Shifts In Process Mean Research Articles

GAN-based statistical process control for the time series data

The cumulative sum (CUSUM) control chart and the multivariate anomaly detection with the generative adversarial network (MAD-GAN) were compared for monitoring the time series data. However, the control boundaries constructed in terms of the one-class classification with only the normal data for the training phase are inappropriate for the test phase because the normal data and the abnormal data should be classified for the test phase. In this regard, we first propose this GAN-based statistical process control (SPC) framework to compare them in terms of detecting the process mean shift based on the perspective of SPC. Second, we propose the residual MAD-GAN in order to improve the detection performance. Third, we develop the loss function of the MAD-GAN. Finally, we find that the maximum mean discrepancy (MMD) as well as the nash equilibrium is useful for the MAD-GAN. Our experiments demonstrate that the residual MAD-GAN is more effective than the residual CUSUM control chart in terms of the run lengths for the time series data. Therefore, we propose SPC practitioners to consider the residual MAD-GAN for detecting the process mean shift in time series data.

A Process Mean Shift Model Considering the Process Variance and Wear Function in Cutting Process

A Process Mean Shift Model Considering the Process Variance and Wear Function in Cutting Process

A distribution-free adaptive CUSUM-sign chart for monitoring shifts in the location of unknown industrial process

In most of the manufacturing industry, the distributional assumption of the online working processes is customarily unknown or hard to meet. In such situations, parametric charting mechanisms generally designed under normality assumptions of the model yield more false alarms and invalid out-of-control (OOC) comparisons. The nonparametric (distribution-free) charts are a better choice for practitioners in such cases as their in-control (IC) run length (RL) profiles remain the same. The study intends to develop a new distribution-free adaptive CUSUM sign (NPACUSUM-SN; named hereafter) chart for monitoring the process location. The proposed NPACUSUM-SN chart estimates the unknown process mean shift using an unbiased function and updates adaptively the reference parameter of the CUSUM statistic. The IC robustness of the conventional adaptive CUSUM and the proposed NPACUSUM-SN charts under the symmetric, skewed, and contaminated normal (CN) distributions have been computed using Monte Carlo simulations. The OOC RL profiles of the proposed study have been assessed for the initial state and the shift delay (steady state) in the processes. The proposed NPACUSUM-SN chart shows more resistance against non-normality and effective behaviour as compared to its conventional competitor. The proposed NPACUSUM-SN chart provides uniformly efficient RL characteristics as compared to its counterparts. Implementation of the proposal is made by using a manufacturing industry dataset along with an artificial dataset.

Designing an efficient adaptive EWMA model for normal process with engineering applications

Stability in process parameters is required to ensure the quality of the finished item. Control charts, as one of the critical parts of statistical process monitoring (SPM), have seen widespread use across many disciplines for detecting and responding to shifts in process parameters. The adaptive EWMA (AEWMA) control chartis a well-known scheme that detects both small and large process shifts by integrating the features of the Shewhart and classical EWMA charts. In this study, we propose an enhanced AEWMA chart, termed the EAEWMA chart, that efficiently monitors small and large process mean shifts simultaneously. The proposed EAEWMA chart enhances the existing AEWMA chart using the shift estimator, based on the hybrid EWMA (HEWMA) statistic. The Monte Carlo simulation approach is employed as the computational method to obtain the numerical findings for the various performance metrics. The EAEWMA chart is compared with various existing charts, including AEWMA, HEWMA, EWMA, ACSUM, and IACCUSUM, in zero- and steady-state scenarios. Conclusively, two practical applications of the EAEWMA chart are presented, demonstrating its value for practitioners and engineers and illustrating its efficacy in real-world scenarios.

