Parametric Control Charts Research Articles

An image-based nonparametric multivariate EWMA control chart for metal additive manufacturing process monitoring

Additive manufacturing offers considerable promise in terms of manufacturing flexibility, but print quality remains a major obstacle to its widespread adoption. Consequently, timely and accurate detection of process variations or anomalies is critical for implementing corrective actions. Melt pool characteristics are crucial to final product quality, and current state-of-the-art studies on melt pool image flow have primarily focused on in-situ sensing, feature extraction, and their relationship with process settings and material properties. This study aims to develop a statistical process control approach to detect process variations immediately using a predefined distribution of monitoring statistics. Two main challenges are addressed: 1) the unknown distribution of melt pool image features, rendering traditional parametric control charts unreliable and 2) the autocorrelation of melt pool image flow features, violating the traditional control chart assumption of independent and identically distributed monitoring data. To overcome these challenges, we propose a multivariate nonparametric Exponential Weighted Moving Average (EWMA) control chart that can appropriately accommodate stationary serial data correlation to monitor process stability by tracking physical features extracted from the original images. Key features of the proposed control chart include its ability to eliminate serial correlation effects and its distribution-free nature, requiring no prior information about the data distribution. Comparative analysis of simulated and real data demonstrates that the proposed approach outperforms baseline methods in anomaly detection accuracy. An actual case study in laser metal deposition (LMD) further validates the effectiveness of the proposed method.

A nonparametric adaptive EWMA control chart for monitoring multivariate time-between-events-and-amplitude data

Multivariate time-between-events-and-amplitude (TBEA) data, which includes the time interval between two consecutive occurrences of the event as well as their amplitudes, is a common data type in manufacturing and service operations. Designing control charts to monitor TBEA data is of great significance to improve product quality. However, most TBEA control charts are typically constructed under the assumption that the data distribution is known. The monitoring performance of these parametric TBEA control charts may become less reliable when the assumed data distribution is unknown. To address this issue, we propose a nonparametric adaptive TBEA (NATBEA) control chart based on the antirank method and adaptive strategy. Firstly, a nonparametric monitoring statistic is constructed by using the antirank method. With using the adaptive strategy, a nonparametric adaptive EWMA control chart is designed to monitor TBEA data, and the monitoring performance of various shifts is improved. Then, we compare the monitoring performance of the NATBEA control chart and other eight control charts, and the numerical simulation results show that the NATBEA control chart has superior monitoring performance for various mean shifts with different data distributions. Finally, an example of a company’s production failure demonstrates that the developed NATBEA control chart outperforms various conventional control charts by providing rapid alarms when the process is out of control.

A nonparametric adaptive EWMA control chart for monitoring mixed continuous and categorical data using self-starting strategy

In the context of big data-driven smart manufacturing, data is often characterized by high dimensionality, numerous variables, and complex associations. As a result, mixed continuous and categorical data are increasingly common. In the case of data that consist of a combination of continuous and categorical variables with unknown distributions, the application of traditional parametric control charts for monitoring purposes becomes challenging. Therefore, a novel nonparametric adaptive exponentially weighted moving average (EWMA) control chart using a self-starting strategy is proposed in this paper. First, the process of converting continuous data into categorical data is conducted using the data categorization method. The log-linear modeling is subsequently employed to investigate the relationships between various variables. Next, a nonparametric adaptive EWMA statistic is constructed to monitor mixed continuous and categorical data, and the self-starting strategy is employed to gradually expand the size of the in-control (IC) dataset and to update the parameters in real time. Then, a numerical simulation is conducted to compare the IC and out-of-control (OC) performance of the proposed chart with other control charts. According to the simulation result, it can be concluded that the proposed chart offers a more effective means of detecting shifts in the production process. Finally, a concrete illustration of an authentic dataset regarding red wine quality is provided to further clarify the effectiveness of the proposed control chart in monitoring mixed continuous and categorical data.

