Types Of Control Charts Research Articles

Performance evaluation of extended EWMA control chart in the presence of measurement error

In any manufacturing or service industry, substantial effort is made to keep a process under control. However, factors such as measurement error are bound to create distortions. Many researchers have studied the effect of measurement error on various types of control charts including the EWMA control chart. In this paper, we study the effect of measurement error on the competency of the extended EWMA control chart. We examine the performance of the chart in the case of a shift in mean taking into account the model with linear covariates. The consequence of making multiple measurements on each sampled unit is also investigated. Last but not the least, we examine the case of linearly increasing variance. Through a simulation study, we demonstrate that the performance of the chart for detecting a shift in the mean is substantially reduced in the presence of measurement error. The important finding, however, is that, in spite of the existence of measurement error, the EEWMA control chart performs better than the EWMA control chart. A practical example is provided to elucidate this finding.

Robust Control Chart Application in Semiconductor Manufacturing Process

Statistical Process Control (SPC) charts are frequently used in the semiconductor manufacturing environment to monitor process quality and detect special-cause variations, hence, to take corrective actions when necessary. The important aspects of control charts to consider on production floors are identifying the primary objective of implementing control charts, the type of data to monitor and the most appropriate control limits to establish. When the quality data is a type of attribute data like the proportion of defectives from a production lot, a p-chart approach is most suitable. In p-chart applications, although the assumption of normally distributed process data is not mandatory, the widespread practice is to assume the normal distribution of process data when establishing the control limits. Yet again, the reality of industrial settings is that process data are most likely influenced by outliers, resulting in highly skewed distributions. This paper addresses these issues by proposing robust SPC charting techniques to detect special-cause variations in the semiconductor manufacturing processes. Here, we present a case study of a semiconductor company in Malaysia, Dominant Opto Technologies Sdn. Bhd. to propose three robust statistical approaches for monitoring the proportion of defectives in production lots. We apply M-estimates, median, and interquartile range to calculate the upper control limits (UCL) and found that robust estimators are more effective in detecting early process deterioration and capturing the out-of-control (OOC) conditions better than traditional control charts. By proposing robust methods, this study enlightens the practical aspects of process quality improvement for real-life manufacturing setups. Because a high OOC rate may impact manufacturing productivity, we recommend the decision-makers choose the types of control charts based on the implications of each robust approach toward quality and productivity. The significance of this study includes providing insights into setting up the appropriate attribute control charts for detecting defective proportions for professionals and SPC researchers working in these areas.

Modified Levey-Jennings Chart with Robust Estimator: A Case of Semiconductor Manufacturing Process

In the era of Industrial Revolution 4.0 and smart manufacturing, the development and deployment of control charts used in the semiconductor industry need to be automated. Consequently, artificial intelligence-based automation methods typically encompass the deployment of statistical software such as JMP. Automation involves frequent dataset updates; the control limits are recalculated as the parameters change (non-stationary behaviour). This requires the user to define the control chart type before its deployment on the production floor. An initially normally distributed dataset may be skewed during the process owing to the influence of outliers. If a user selects a chart based on normality assumptions, detecting a process-mean shift may be impossible if the recalculated limit fluctuates. In the semiconductor industry, a process-mean shift occurs owing to special cause variations in the process. This signals process deterioration, which may affect the quality of the product. It is unknown when outliers will affect the equilibrium of normality assumptions; therefore, it is important to develop an automated, robust control chart that can detect special cause variations under non-stationary conditions. This study proposes the use of Huber’s M-estimators in the Levey-Jennings chart to detect special cause variations in a semiconductor manufacturing process. This study computes the robust M-estimates of all available samples to calculate the new limits in the Levey-Jennings chart. This new chart is referred to as the modified Levey-Jennings with a robust Huber M-estimator (MLVHM). Using production data from Dominant Opto Technologies Sdn. Bhd., Malaysia, a statistical comparison of the MLVHM and Levey-Jennings charts was performed. While the MLVHM is stable, the absolute difference in dispersion between the two charts ranges between 25.26% and 47.91% owing to standard deviation variation in the Levey-Jennings chart in non-stationary situations with outliers. The study concludes that the MLVHM chart is robust and suitable for industrial automatic flow applications.