Optimal design of the side sensitive group runs double sampling (SSGRDS) X¯ scheme with estimated process parameters

The side sensitive group runs double sampling (SSGRDS) [Formula: see text] scheme is previously studied under the known process parameters (Case-K) assumption. As the process parameters are hardly known in practical situations, they must be estimated using a suitably chosen in-control (IC) Phase-I sample. However, various studies demonstrated that a substantial amount of Phase-I sample is necessary so that the scheme with unknown process parameters (Case-U) attains a performance almost similar to that of the Case-K counterpart. Since it is challenging to acquire a vast number of IC samples, we examine the optimal designs of the Case-U SSGRDS [Formula: see text] scheme such that the average number of observations to signal (ANOS) and expected ANOS (EANOS) are minimised. The optimal parameters obtained for the Case-U SSGRDS [Formula: see text] scheme enable it to have a performance comparable to that of the Case-K counterpart, without the need for a large number of Phase-I samples. We show that the Case-U SSGRDS [Formula: see text] scheme is effective in identifying the process mean shift of a silicon epitaxial process.

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.

Novel combined Shewhart-CUmulative EWMA-SUM mean charts without- and with measurement error

The precision of process monitoring often encounters challenges in determining the exact shift size. Therefore, combined control charts have gained considerable attention because of their excellent speed to detect simultaneously small-to-moderate and large-size shifts. The effectiveness of the applied quality control methods strongly depends on the performance of the measurement system. Measurement error presence contributes significantly negatively toward the performance of the usual control charting schemes. This article proposes novel two-sided combined Shewhart-Cumulative EWMA-sum (Shewhart-CUESUM) control charts designed to efficiently monitor the mean of normally distributed processes. In addition, to address measurement errors, the M-Shewhart-CUESUM chart is proposed, incorporating an additive measurement error model. Evaluation of the charts through Monte-Carlo simulations, considering metrics such as average run length (ARL), extra quadratic loss, relative ARL, and performance comparison index. It is found that the combined Shewhart-CUESUM outperforms than CUESUM chart. The results show that the presence of measurement errors can significantly diminish the charts’ performance, which can be mitigated by utilizing a multiple measurements scheme. Among the different well-established combined charts examined, the M-Shewhart-CUESUM chart shows considerably more sensitive to detecting simultaneously detect small and large size shifts. To employ simulated datasets to illustrate the impact of measurement errors and demonstrate the implications of the proposed charts on process mean shifts.

Pareto Distribution-Based Shewhart Control Chart for Early Detection of Process Mean Shifts

The Pareto distribution is of paramount importance in actuarial science, wealth distribution, finance, etc. This paper introduces a control chart inspired by Shewhart's methodology, designed for monitoring shifts in the Pareto distribution through a repetitive sampling approach. The chart employs a modified statistic that combines shape and threshold parameters as its plotting statistic. Coefficients for the Shewhart-type Pareto chart are computed for two-phase limits. The performance of the suggested chart is assessed in terms of run length characteristics, assuming a shift in the process mean. Additionally, we conduct an efficiency comparison with existing control charts. The findings suggest that, on average, the proposed Pareto chart demonstrates greater efficiency in promptly detecting changes compared to alternative methods. To illustrate the practical application of our approach, we present an example using revenue data.

Facility Maintenance Model for Process Mean Shift Problem in Automated Process

Facility Maintenance Model for Process Mean Shift Problem in Automated Process

Monitoring of semiconductor manufacturing process on Bayesian AEWMA control chart under paired ranked set sampling schemes

Quality control often employs memory-type control charts, including the exponentially weighted moving average (EWMA) and Shewhart control charts, to identify shifts in the location parameter of a process. This article pioneers a new Bayesian Adaptive EWMA (AEWMA) control chart, built on diverse loss functions (LFs) such as the square error loss function (SELF) and the Linex loss function (LLF). The proposed chart aims to enhance the process of identifying small to moderate as well as significant shifts in the mean, signifying a notable advancement in the field of quality control. These are implemented utilizing an informative prior for both posterior and posterior predictive distributions, employing various paired ranked set sampling (PRSS) schemes. The effectiveness of the suggested chart is appraised using average run length (ARL) and the standard deviation of run length (SDRL). Monte Carlo simulations are employed to contrast the recommended approach against other control charts. The outcomes demonstrate the dignitary performance of the recommended chart in identifying out-of-control signals, especially applying PRSS designs, in comparison to simple random sampling (SRS). Finally, a practical application was conducted in the semiconductor manufacturing context to appraise the efficacy of the offered chart using various paired ranked set sampling strategies. The results reveal that the suggested control chart performed well in capturing the out-of-control signals far better than the already in use control charts. Overall, this study interposes a new technique with diverse LFs and PRSS designs, improving the precision and effectiveness in detecting process mean shifts, thereby contributing to advancements in quality control and process monitoring.