Control theory for skewed distribution under operation side of the telecommunication industry and hard-bake process in the semiconductor manufacturing process

Statistical process control basically involves inspecting a random sample of the output from a process and deciding whether the process is producing products with characteristics that fall within a predetermined range. It is used extensively in the field of reliability engineering. The reliability of the production process is thoroughly monitored for any internal variation using the SPC. The aim is always to settle such variations through a proper control monitoring. If the underlying distribution of the process is known to the researcher than the use of parametric control charts are useful but in many cases when there is doubt about the distribution of the process then it is preferred to use non parametric control charts. In this paper we propose the modified Exponentially weighted moving average (EWMA), Double Exponentially weighted moving average (DEWMA), Hybrid Exponentially weighted moving average (HEWMA), Extended Exponentially weighted moving average (EEWMA), Modified Exponentially weighted moving average (MEWMA) and mix- type control charts by mixing these control charts with Tukey control chart EWMA-TCC, DEWMA-TCC, HEWMA-TCC, EEWMA-TCC, MEWMA-TCC for the shape parameter of the Kumaraswamy Lehmann-2 Power function distribution (KL2PFD).

Simulation Study for Parametric EWMA and NPWEWPA-SR Control Charts Against Non-Normality Assumptions

Common control chart types such as EWMA require assumptions to have valid information. The study compares IC robustness and OOC performance for parametric EWMA and NPEWMA-SR control charts in violation of symmetrical assumption. The Monte Carlo simulation study held scale parameters with various shape parameters in Weibull distribution. First finding in this paper was both parametric EWMA and NPEWMA-SR control charts were not suitable for the application in asymmetrical distribution due to weak IC robustness and frequent false alarm will be occurred. Although EWMA-X ̅ The control chart showed a most stable OOC performance; the weak IC robustness made the control chart unacceptable. Whereas, NPEWMA-SR control chart lost the ability in small shift detection when symmetrical assumption violated. Moreover, two different weightage of current sample for both parametric EWMA and NPEWMA-SR control charts were also investigated. The results showed that weightage of current sample for both parametric EWMA and NPEWMA-SR control charts did not affect the ARL value trend in different skewness of Weibull distribution.

A nonparametric control chart for monitoring count data mean

AbstractCount data monitoring has important applications in many fields. However, most of the existing control charts for monitoring count data are parametric. Parametric control charts can be problematic when the underlying parametric distributional assumption does not hold for the particular application. On the other hand, nonparametric control charts do not require such distributional assumptions, and are more desirable in real‐world situations where the underlying distribution cannot be easily described using a parametric distribution. In this paper, we extend the nonparametric control chart for continuous data monitoring proposed by Li to count data monitoring. To guarantee a desired in‐control performance, we further adopt the bootstrap procedure proposed by Gandy and Kvaløy to help determine the control limit of our proposed control chart. Our simulation studies and real data analysis show that the proposed control chart performs well across a variety of settings, and compares favorably with other existing nonparametric control charts for count data.

Statistical parametric and non-parametric control charts for monitoring residential water consumption

The adoption of strategies for monitoring water consumption is essential for water resources management, contributing to the promotion of the sustainability in the water sector. Statistical process control (SPC) charts, which are widely used in the industrial sector, are statistical methods developed to improve the quality of products and processes. The application of this method has reached other areas over the last decades and has recently been identified as an option for environmental monitoring. In this context, the application of SPC charts emerges as an option for water consumption monitoring, whether in a building or an urban scale. Thus, this article aims to analyze the application of statistical process control charts in the monitoring of water consumption of two housing compounds in Joinville, southern Brazil. The methodological procedures include the use of the Shewhart and the EWMA control charts in addition to the non-parametric alternative, the EWMA-SN, assessing the effectiveness of these techniques in detecting water leaks in residential apartment buildings. The data sets, obtained through a telemetry metering system from the water utility, represent a period of 243 days. The results show that control charts are a powerful tool in identifying changes in water consumption patterns, with the EWMA chart flagging the leaks sooner.

The Poisson–Lindley Distribution: Some Characteristics, with Its Application to SPC

Statistical process control (SPC) is a significant method to monitor processes and ensure quality. Control charts are the most important tools in SPC. As production processes and production parts become more complex, there is a need to design control charts using more complex distributions. One of the most important control charts to monitor the number of nonconformities in production processes is the C-chart, which uses the Poisson distribution as a quality characteristic distribution. However, to fit the Poisson distribution to the count data, equality of mean and variance should be satisfied. In some cases, such as biological and medical sciences, count data exhibit overdispersion, which means that the variance of data is greater than the mean. In such cases, we can use the Poisson–Lindley distribution instead of the Poisson distribution to model the count data. In this paper, we first discuss some important characteristics of the Poisson–Lindley distribution. Then, we present parametric and bootstrap control charts when the observations follow the Poisson–Lindley distribution and analyze their performance. Finally, we provide a simulated example and a real-world dataset to demonstrate the implementation of control charts. The results show the good performance of the proposed control charts.