Use of improved memory type control charts for monitoring cancer patients recovery time censored data

Control charts are a statistical approach for monitoring cancer data that can assist discover patterns, trends, and unusual deviations in cancer-related data across time. To detect deviations from predicted patterns, control charts are extensively used in quality control and process management. Control charts may be used to track numerous parameters in cancer data, such as incidence rates, death rates, survival time, recovery time, and other related indicators. In this study, CDEC chart is proposed to monitor the cancer patients recovery time censored data. This paper presents a composite dual exponentially weighted moving average Cumulative sum (CDEC) control chart for monitoring cancer patients recovery time censored data. This approach seeks to detect changes in the mean recovery time of cancer patients which usually follows Weibull lifetimes. The results are calculated using type I censored data under known and estimated parameter conditions. We combine the conditional expected value (CEV) and conditional median (CM) approaches, which are extensively used in statistical analysis to determine the central tendency of a dataset, to create an efficient control chart. The suggested chart's performance is assessed using the average run length (ARL), which evaluates how efficiently the chart can detect a change in the process mean. The CDEC chart is compared to existing control charts. A simulation study and a real-world data set related to cancer patients recovery time censored data is used for results illustration. The proposed CDEC control chart is developed for the data monitoring when complete information about the patients are not available. So, instead of doping the patients information we can used the proposed chart to monitor the patients information even if it is censored. The authors conclude that the suggested CDEC chart is more efficient than competitor control charts for monitoring cancer patients recovery time censored data. Overall, this study introduces an efficient new approach for cancer patients recovery time censored data, which might have significant effect on quality control and process improvement across a wide range of healthcare and medical studies.

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).

Using the attribute control chart to monitor a chemical manufacturing process

The chemical and pharmaceutical industries have quality as a prerequisite for the smooth running of their processes. Quality monitoring in this type of industrial activity is carried out using attribute control charts, among others. The aim of this article is to show a case study carried out in a company in the south of the state of Rio de Janeiro which used this type of control chart, more specifically the NP control chart, to monitor an antibiotic manufacturing process. The results showed the need for some adjustments and management actions will be taken to improve the process.

Statistical Analysis and Evaluation of Claims Using Control Charts in Certification Bodies

The article discusses the basic principles of using control charts in relation to the process of analyzing claims from consumers, namely the types of control charts, their main characteristics, and issues of their practical application. The scientific novelty of the conducted research lies in identifying the main aspects of the use of the control chart methodology in the assessment and analysis of claims received from consumers by the certification body. The purpose of the study is to assess the causes of variability affecting the number of claims received from consumers by the certification body. To achieve this goal, the following tasks were solved: types of control charts were selected, taking into account the specifics of the collected statistical information on types of claims and types of services; the basic principles of using control charts to the claims analysis process have been adapted; control charts were constructed and an analysis of the causes of variability was carried out using the example of a certification body. Based on the conducted research, claims were identified whose occurrence is influenced by special reasons; for the remaining reasons, it was established that their variability is due to ordinary reasons. To determine the most significant factors influencing the special causes of claims, it is recommended to apply the Ishikawa diagram, and then develop measures aimed at reducing the influence of these factors. The data and recommendations obtained by the author as a result of the study can be used by various enterprises and organizations to analyze claims within the framework of the quality management system. The proposed approach will make it possible to make informed management decisions and increase customer satisfaction.

Application of the control chart for variables in a vehicle assembly plant in the south of the state of Rio de Janeiro

Vehicle assemblers have quality as a prerequisite for the proper functioning of their process. The monitoring of the quality of this type of industrial activity is carried out by means of control charts by variables. The objective of this article is to show a case study carried out in a company in the south of the State of Rio de Janeiro that used this type of control chart, more specifically the control chart of the mean and amplitude to evaluate a process carried out by three machines. The results showed the need for some adjustments and managerial attitudes will be taken to improve the process.

Use of Statistical Process Control for Coking Time Monitoring

Technical and technological developments in recent decades have stimulated the rapid development of methods and tools in the field of statistical process quality control, which also includes control charts. The principle of control charts defined by Dr. W. Shewhart has been known for more than 100 years. Since then, they have been used in many industries to monitor and control processes. This paper aims to assess the possibilities of use and the selection of the most suitable type of control chart for monitoring the quality of a process depending on its nature. This tool should help operators in monitoring coking time, which is one of the important control variables affecting the quality of coke production. The autoregressive nature of the variable being monitored was considered when selecting a suitable control chart from the group of options considered. In addition to the three traditional types of control charts (Shewhart’s, CUSUM, and EWMA), which were applied to the residuals of individual values of different types of ARIMA models, various statistical tests, and plots, a dynamic EWMA control chart was also used. Its advantage over traditional control charts applied to residuals is that it works with directly measured coking time data. This chart is intended to serve as a method to monitor the process. Its role is only to alert the process operator to the occurrence of problems with the length of the coking time.

