Performance Of Control Charts Research Articles

Assessing the economic-statistical performance of an attribute SVSSI-np control chart based on genetic algorithms

The SVSSI scheme, featuring three variable sample sizes and two variable sampling intervals, considerably enhances the performance of control charts in detecting shifts. As a novel contribution, this study proposes an optimized design of the SVSSI-np control chart using genetic algorithms, illustrating its superior performance over other sampling schemes by considering economic and statistical perspectives in a unified model. The outcomes of implementing the SVSSI alongside other sampling schemes are assessed via a numerical example, demonstrating the influence of varying parameters such as process failure rate, shift value, and proportion of nonconforming items. Based on the obtained results, the SVSSI scheme outperforms other schemes by achieving over a 10% reduction in costs and over a 30% improvement in reducing time to signal and false alarm rates in most runs. The impact of inaccurately estimating the shift size is also investigated, revealing that incorrect estimates can lead to ineffective adjustments and improvements. Finally, optimal SVSSI designs are explored through comprehensive sensitivity analysis and robust optimization to address uncertainty, and the results of applying fractional factorial design are statistically analyzed. In summary, the SVSSI-np control chart demonstrates potential for enhanced cost reduction, process monitoring, and efficiency gains.

Optimal design of time-between-event control charts with parameter estimation

The tr chart is a Shewhart-type control chart used to monitor the time between events, especially in high-quality processes. It has been shown to be more efficient than classical attribute control charts based on count data. In practical applications, the in-control process parameters are often unknown and need to be estimated from a Phase I reference sample. When the available Phase I data are small and the chart parameters have to be estimated, a popular approach is to adjust the control chart limits from a conditional perspective to avoid frequent false alarms using the exceedance probability criterion. However, this approach ignores the practitioner-to-practitioner (p-to-p) variation caused by the random Phase I reference samples, which results in getting different control limits and chart performance for each practitioner Large p-to-p variation makes practitioners to have a limited confidence on using their own estimated charts. Hence, in this article, we propose to optimize the tr chart via an exact method so that it has a minimum p-to-p variation. Comparisons between the optimal and conventionally adjusted charts are made in both the in- and out-of-control cases. The most important results are that the optimal chart has a far smaller p-to-p variation and its unconditional average run length values are closer to the desired ones compared to the conventional approach regardless of the in- or out-of-control cases. Finally, two real examples are presented to illustrate the implementation of the proposed chart.

Optimal design of time-between-event control charts with parameter estimation

The tr chart is a Shewhart-type control chart used to monitor the time between events, especially in high-quality processes. It has been shown to be more efficient than classical attribute control charts based on count data. In practical applications, the in-control process parameters are often unknown and need to be estimated from a Phase I reference sample. When the available Phase I data are small and the chart parameters have to be estimated, a popular approach is to adjust the control chart limits from a conditional perspective to avoid frequent false alarms using the exceedance probability criterion. However, this approach ignores the practitioner-to-practitioner (p-to-p) variation caused by the random Phase I reference samples, which results in getting different control limits and chart performance for each practitioner Large p-to-p variation makes practitioners to have a limited confidence on using their own estimated charts. Hence, in this article, we propose to optimize the tr chart via an exact method so that it has a minimum p-to-p variation. Comparisons between the optimal and conventionally adjusted charts are made in both the in- and out-of-control cases. The most important results are that the optimal chart has a far smaller p-to-p variation and its unconditional average run length values are closer to the desired ones compared to the conventional approach regardless of the in- or out-of-control cases. Finally, two real examples are presented to illustrate the implementation of the proposed chart.