Online monitoring of dynamic networks using flexible multivariate control charts

Change-point detection in dynamic networks is a challenging task which is particularly due to the complex nature of temporal graphs. Existing approaches are based on the extraction of a network’s information by the reduction to a model or to a single metric. Whereas the former one requires restrictive assumptions and has limited applicability for real-world social networks, the latter one may suffer from a huge information loss. We demonstrate that an extension to a well-balanced multivariate approach that uses multiple metrics jointly to cover the relevant network information can overcome both issues, since it is applicable to arbitrary network shapes and promises to strongly mitigate the information loss. In this context, we give guidelines on the crucial questions of how to properly choose a suitable multivariate metric set together with the choice of a meaningful parametric or nonparametric control chart and show that an improper application may easily lead to unsatisfying results. Furthermore, we identify a solution that achieves reasonable performances in flexible circumstances in order to give a reliably applicable approach for various types of social networks and application fields. Our findings are supported by the use of extensive simulation studies, and its applicability is demonstrated on two real-world data sets from economics and social sciences.

An efficient adaptive r-MD multivariate single control chart for nonlinear multiple quality characteristics

An efficient multivariate single control chart to simultaneously monitor ‘location or mean’ and ‘scale or variabilities’, based on individual observations of multiple quality characteristics (MQC), is a continuous research endeavour. Compared to rational subgroups, time-ordered individual sample observations of MQC are common in manufacturing. However, few researchers proposed parametric and nonparametric multivariate control charts to monitor individual observations in this context. The proposed parametric approach has limited applicability due to the restrictive distribution assumption of MQC. In addition, most of the suggested parametric or nonparametric approaches recommend multiple charts to monitor process ‘location’ and ‘scale’ parameters simultaneously. Multiple charts can increase the control complexities and overall false-alarm-rate . MQC can also have significant nonlinear correlation structures and follow unknown or nonnormal distributions in real-life scenarios. Single parametric or nonparametric multivariate charts for individual observations can exhibit poor performance in such situations. In this study, an adaptive Mahalanobis depth and k-nearest neighbour (k-NN) rule-based r-AMD chart is proposed and verified to address the lacuna mentioned above. Monte-Carlo simulation studies are used to evaluate the performance of the r-AMD chart. Four real-life manufacturing scenarios are also considered to validate the suitability and superiority of r-AMD over the existing ‘r-MD’ and other competing charts.

Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process

Nonparametric (distribution-free) control charts have been introduced in recent years when quality characteristics do not follow a specific distribution. When the sample selection is prohibitively expensive, we prefer ranked-set sampling over simple random sampling because ranked set sampling-based control charts outperform simple random sampling-based control charts. In this study, we proposed a nonparametric homogeneously weighted moving average based on the Wilcoxon signed-rank test with ranked set sampling () control chart for detecting shifts in the process location of a continuous and symmetric distribution. Monte Carlo simulations are used to obtain the run length characteristics to evaluate the performance of the proposed control chart. The proposed control chart’s performance is compared to that of parametric and nonparametric control charts. These control charts include the exponentially weighted moving average (EWMA) control chart, Wilcoxon signed-rank with simple random sampling based the nonparametric EWMA control chart, the nonparametric EWMA sign control chart, Wilcoxon signed-rank with ranked set sampling-based the nonparametric EWMA control chart, and the homogeneously weighted moving average control charts. The findings show that the proposed control chart performs better than its competitors, particularly for the small shifts. Finally, an example is presented to demonstrate how the proposed scheme can be implemented practically.

A Distribution-Free THWMA Control Chart under Ranked Set Sampling

The basic assumption of the parametric control charts is that the underlying process follows the specific distribution. The appropriateness of parametric control charts is questionable when different industrial applications do not support this desired assumption. Recently, nonparametric control charts have been introduced to overcome this deficiency of parametric control charts. Nonparametric control charts have the same in-control run-length characteristics for all continuous distributions and are in-control robust. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique with control charts because it reduces variability and improves the control chart’s performance. So, this study aims to propose a nonparametric triple homogenously weighted moving average control chart under Wilcoxon signed-rank test with a ranked set sampling technique (regarded as NPTHWMA RSS ) to further enhance the process location monitoring. Monte Carlo simulations are used for computational purposes. The proposed control chart’s run-length performance is compared with competing control charts, like TEWMA-SR, TEWMA- X ¯ , TEWMA-SN, TEWMA- SR RSS , and NPDHWMA RSS control charts. The comparison revealed that the proposed NPTHWMA RSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is presented for quality practitioners to illustrate the effectiveness of the proposed control chart.

Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling

The statistical performance of parametric control charts is questionable when the underlying process does not follow any specified probability distribution. Nonparametric control charts are the best substitute for this situation. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique because it reduces the variability of process parameters and improves the control chart’s performance. This study aims to offer a nonparametric double homogeneously weighted moving average control chart under Wilcoxon signed-rank test considering the ranked set sampling technique (regarded as NPDHWMA RSS ), to further enhance the process location monitoring. The proposed chart’s run-length performance is compared with competing control charts, such as DEWMA- X ¯ , NPDEWMA-SR, NPRDEWMA-SR, DHWMA, and NPHWMA RSS control charts. The comparison revealed that the proposed NPDHWMA RSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is also offered for quality practitioners to show the strength of the proposed control chart.

A Shewhart-type nonparametric multivariate depth-based control chart for monitoring location

Parametric multivariate control charts like Hotelling’s rely on certain distributional assumptions that if these assumptions are not met, it leads us to an excessive number of false alarms and reduces the effectiveness of the monitoring strategy. In contrast, nonparametric multivariate control charts, specifically data-depth-based charts and related inferences, do not require any distributional assumptions and no constraints on data dimensions. In this paper, based on a family of multivariate affine invariant distribution-free data-depth-based tests for the multivariate one-sample location problem, a Shewhart-type nonparametric multivariate phase-II control chart is proposed. The performance of the proposed control chart is evaluated with a Monte Carlo simulation study using the average run length measure and is compared to that of competitors. It is observed that the proposed control chart maintained a desirable performance and leads to quicker detection of shifts. It is also a close competitor to Hotelling’s chart when the underlying distribution of the process is bivariate normal. Moreover, it performs better than its nonparametric competitor under the bivariate non-normal elliptical direction class of distributions, specifically heavy-tailed, light-tailed, and t-distributions, in a variety of settings. The control chart procedure is illustrated as an application to real-life data.

Nonparametric multivariate covariance chart for monitoring individual observations

Parametric and nonparametric multivariate control charts that are proven very useful in monitoring the covariance matrix of multivariate normally or “nearly” normally distributed continuous datasets have been proposed in statistical process control (SPC) literature. However, in many recent practical applications of SPC, the underlying systems or processes are characterised by discrete or a mixture of discrete and continuous multivariate random variables. In such cases, the available multivariate control charts for monitoring the covariance matrix of continuous processes are inadequate. We propose a multivariate nonparametric Shewhart-type chart for monitoring shifts in the covariance matrix of multivariate discrete or mixture of discrete and continuous random variables. The proposed chart first projects the multivariate dataset into Euclidean space. It then uses the Alt’s likelihood ratio obtained from the least absolute shrinkage and selection operator estimator that guarantees a well-conditioned estimate of the covariance matrix as the monitoring statistic. The proposed scheme does not require any parametric model assumptions and can be based on any distance measure of choice. It has the advantage of handling multivariate datasets of any type, including discrete, continuous or a mixture of discrete and continuous random variables. It uses the relationships among the process variables to build new variables that capture the dominant structure among the original variables. A bootstrap procedure is employed to obtain the control limit of the proposed chart for a suitable distance-based model through time. Simulation results show the advantage of the proposed chart in monitoring shifts in the covariance matrix. An illustrative example involving monitoring covariance structures of the lapping process in wafer semiconductor manufacturing and diagnosis single-proton emission computed tomography are provided to show the applications of the proposed chart.

A New Distribution-Free Control Chart for Monitoring Process Median Based on the Statistic of the Sign Test

Abstract Control charts are used to improve the quality of outputs in manufacturing, industrial, and service processes. The parametric control charts produce more false alarms and unacceptable out-of-control signals when the underlying distribution of the process is not normal. Nonparametric/distribution-free control charts are efficient alternatives to overcome the said situation. In this article, the performance of a distribution-free double exponentially weighted moving average (EWMA) chart has been investigated based on the sign test statistic under simple and ranked set sampling schemes. The run-length properties of the proposed charts have been evaluated and compared with nonparametric EWMA sign, parametric EWMA, and parametric double EWMA control charts, using different run-length measures. The comparison reveals the efficiency of the proposed chart over its alternatives in detecting small and medium shifts in the process location. A real-data application using the substrate manufacturing process has been provided to show the implementation of the proposed chart.