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

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

THE PERFORMANCES OF MIXED EWMA-CUSUM CONTROL CHARTS BASED ON MEDIAN-BASED ESTIMATORS UNDER NON-NORMALITY

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts have been regularly used to monitor small process mean shifts. More recently, a mixture of EWMA and CUSUM charts known as mixed EWMA-CUSUM (MEC) control chart has been introduced for better small shift detection. However, like its predecessor, the MEC chart requires the normality assumption to ensure optimal performances. In the presence of outliers, which is the cause of non-normality, the parameters of the chart may be overestimated, leading to an unreliable monitoring process. To mitigate this problem, this paper employed median-based estimators namely, the median and modified one-step M-estimator (MOM), to control the location parameter via the MEC control chart. In this study, the performance of robust MEC charts for Phase II monitoring of location was compared with the standard MEC chart that is based on the sample mean. The performance of the robust MEC charts in terms of the average run length (ARL) on various g-and-h distributions clearly shows that a robust MEC chart based on the MOM estimator performs well regardless of the distributional shapes.

Single and dual reference-free CUSCORE charts for detecting unknown patterned mean shifts

Most of the control charts in the literature focus on detecting constant mean shifts. In practice, dynamic and time-varying process mean shifts are prevalent in the monitoring of feedback-control and autocorrelated processes. The cumulative score (CUSCORE) charts have been proposed in the literature to detect dynamic and time-varying process shifts. One of such control charts is a reference-free CUSCORE (called RFCS-I) chart that may detect unknown patterned mean shifts effectively. In this paper, single and dual CUSCORE charts are developed to enable an efficient detection of unknown patterned mean shifts. The developed single CUSCORE chart, called the RFCS-II chart, is based on the control charting structure of the Crosier CUSUM (called CU-II) chart. Additionally, two RFCS-I charts are integrated with reflecting boundaries, while an integration of two RFCS-II charts is also made, to develop the dual RFCS-I (DRFCS-I) and dual RFCS-II (DRFCS-II) charts, respectively. In addition, the RFCS-I and RFCS-II charts are integrated to propose the mixed dual reference-free CUSCORE chart, called the MDRFCS chart. In essence, four CUSCORE charts, i.e. the RFCS-II, DRFCS-I, DRFCS-II and MDRFCS charts are suggested in this paper. The Monte Carlo simulation and a real application illustrate the superiority of these developed CUSCORE charts over their existing counterparts when detecting patterned mean shifts in terms of zero-state and steady-state relative mean indexes.

Symmetry of gamma distribution data about the mean after processing with EWMA function

Statistical Process Control (SPC) plays a vital role in maintaining quality and reducing variability in manufacturing processes. Among SPC techniques, the Exponentially Weighted Moving Average (EWMA) stands out for its ability to detect small process shifts quickly, making it a valuable tool in ensuring product consistency and preventing quality issues. EWMA constructs control charts to monitor process mean shifts, tracks product/service quality by identifying variations, and monitors manufacturing process parameters for early detection of deviations and necessary adjustments. EWMA control chart has been proposed as an alternative to the Shewhart control chart. Sequential measurements are processed using the EWMA function before being placed on the control chart. One of the crucial concerns about the EWMA control chart is the asymmetry of the data around the mean. Although processing with the EWMA function reduces data skewness, the problem of asymmetric data may not be solved. The control chart is designed to leave in front of the upper control limit (UCL) α/2 of the data and behind the lower control limit (LCL) another α/2 of the data, and this does not occur in the case of symmetric data. α/2 represents the significance level for each tail in a two-tailed hypothesis test, indicating the probability of incorrectly rejecting the null hypothesis for each side of the distribution. Since many of the distributions in real life can be approximated by the Gamma distribution, the Gamma distribution was adopted in this study. The Monte Carlo simulation methodology was implemented to generate Gamma distributed data, process it with EWMA function and assess the skewness and kurtosis. The purpose of this paper is to evaluate the effect of EWMA parameters on the performance of the EWMA control chart. Moreover, it focuses on skewness and kurtosis reduction after data processing using the EWMA function. The findings help researchers and practitioners to select the best parameters. Further, the research investigates the effect of EWMA parameter on the shape of distribution.