Approximating the ARL to Monitor Small Shifts in the Mean of an AR Fractionally Integrated with an exogenous variable Process Running on an EWMAControl Chart

Control charts are used to monitor processes and detect changes in a given control scheme. The Exponential Weighted Moving Average (EWMA) control chart is a well-recognized control chart used to detect small changes in parameters. The efficiency of the chart studied is usually achieved using ARL. Approximating ARL using the Gauss-Legendre quadrature method, also known as NIE,. This approach is used to evaluate the ARL of developments, such as explicit formulas because it provides a robust way to validate their validity and accuracy. Moreover, it evaluates the performance of control charts for time series under exponential white noise. Exponential white noise is obtained from a long-memory fractionally integrated AR with exogenous variables or the long-memory ARFIX process. Under the long-memory ARFIX model, the proposed technique compares the control chart's performance to an explicit formula using the criterion of percentage accuracy. The results of the comprehensive numerical study include investigations into a wide range of out-of-control processes and situations. Specifically, the results from the accuracy percentage in all cases are more than 95%, which means that the proposed technique is accurate and completely consistent with the well-defined explicit formula. Therefore, it is recommended that it be used in this situation. There are examples from real data that were found to be consistent with the research results.

Average Run Length Computations of Autoregressive and Moving Average Process using the Extended EWMA Procedure

In the past, the control chart served as a statistical tool for detecting process changes. The Exponentially Weighted Moving Average (EWMA) control chart is highly effective for detecting small changes. This research introduces the Extended Exponentially Weighted Moving Average (Extended EWMA) control chart for the Autoregressive and Moving average process with order p = 1 and q = 1 (ARMA(1,1)) The Extended EWMA control chart incorporates two smoothing parameters ( λ1 and λ2 ) derived from the EWMA control chart. A comparative analysis of the performance of the EWMA control chart. The Average Run Length (ARL) value as determined by the explicit formulas in this research, serves as a metric for evaluating the performance of the Extended EWMA control chart and the EWMA control chart. The Numerical Integral Equation (NIE) method is used to verify the accuracy of the ARL for the explicit formulas of the two control charts which has not been before discovered. The effectiveness of control charts can also be evaluated by analyzing SDRL, ARL, MRL, RMI, AEQL, and PCI values as metrics for various design parameter values. After analyzing the results of the ARL and all five performance meters, it was determined that the Extended EWMA control chart is better than the EWMA control chart at all shift sizes of process changes. Finally, the assessment of the ARMA process is being conducted to evaluate the ARL using a dataset on PM2.5 dust levels in Bangkok, Thailand during January and February of 2024.

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.

An adaptive Bayesian approach for improved sensitivity in joint monitoring of mean and variance using Max-EWMA control chart

This article introduces an adaptive approach within the Bayesian Max-EWMA control chart framework. Various Bayesian loss functions were used to jointly monitor process deviations from the mean and variance of normally distributed processes. Our study proposes the mechanism of using a function-based adaptive method that picks self-adjusting weights incorporated in Bayesian Max-EWMA for the estimation of mean and variance. This adaptive mechanism significantly enhances the effectiveness and sensitivity of the Max-EWMA chart in detecting process shifts in both the mean and dispersion. The Monte Carlo simulation technique was used to calculate the run-length profiles of different combinations. A comparative performance analysis with an existing chart demonstrates its effectiveness. A practical example from the hard-bake process in semiconductor manufacturing is presented for practical context and illustration of the chart settings and performance. The empirical results showcase the superior performance of the Adaptive Bayesian Max-EWMA control chart in identifying out-of-control signals. The chart’s ability to jointly monitor the mean and variance of a process, its adaptive nature, and its Bayesian framework make it a useful and effective control chart.

Performance of T2-based PCA mix control chart with KDE control limit for monitoring variable and attribute characteristics

In this work, the mixed multivariate T2 control chart’s detailed performance evaluation based on PCA mix is explored. The control limit of the proposed control chart is calculated using the kernel density approach. Through simulation studies, the proposed chart’s performance is assessed in terms of its capacity to identify outliers and process shifts. When 30% more outliers are included in the data, the proposed chart provides a consistent accuracy rate for identifying mixed outliers. For the balanced percentage of attribute qualities, misdetection happens because of the high false alarm rate. For unbalanced attribute qualities and excessive proportions, the masking effect is the key issue. The proposed chart shows the improved performance for the shift in identifying the shift in the process.