Reevaluating the performance of control charts based on ranked-set sampling

Nearly one hundred types of control charts have been proposed that incorporate ranked-set sampling (RSS) methods. The performance of these charts has been evaluated with comparisons to existing charts based on simple random sampling. The reduction of the standard error in estimating the parameter being monitored with RSS leads to uniformly better average run length performance. We show, however, that these performance comparisons can be very misleading once the sampling strategy over time is considered more carefully with the benefits of RSS being considerably overstated. We consider the most basic RSS method when monitoring the mean of the process, but the approach can be applied to evaluate other RSS monitoring methods.

ON THE COMPARATIVE EFFICIENCY OF CHANGE POINT DETECTION IN MULTIVARIATE TECHNOLOGICAL PROCESSES USING MULTIDIMENSIONAL DOUBLE CONTROL CHARTS

The problem of change point detection in multiparametric technological processes having a normal distribution and consisting in a shift from a given value of the sample mean and sample variance is investigated. Various types of control charts are considered, which make it possible to effectively detect simultaneous changes in the mean value and variance in multiparametric technological processes. By the method of statistical modeling, an analysis of the comparative effectiveness of control charts is carried out, practical recommendations are given.

Adjustment of Measurement Error Effects on Dispersion Control Chart with Distribution-Free Quality Variable

In industrial processes, control charts are useful tools to monitor the quality of products and detect possibly out-of-control processes. While many types of control charts have been available for data analysts, they were developed by assuming that the variables are precisely measured. In applications, however, measurement error is ubiquitous when data are falsely recorded by investigators or imprecisely collected by unadjusted machines. Even though the impacts of measurement error for different types of control charts have been explored, error-corrected control charts are still unavailable. In this study, we propose a new dispersion control chart with error correction to fill out this research gap. Our key idea is to convert the observed distribution-free process variables into a flexible sign statistic, and then adopt a function to adjust the measurement error effects on the sign statistic. Finally, we develop an exponentially weight-moving average dispersion control chart with measurement error correction based on the corrected sign statistic. The proposed error-corrected dispersion control chart not only eliminates measurement error effects, but also provides more reliable control limits for monitoring process dispersion. Throughout the numerical examination, we find that the proposed error-corrected dispersion control chart is effective in handling moderate and large levels of measurement error and shows good out-of-control detection performance. Finally, the proposed error-corrected dispersion control chart is implemented in the semiconductor data.

A review and comparison of control charts for ordinal samples

Qualitative, more specifically, ordinal data generating processes are common in real-world process control implementations. In this study, a survey of control charts for the sample-based monitoring of independent and identically distributed ordinal data is provided together with critical comparisons of the control statistics, for memory-less Shewhart-type and for memory-utilizing exponentially weighted moving average (EWMA) and cumulative-sum types of control charts. New results and proposals are also provided for process monitoring. Using some real-world quality scenarios from the literature, a simulation study for performance comparisons is conducted, covering sixteen different types of control chart. It is shown that demerit-type charts used in combination with EWMA smoothing generally perform better than the other charts, which may rely on quite sophisticated derivations. A real-world data example for monitoring flashes in electric toothbrush manufacturing is discussed to illustrate the application and interpretation of the control charts in the study.

EWMA control chart using Bayesian approach under paired ranked set sampling schemes: An application to reliability engineering

<abstract> <p>Control charts are widely used to efficiently detect small to moderate shifts and they include exponentially moving average control charts, named memory type control charts. Today, memory type control charts are a significant tool to assure quality standards and monitor manufacturing goods. The proposed study suggests a novel Bayesian exponentially weighted moving average (EWMA) control chart design utilizing various pair ranked set sampling schemes for posterior and posterior predictive distributions given an informative prior. The proposed chart strategy is evaluated in terms of the small run length characteristic by using Monte Carlo simulation methods. The comparative analysis is also carried out by using a Bayesian EWMA control chart to apply simple random sampling for the respective average and standard deviation of the run length values in the both control chart designs. The results revealed efficient and rapid detection of shifts in process means which proves the success and superiority of the suggested design. A real-life data sets is used to elaborate the efficient application of the suggested Bay-EWMA-PRSS control chart design. The overall research findings support the theoretical and simulation results, which are provided in the form of extensive tables.</p> </abstract>

Time and magnitude monitoring using Weibull based Max-EWMA chart

To monitor time and magnitude, different types of control charts have been proposed in the literature. This article proposes a new maximum exponentially weighted moving average (Max-EWMA) control chart by assuming Weibull distribution. The test-statistic of the Max-EWMA chart consists of two EWMA statistics, where one statistic is used for monitoring magnitude while the other to monitor time interval between events. The performances of the proposed chart is assessed on the basis of run length characteristics like, average run length (ARL), standard deviation of the run length (SDRL), and quantiles of the run length distribution. Besides extensive simulation studies, real data sets are also considered to show the applications of the proposed chart. The results show that the proposed chart is efficient in detecting different size of small shifts.