Control chart using bootstrap method for logistic-exponential percentiles

Lan and Leemis (2008) introduced logistic-exponential (LE) distribution which has varied applications in lifetime modellings. In this article, we consider parametric bootstrap control charts (BCCs) for detecting a shift in the percentile of LE distribution in a process monitoring situation. Four parametric BCCs based on maximum likelihood method, method of least squares, method of Cramer-von-Mises and ` method of maximum product of spacings are used for monitoring percentiles of LE distribution. We perform simulations to see the performances of the proposed four BCCs with respect to average run length. Finally, one data set is analyzed to illustrate our results.

An unsupervised one-class-classifier support vector machine to simultaneously monitor location and scale of multivariate quality characteristics

PurposeThe purpose of this study is to propose an effective unsupervised one-class-classifier (OCC) support vector machine (SVM)-based single multivariate control chart (OCC-SVM) to simultaneously monitor “location” and “scale” shifts of a manufacturing process.Design/methodology/approachThe step-by-step approach to developing, implementing and fine-tuning the intrinsic parameters of the OCC-SVM chart is demonstrated based on simulation and two real-life case examples.FindingsA comparative study, considering varied known and unknown response distributions, indicates that the OCC-SVM is highly effective in detecting process shifts of samples with individual observations. OCC-SVM chart also shows promising results for samples with a rational subgroup of observations. In addition, the results also indicate that the performance of OCC-SVM is unaffected by the small reference sample size.Research limitations/implicationsThe sample responses are considered identically distributed with no significant multivariate autocorrelation between sample observations.Practical implicationsThe proposed easy-to-implement chart shows satisfactory performance to detect an out-of-control signal with known or unknown response distributions.Originality/valueVarious multivariate (e.g. parametric or nonparametric) control chart(s) are recommended to monitor the mean (e.g. location) and variance (e.g. scale) of multiple correlated responses in a manufacturing process. However, real-life implementation of a parametric control chart may be complex due to its restrictive response distribution assumptions. There is no evidence of work in the open literature that demonstrates the suitability of an unsupervised OCC-SVM chart to simultaneously monitor “location” and “scale” shifts of multivariate responses. Thus, a new efficient OCC-SVM single chart approach is proposed to address this gap to monitor a multivariate manufacturing process with unknown response distributions.

NEW APPROACH FOR DETECTING SLIGHT SHIFT ON PROCESS MEAN IN CHIP RESISTOR PRODUCTION

This article highlights an alternative approach to identify a slight shift of the process mean for resistor production. Commonly, the industries use exponentially weighted moving average (EWMA) or classic I-MR charts for this kind of product. The parametric control chart consists of few underlying assumptions, especially observations that come from a normal distribution. A misleading conclusion was mainly made when non-normal distributed data were analyzed using a parametric control chart. A chip resistor manufacturing company provided the data for the study for future quality monitoring purposes. This study aims to determine a more appropriate analysis method according to the characteristics of the chip resistor data distribution. This article discusses the results of implementing one of the nonparametric methods that are still rarely known. The company’s current I-MR, corrective I-MR, parametric EWMA, and NPEWMA-SR control charts are used and compared in the analysis part. In the comparison, the I-MR control chart cannot detect a slight shift in the process mean. In contrast, the parametric EWMA control chart is not robust for data from a non-normal population. Since the data was not naturally from a normally distributed population, the nonparametric control chart is more appropriate, and the NPEWMA-SR control chart is suggested.

An Enhanced Performance to Monitor Process Mean with Modified Exponentially Weighted Moving Average – Sign Control Chart

The purpose of this research is to enhance performance for detecting a change in process mean by combining modified exponentially weighted moving average and sign control charts. This is nonparametric control chart which effective alternatives to the parametric control chart so called MEWMA-Sign. The nonparametric control chart can serve when process observations is deviated from normal distribution assumption. Generally, the performance of control charts are widely measured by average run length (ARL) divided into two cases; in control ARL (ARL0) and out of control ARL (ARL1). In this paper, the performance comparison is investigated when processes are non-normal distributions. The performance of the MEWMA-Sign is compared EWMA-Sign control chart by considering from a minimum value of ARL1. The numerical results found that the MEWMASign performs better than EWMA-Sign in order to detect a very small shift of mean process. Additionally, the real application of the MEWMA-Sign and EWMA-Sign are presented.