Efficient Monitoring of Autoregressive and Moving Average Process using HWMA Control Chart

Quality control is an essential process for manufacturing and industry because it enhances product quality, consumer satisfaction, and overall profitability. Among many other statistical process control tools, quality practitioners typically employ control charts to monitor the industrial process and detect production changes. Control charts are widely used to detect flaws in many applications, such as distributed circuits and systems, electronic devices, and systems and signals. In this study, we derived an explicit formula for Average Run Length (ARL) of the Homogenously Weighted Moving Average control chart (HWMA) under the ARMA (p,q) process. The accuracy was checked using the numerical integral equation (NIE) technique. The finding showed that the explicit formulas and numerical solutions presented an outstanding level of agreement. However, the computational time for the explicit formulas was approximately one second, which was less than that required for the NIE. Moreover, the performance efficiency of the HWMA control chart is compared with the cumulative sum control chart for ARMA (p, q) processes including ARMA (2,1), ARMA (2,3), and ARMA (1,1) processes. The results found that the HWMA control chart performance is found to be preferable to the CUSUM control chart performance. Additionally, the explicit formula of the HWMA control chart was implemented in a practical application of the count of nonconformities in printed circuit boards (PCBs).

Wilcoxon-Type Control Charts Based on Multiple Scans

In this article, we establish new distribution-free Shewhart-type control charts based on rank sum statistics with signaling multiple scans-type rules. More precisely, two Wilcoxon-type chart statistics are considered in order to formulate the decision rule of the proposed monitoring scheme. In order to enhance the performance of the new nonparametric control charts, multiple scans-type rules are activated, which make the proposed chart more sensitive in detecting possible shifts of the underlying distribution. The appraisal of the proposed monitoring scheme is accomplished with the aid of the corresponding run length distribution under both in- and out-of-control cases. Thereof, exact formulae for the variance of the run length distribution and the average run length (ARL) of the proposed monitoring schemes are derived. A numerical investigation is carried out and depicts that the proposed schemes acquire better performance towards their competitors.

The Development and Evaluation of Homogenously Weighted Moving Average Control Chart based on an Autoregressive Process

This research aims to investigate a Homogenously Weighted Moving Average (HWMA) control chart for detecting minor and moderate shifts in the process mean. A mathematical model for the explicit formulae of the average run length (ARL) of the HWMA control chart based on the autoregressive (AR) process is presented. The efficacy of the HWMA control chart is evaluated based on the average run length, the standard deviation of run length (SDRL), and the median run length (MRL). As illustrations of the design and implementation of the HWMA control chart, numerical examples are provided. In numerous instances, a comparative analysis of the HWMA control chart relative to the Extended Exponentially Weighted Moving Average (Extended EWMA) and cumulative sum (CUSUM) control charts with mean process shifts is performed in detail. Additionally, the relative mean index (RMI), the average extra quadratic loss (AEQL), and the performance comparison index (PCI) are utilized to evaluate the performance of control charts. For various shift sizes, the HWMA control chart is superior to the Extended EWMA and CUSUM control charts. This study applies empirical data from the area of economics to validate the explicit formula of ARL values for the HWMA control chart. Doi: 10.28991/HIJ-2024-05-01-02 Full Text: PDF

Double Moving Average Control Chart for Time Series Data with Poisson INARCH(1)

The objectives of this research are to find the explicit formulas of the average run length (ARL) of a double moving average (DMA) control chart for first-order integer-valued autoregressive conditional heteroscedasticity (INARCH1))) of Poisson count data. In addition, the numerical results obtained from the proposed explicit formulas are compared with those obtained from Monte Carlo simulations (MC) for the Poisson INARCH(1) counting process. An out-of-control ARL (ARL1) is the criteria for measuring the performance of control charts. The numerical results found that the values of both ARL0 and ARL1 obtained from explicit formulas agree with the numerical results obtained from the Monte Carlo simulation (MC), but the latter is very timeconsuming.

Detecting outliers in the multivariate control charts for dispersion monitoring

AbstractOutlier detection is an important aspect of statistical process monitoring (SPM) because outliers affect the performance of control charts. SPM researchers study the negative impact of outliers on control charts for monitoring location parameters. However, there is little research on outlier detection in multivariate charts for monitoring process dispersion. This study aims to investigate the impact of outliers in multivariate control charts for monitoring covariance matrix of a process, and then to recommend techniques for detecting potential outliers present from Phase I samples. We propose a new multivariate dispersion chart that employs the determinant of logarithm of estimated covariance matrix as the monitoring statistic. Through Monte Carlo simulations, the results show how outliers from the first phase affect the overall performance of multivariate charts. The results also demonstrate that the minimum volume ellipsoid (MVE) estimator is effective in reducing the effect of outliers on the proposed control scheme than the other compared estimators.

