits to enable sustainable development by developing a mechanism for surveying medical care expenses.

ABSTRACTCompared to the grid search approach to optimal design of control charts, the gradient-based approach is more computationally efficient as the gradient information indicates the direction to search the optimal design parameters. However, the optimal parameters of multivariate exponentially weighted moving average (MEWMA) control charts are often obtained by using grid search in the existing literature. Note that the average run length (ARL) performance of the MEWMA chart can be calculated based on a Markov chain model, making it feasible to estimate the ARL gradient from it. Motivated by this, this paper develops an ARL gradient-based approach for the optimal design and sensitivity analysis of MEWMA control charts. It is shown that the proposed method is able to provide a fast, accurate, and easy-to-implement algorithm for the design and analysis of MEWMA charts, as compared to the conventional design approach based on grid search.

Quality control of products and services is essential across various industries and sectors, including manufacturing, engineering, public health, economics, finance, and medicine. It is critical to ensure that product characteristics align with customer requirements while maintaining consistent quality and standards. Control charts are essential tools in Statistical Process Control (SPC), used to detect changes in process means or variability, and play a critical role in monitoring, controlling, and enhancing quality within production processes. This study evaluates the Average Run Length (ARL) of the Double Homogeneously Weighted Moving Average (DHWMA) control chart for Moving Average processes (MA(q)) with exponential white noise, using Numerical Integral Equation (NIE) methods. These methods include Simpson’s Rule, the Midpoint Rule, the Trapezoidal Rule, and the Gauss–Legendre Quadrature. Additionally, the study compares the performance of the DHWMA and HWMA control charts. The results indicate that all four NIE methods yield similar ARL values. However, CPU time analysis shows that the Midpoint Rule generally requires less computation time than the other methods. Furthermore, when evaluating change-point detection effectiveness, the DHWMA control chart consistently outperforms the HWMA chart across all shift sizes, as demonstrated by its lower Expected Average Run Length (EARL).

DAMAGE DETECTION OF THE Z24 BRIDGE USING CONTROL CHARTS

Control charts (CCs) are one of the main tools in Statistical Process Control that have been widely adopted in manufacturing sectors as an effective strategy for malfunction detection throughout the previous decades. Measurement errors (M.E's) are involved in the quality characteristic of interest, which can effect the CC's performance. The authors explored the impact of a linear model with additive covariate M.E on the multivariate cumulative sum (CUSUM) CC for a specific kind of data known as compositional data (CoDa). The average run length is used to assess the performance of the proposed chart. The results indicate that M.E's significantly affects the multivariate CUSUM-CoDa CCs. The authors have used the Markov chain method to study the impact of different involved parameters using six different cases for the variance-covariance matrix (VCM) (i.e., uncorrelated with equal variances, uncorrelated with unequal variances, positively correlated with equal variances, positively correlated with unequal variances, negatively correlated with equal variances and negatively correlated with unequal variances). The authors concluded that the error VCM has a negative impact on the performance of the multivariate CUSUM-CoDa CC, as the increases with an increase in the value of the error VCM. The subgroup size m and powering operator b positively impact the proposed CC, as the decreases with an increase in m or b. The number of variables p also has a negative impact on the performance of the proposed CC, as the values of increase with an increase in p. For the implementation of the proposal, two illustrated examples have been reported for multivariate CUSUM-CoDa CCs in the presence of M.E's. One deals with the manufacturing process of uncoated aspirin tablets, and the other is based on monitoring the machines involved in the muesli manufacturing process.

Nowadays, statistical process control (SPC) is extensively utilized in manufacturing companies. Control charts are the foremost tool in SPC because they can timely detect assignable causes that influence the quality of the production process. Mostly, the control charts are used to monitor the process variability and the process mean. However, when the mean changes but is appraised as in-control and the standard deviation is linear to the mean, the Coefficient of Variation (CV) chart is suitable for evaluating process variability. In this study, we suggest a Generally Weighted Moving Coefficient of Variation (GWMCV) control chart using three-parameter logarithmic transformations which parameter weight for each time (ω) is more flexible than the Exponentially Weighted Moving Coefficient of Variation (EWMCV) control chart that has ω = 1. The Simulation studies show that when parameter weight 0.6≤ω≤0.9,GWMCV chart is more sensitive than EWMCV chart. As a result, the flexible parameter weights increase the diagnosis ability of the control chart. The chart is also applied to monitor the process production of NPK fertilizer. The result shows that proposed chart detect out-of-control signal rapidly than the EWMCV.

Moving towards process-based radiotherapy quality assurance using statistical process control

Purpose: This article aims to present successful practices in the management of training processes based on virtual reality and augmented reality, namely a strategy for evaluating the process with the principle of continuous improvement in mind, and monitoring its performance in terms of productivity and waste levels. It is proposed to apply Statistical Process Control (SPC) tools to develop control charts for monitoring individual events (i-charts).Design/methodology/approach: The methodology is based on a case study developed in an industrial project and is guided by a literature review on Work-Based Learning (WBL) and SPC.Findings: The developed work shows that SPC tools are suitable for supporting decision making in situations where the data to be analyzed is generated by human-computer interactions, e.g., involving students and virtual learning environments.Originality/value: The innovative aspect presented in the article lies in the evaluation of the effectiveness of pedagogical resources arranged in simulation environments based on virtual and augmented reality. The accumulated knowledge about the application of SPC in service areas, and others that demand data analysis, reinforces the hypothesis of the suitability of its application in the case presented. This is an original application of SPC, normally used in business processes quality control, but which in this case is applied in an innovative way to the evaluation of industrial training processes, with the same spirit for which it was designed, i.e. to provide the means to manage the quality of a process.