Triple exponentially weighted moving average control chart with measurement error

Measurement error (M.E) can have a substantial impact on quality control applications, diminishing the sensitivity to detect changes in the mean or variance of quality characteristics. To monitor shifts in process mean and dispersion, Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts are commonly employed. In our research, we investigated the influence of M.E on the Triple Exponentially Weighted Moving Average (TEWMA) control chart. We assessed the performance of the control chart using Average Run Length (ARL) as the evaluation metric. To compute the ARL properties, we adopted the Monte-Carlo simulation method. A comparison section has been made to check the performance efficiency of the control chart with the existing EWMA control chart. The implementation of a control chart on a real data set is also presented.

Integration of hybrid score functions to design new adaptive EWMA control chart to monitor the process mean shift

Small-to-moderate shifts in the process parameters can be detected using the traditional Exponentially Weighted Moving Average (EWMA) control chart. The classical EWMA control chart's parameter helps only to identify the specific size of the shift. However, various shifts occur in real-world processes, so the conventional EWMA control chart performs inefficiently for off-target shifts. This problem has been confronted by applying an adaptive EWMA (AEWMA) control chart, an advanced version of the classical EWMA control chart. The score functions are utilized to design the AEWMA control chart. Generally, the Huber and Bi-square (score) functions have unique characteristics, such as monotone and redescended, respectively.There has not been any investigation into the simultaneous and/or joint deployment of score functions. So, by taking this point as motivation, this study aims to propose a new score function by blending the Huber and Bi-square characteristics into one hybrid formulation and then utilize it to design a new AEWMA control chart to monitor different sizes of the shift in the process location parameter. To evaluate the proposed control chart performance against other control charts, Monte Carlo simulation is applied to obtain the run length properties under zero-state and steady-state environments. Performance measures, such as average run length, standard deviation of run length, and median of run length, are considered to evaluate the performance at a single shift. In contrast, extra quadratic loss, relative average run length, and performance comparison index are utilized to evaluate effectiveness for a specific range of shifts. The comparison based on performance measures and visual presentation reveals the superiority of the proposed control chart. Besides, the proposed control chart is employed in the real-world chemical engineering process industry problem, demonstrating excellent detection ability of anomalies in air pollutant data. The comparison based on performance measures and visual presentation reveals the good performance of the proposed control chart.

Efficient control charting methodology based on Distance Weighted Mean for normal distribution

This research suggests a Distance Weighted Mean (DWM) based control chart under normal distribution implementing Simple Random Sampling (SRS). The control limits are calculated using the quantile point method. The control chart's performance is assessed using the Average Run Length (ARL) statistic. The numerical findings are illustrated using samples of sizes 3 and 5. The ARL1 values are determined using Monte Carlo Simulation for increasing and decreasing shifts in the location parameter ranging from 5% to 30%. Using the ARL1 measurement, the proposed DWM control charts are compared to the existing Shewhart control charts. According to the comparison analysis, the suggested DWM control chart surpasses the competing Shewhart control chart. The real-life application of the proposed DWM control chart is also shown by using the lifetime of the light bulb (in hours). The results suggest that the proposed DWM control chart can be a useful tool for monitoring process mean shifts, especially when the sample size is large, and the magnitude of the shift is significant.