Optimization design of control charts: A systematic review

AbstractIn today's competitive landscape, fulfilling customer expectations and achieving a competitive edge are crucial for business success. These objectives can be attained by effective monitoring in both manufacturing and service sectors to enhance quality, reduce variation, and augment productivity. The control chart, a widely used tool for this purpose, has attracted significant attention from researchers for its ability to detect anomalies and manage out‐of‐control situations. The optimization of control charts, a central focus of this review, not only enhances the detection effectiveness but also maintains the desired false alarm rate, thus ensuring efficient process control without additional cost, complexity, or operational challenges for shop floor personnel. The optimization process involves adjusting charting parameters like the sample size, sampling interval, and control limits within a hypothesis testing framework, thereby achieving optimal system performance. Numerous optimization models have been developed to enhance control chart performance. This paper introduces a classification scheme to analyze and categorize the existing research on control chart optimization. By conducting a thorough review of more than 240 articles, the study pinpoints research gaps and offers valuable insights, thereby advancing the future research in this domain.

Memory type Max-EWMA control chart for the Weibull process under the Bayesian theory

The simultaneous monitoring of both process mean and dispersion, particularly in normal processes, has garnered significant attention within the field. In this article, we present a new Bayesian Max-EWMA control chart that is intended to track a non-normal process mean and dispersion simultaneously. This is accomplished through the utilization of the inverse response function, especially in cases where the procedure follows a Weibull distribution. We used the average run length (ARL) and the standard deviation of run length (SDRL) to assess the efficacy of our suggested control chart. Next, we contrast our suggested control chart's performance with an already-existing Max-EWMA control chart. Our results show that compared to the control chart under consideration, the proposed control chart exhibits a higher degree of sensitivity. Finally, we present a useful case study centered around the hard-bake process in the semiconductor manufacturing sector to demonstrate the performance of our Bayesian Max-EWMA control chart under different Loss Functions (LFs) for a Weibull process. The case study highlights how flexible the chart is to various situations. Our results offer strong proof of the outstanding ability of the Bayesian Max-EWMA control chart to quickly identify out-of-control signals during the hard-bake procedure. This in turn significantly contributes to the enhancement of process monitoring and quality control.

Patient‐based real‐time quality control in medical laboratories: On the design and robustness of the moving average control chart with truncation limits

AbstractQuality is an indispensable requirement in medical laboratories, where controls are performed at different phases of the laboratory processes. In the following, we consider the internal quality control activities during the analytical phase of medical laboratories for verifying the test results prior to their release. To monitor the measurement process for errors in the test results, one approach that is considerably attracting the health professionals is patient‐based real‐time quality control. In this respect, real‐time patient test results are monitored, commonly by implementing the Moving Average (MA) control chart with truncation limits. A usual practice is the use of truncation limits to exclude abnormal patient test results from the MA calculations. However, an open issue in the literature is how to determine the width of the truncation limits and the window size in the MA calculations. Furthermore, the distributions of the test results are often nonnormal and difficult to model by personnel having insufficient training in statistics. Consequently, robustness of the performance of the MA control chart to non‐normal distributions of test results is another open topic in the literature. In this study, a detailed robustness analysis is performed by considering various distributions having different shapes. Performance of several MA control chart designs constructed by altering the truncation limits and window sizes are investigated. Based on our simulation results with selected distributions, we conclude that the truncation limits should not be used and a window size of 20 is recommended. Under such a setting, the MA control chart performs similar to its intended performance in terms of false alarms and in detecting systematic errors, hence being robust to non‐normality of the test results.