Comparing the performance of Kernel PCA Mix Chart with PCA Mix Chart for monitoring mixed quality characteristics

Along with the development of information and technology, the quality characteristics of a product cannot be monitored separately in the different types of control charts. In the past, conventional control charts were developed to monitor only one type of quality characteristic. The variable control charts are used to observe the variable or metric quality characteristics. Meanwhile, in monitoring non-metric characteristics or categorical data, attribute control charts are employed. To accommodate these two types of data, the PCA Mix control chart is suggested to simultaneously monitor these two types of data in one chart. However, some drawbacks occur when this chart is applied to monitor non-metric data which has an imbalanced proportion. Therefore, the Kernel PCA Mix control chart is created to overcome the gaps that occurred in the PCA Mix chart. Similar to the previous chart, this chart is also constructed using Hotelling’s T2 statistics with Kernel Density Estimation control limit. Several simulations are used to evaluate the performance of the proposed control charts. The simulation results show that the proposed chart has a better result than the previous control chart, especially for a small mean shift with an imbalanced proportion of non-metric data. However, the PCA Mix chart has a similar performance to the proposed chart when it is applied to monitor the balanced proportion of categorical data with a large mean shift. The application with simulated data with various scenarios and the real-world case also shows that the Kernel PCA Mix chart performs better compared to the performance of the PCA Mix chart.

Adaptive risk adjusted exponentially weighted moving average control chart based on accelerated failure time regression

AbstractControl charts play an effective role in monitoring and controlling the performance of health care. It helps to determine the strategy to improve the process and identify the causes of variations. In recent years, the risk adjusted memory type control charts have received reasonable attention in monitoring surgical outcomes. In this research, we used the concept of an adaptive exponentially weighted moving average (AEWMA) control chart and proposed a new adaptive risk adjusted exponentially weighted moving average (ARAEWMA) control chart by using the accelerated failure time (AFT) regression. A real data set of the cardiac surgery patients is used for analysis and the patient condition is counted by personnet score method. The proposed ARAEWMA control chart is fitted by using the AFT model and run length profiles are computed at different shifts. The proposed ARAEWMA chart is better in shift detection and showed efficient results than the risk adjusted exponentially weighted moving average control chart.

On enhanced estimation and monitoring of population variance using robust auxiliary parameters based estimators

SummarySearching for efficient estimators of population variance as compared to sample variance has been the key area of interest of the researchers. Auxiliary variable has helped very much in finding estimators more efficient than sample variance. Auxiliary variable is greatly correlated with main study variable. Many authors including Isaki (J Am Stat Assoc 1983, 78, 117) used positively correlated auxiliary variable in the form of various conventional and non‐conventional auxiliary parameters and suggested different ratio type estimators of population variance. In this article, we have suggested a naïve class of variance estimators based on some robust auxiliary parameters, which deals with the outliers in the data. The properties including bias and Mean Square Error (MSE) of suggested family of estimators are studied up to first order of approximation. The theoretical as well as empirical comparison of introduced family of estimators is carried out with competing variance estimators. The estimator with the least MSE is recommended in different areas of applications. At last, the Shewhart type control charts based on the proposed estimators are also studies for application in quality control.

On Reassessment of the HWMA Chart for Process Monitoring

In the recent literature of process monitoring, homogeneously weighted moving average (HWMA) type control charts have become quite popular. These charts are quite efficient for early detection of shifts, especially of smaller magnitudes, in process parameters such as location and dispersion. A recent study pointed out a few concerns related to HWMA charts that mainly relate to its steady-state performance. It needs to be highlighted that the initial studies on HWMA focused only on the zero-state performance of the chart relative to other well-known memory charts. This study reinvestigates the performance of the HWMA chart under zero and steady states at various shifts. Using the Monte Carlo simulation method, a detailed comparative analysis of the HWMA chart is carried out relative to the exponentially weighted moving average (EWMA) chart with time-varying limits. For several values of design parameters, the in-control and out-of-control performance of these charts is evaluated in terms of the average run length (ARL). It has been observed that the structure of the HWMA chart has the ability to safeguard the detection ability and the run-length properties under various delays in process shifts. More specifically, it has been found that HWMA chart is superior to the EWMA chart for several shift sizes under zero state and is capable of maintaining its dominance in case the process experiences a delay in shift. However, the steady-state performance depends on the suitable choice of design parameters. This study provides clear cut-offs where HWMA and EWMA are superior to one another in terms of efficient monitoring of the process parameters.

On the location‐based memory type control charts under modified successive sampling scheme

AbstractThe 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.