Memory-Type Control Charts Through the Lens of Cost Parameters

A memory-type control chart utilizes previous information for chart construction. An example of a memory-type chart is an exponentially-weighted moving average (EWMA) control chart. The EWMA control chart is well-known and widely employed by practitioners for monitoring small and moderate process mean shifts. Meanwhile, the EWMA median chart is robust against outliers. In light of this, the economic model of the EWMA and EWMA median control charts are commonly considered. This study aims to investigate the effect of cost parameters on the out-of-control average run length in implementing EWMA and EWMA median control charts. The economic model was used to compute the parameter. The 14 input parameters were identified and the analysis was carried out based on the one-parameter-at-a-time basis. When the input parameters change based on a predetermined percentage, the is affected. According to the results of the EWMA chart, nine input parameters had an effect and five input parameters had no effect on the parameter. Further, only seven of the 14 input parameters had an effect on the ARL1 of the EWMA median chart. However, the effect of each input parameter on the was different. Moreover, the for the EWMA median chart was smaller than the EWMA chart. This analysis is crucial to observe and determine the input parameters that have a significant impact on the of the EMWA and EWMA median control charts. Hence, practitioners can obtain an overview of the influence of the input parameters on the when implementing the EWMA and EWMA median control charts.

On designing an optimal SPRT control chart with estimated process parameters under guaranteed in-control performance

Being one of the most sophisticated control charts, the sequential probability ratio test (SPRT) chart possesses fast detection ability across a broad range of process shifts. The SPRT chart has the advantage of sampling only a modest number of observations. Thus far, the SPRT chart has been developed under the assumption that the process parameters are known. As process parameters are often unknown in practice, this article reveals that parameter estimation from a limited amount of Phase-I data, leads to excessive false alarms and unstable chart’s performances. To counter these problems, this article advocates the use of adjusted control limits to ensure that a sufficiently high proportion of the in-control conditional average time to signal value, is greater than a pre-specified level. This increasingly prevalent design of control charts is known as Guaranteed In-Control Performance (GICP). In this article, we propose an optimization design for the SPRT chart with estimated process parameters, by minimizing the expected value of the average extra quadratic loss under the GICP framework. Theoretical derivations by means of the Markov chain approach are developed in this article to evaluate the run-length properties of the SPRT chart with estimated process parameters. Results show that the overall performance of the proposed optimal SPRT chart is almost twice as good as the optimal CUSUM chart over a given range of process mean shifts. Finally, an implementation of the proposed optimal SPRT chart is demonstrated with real industrial data obtained from an epitaxial process.

Robust Point M-Scale Estimators for Monitoring the Mean of EWMA Control Chart under the Normal Process

The Exponentially Weighted Moving Average (EWMA) control chart is well known in statistical process control (SPC) for identifying small shifts in process parameters. In general, the EWMA control chart is focused on data set estimates of the process characteristics under study. In this research, for observing the process mean, we modify the control limits of the EWMA control chart by using robust point M-scale estimators under the normal process. We compare five robust point M-scale estimators proposed in SPC literature, namely Sn, Qn, MAD, Tauτ^ and FQn. The traditional control limits are evaluated and distinctions are also made based on true process control limits. The control charts performances under study are estimated via a Monte-Carlo simulation analysis by calculating the interval widths (IWs) and optimal out-of-control average run length (ARL1). From the simulation studies results, it is seen that although all proposed and traditional control limits are closely approximating the true limits of the process but the proposed control limits based on robust FQn, Tauτ^ and MAD estimators are comparatively more stringent for detecting the small shifts in process mean. Moreover the results demonstrates that at optimal size of interval L, the control charts based on MAD, Tauτ^ as well as FQn estimators demonstrate higher sensitivity in comparison to the traditional control chart based on sample standard deviation (S) and proposed control charts based on QnandSn estimators in terms of having smaller ARL1 values. The OC curves of ARL1 indicate similar findings. For the purposes of illustration, a real-life data set is analyzed that also confirms our conclusions from the simulation analysis to a certain degree.