On the performance and comparison of various memory-type control charts

Several versions of the exponentially weighted moving average (EWMA) control chart, such as the generally weighted moving average (GWMA), the double, triple, and quadruple EWMA (DEWMA, TEWMA, and QEWMA), and the homogeneously weighted moving average (HWMA) charts, have been developed to enhance its detection ability, especially for small and moderate shifts. These charts have been criticized as it is considered that an appropriately designed EWMA chart provides as good or better zero-state and steady-state average run-length (ARL) performance. In this article, we perform a careful comparison study of the above control charts under similar in-control (IC) run-length properties. We show that the “new” memory-type control charts have better out-of-control (OOC) run-length characteristics, especially for small to moderate shifts in the process mean for both the zero-state and steady-state cases, except for the HWMA chart where its steady-state OOC performance is very poor. We also present a comparison study based on the worst-case ARL measure. Finally, the extensions of the EWMA chart have better IC robustness ability than the EWMA and HWMA charts.

Peta Kendali p Berdasarkan Metode Peningkatan Transformasi Akar Kuadrat

When the proportion of nonconformities is small, the effectiveness of the control chart performance becomes inadequate because it has a skewness that causes asymmetryc. Therefore, the Improved Square Root Transformation (ISRT) method is used to construct the attribute control chart to increase the accuracy of the chart control limit which is called the ISRT- control chart. In this study, the effectiveness of the ISRT- control chart perfomance is compared with the control chart after being applied to the data on the number of defects in the newspaper production process at PT. Radar Sulteng Membangun. The results showed that the production process at PT. Radar Sulteng Membangun was not in a statistically controlled and the ARL value obtained on the ISRT- control chart is much smaller than the ARL value for the control chart, so that the ISRT- chart is more effective and sensitive to detecting changes in the production process which produces in a small proportion of nonconformities.

Re-Evaluating the SPRT Chart with Estimated Process Parameters When the Underlying Distributions Are Gamma, Lognormal, and Weibull

To reduce the impact of Phase-I parameter estimation on the performances of Phase-II control charts, researchers have incorporated the ideology of Guaranteed In-control Performance (GICP) in their statistical designs to limit the risk of excessive false alarms. At present, most research works have primarily focused on normally distributed data. However, the assumption of normality is often violated in manufacturing environments, and certain data may exhibit positively skewed distributions. In this paper, we investigate the performance of the SPRT control chart with estimated process parameters designed using the GICP method under three different skewed distributions, i.e., the Gamma, Lognormal, and Weibull distributions. The study is conducted by varying the Phase-I sample size and the degree of skewness in order to reveal their impacts upon the in-control and out-of-control performances of the SPRT chart with estimated process parameters. Results show that an increase in the skewness level leads to rapid deterioration in both the in-control and out-of-control expected values of the average time to signal (AATS) and the average standard deviation of the time to signal (ASDTS). Interestingly, we have found that increasing the Phase-I sample size leads to deterioration in the conditional in-control performance, but an improvement in the out-of-control AATS and ASDTS values. Furthermore, it is found that, among the three distributions, the Lognormal distribution produces the least stable performance when skewness is large and the Phase-I sample size is small.

The effects of large round‐off errors on the performance of control charts for the mean when the quality characteristic is normally distributed with a known variance

AbstractThis research discusses the effects of large round‐off errors on the performance of control charts for means when a process is normally distributed with a known variance and a fixed sample size. Quality control in practice uses control charts for means as a process monitoring tool, even when the data is significantly rounded. The objective of this research is to demonstrate how ignoring the round‐off errors and using a standard Shewhart chart affects the quality control of a measured process. The first part of the research includes theoretical calculations for estimating the values of alpha and beta, relating to the unrounded data and the large‐rounded data. For the rounded data, normality can no longer be assumed because the data is discrete; therefore, the multinomial distribution is used. The results show that given an in‐control process, alpha indicates that false alarms are more frequent, whereas given an out‐of‐control process, the influence on beta is minor and inconsistent. For some rounding levels, there is a decline in the control chart performances, and in others, there is an improvement. In the second part, a simulation study is used to evaluate the performances of the control chart based on a single sample, checking whether the conclusion (reject or fail to reject) for a sample is consistent for rounded and unrounded data. The results of the simulation match the theoretical calculations.