Small Process Shifts Research Articles

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.

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.

A simple procedure to improve the performance of Klein's 2‐of‐2 run rule in the Shewhart X¯$\bar{X}$ control chart

AbstractSupplementary run‐rules have been used since the 1950s to improve the performance of the basic Shewhart control chart. A procedure known as Klein's 2‐of‐2, a simple and efficient supplementary rule, signals that the process is out‐of‐control only when two sequential sample averages are observed above the upper control limit (UCL) or below the lower control limit (LCL). The use of this rule results in a substantial reduction of the average run length (ARL) in detecting small process shifts when compared to the traditional control chart. However, it presents a poor performance of the out‐of‐control ARL for moderate to large process shifts (the converges to 2 for large shifts in the mean). In order to minimize this issue, some authors introduce additional control limits to delimit decision zones in relation to deciding whether the process is in control or out‐of‐control. Despite a better performance for moderate‐to‐large process shifts, the process complexity is also higher. In this paper, we include a simple procedure (with no additional control limits) in relation to the 2‐of‐2 rule by examining if all values of each unit of the sample are beyond the control limits whenever its average is beyond the control limits. The new procedure has a similar performance in terms of ARL for small shifts in the mean and a better performance for moderate‐to‐large shifts (the now converges to 1) when compared to the standard 2‐of‐2 rule (where the converges to 2).

Optimized control charts using indifference regions

In statistical process monitoring, the CUSUM and EWMA control charts have received considerable attention because of their remarkable ability to detect small sustained shifts. In practice, small process variation and shifts are anticipated beforehand in many processes, so the focus should be on detecting a moderate to a large shift. The aforementioned charts identify minor changes in population parameters as out-of-control scenarios; thus, “small” and potentially practically insignificant shifts are producing signals. To counteract this, both charts are amended to accommodate an indifference region by optimizing the detection of a shift at the outer boundaries of the indifference region. The results show that the adapted CUSUM and EWMA monitoring schemes yield comparable results. On nearly all occasions, the CUSUM chart outperforms the EWMA chart, yet the EWMA chart seems more robust and is easier to interpret. Furthermore, we provide two practical examples to illustrate the use-case of optimized charts to mitigate small (unimportant) variations, such as seasonality and modest temporary shifts. Overall, this work provides a general approach tailored to practice in quality control, e.g., as prescribed by ISO standards. It also answers a recent call in statistical process monitoring literature to reconsider the design of control charts.

Generalized new exponentially weighted moving average control charts (NEWMA) for monitoring process dispersion

PurposeThis work aims to focuse on improving the performance of the new exponentially weighted moving average (NEWMA) scheme for monitoring process dispersion. The authors use the generalized time-varying fast initial response (GFIR) to further enhance the detection ability of variability NEWMA control charts at the process startup. The performance of the proposed chart and other schemes discussed in this article are evaluated; and compared using the average run length (ARL) and standard deviation run length (SDRL) measures. It is observed that the ARL of the proposed scheme is quicker in detecting small and moderate shifts in the process dispersion than its counterparts. The real-life application of the proposed scheme is presented.Design/methodology/approachThe dynamic parameter of GFIR is used to enhance the detection ability of variability NEWMA control charts. The authors apply GFIR to the control limit of variability NEWMA scheme. This further narrows the control limit, hence enabling it to swiftly detect small and moderate changes in process dispersion.FindingsThe authors present the performance comparisons by examining the ARL properties of the proposed chart and its counterparts. The performance comparison shows that the proposed chart is highly sensitive in detecting small and intermediate process shifts. The real-life application presented also supports the study’s conclusion from the simulation studies. The performance comparison of the proposed chart and its counterparts shows that the proposed scheme is efficient in detecting process abnormalities, especially at the startup.Originality/valueIn terms of the control limits, the proposed chart is the generalized variability NEWMA control chart in which all the previously proposed NEWMA variant schemes can be obtained. Also, the newly proposed control scheme is more efficient in detecting small or moderate persistent shifts in the process dispersion.

The Inertial properties of EWMA control charts

Since exponentially weighted moving average (EWMA) control charts combine information from the current and past samples, they are relatively more effective in detecting small process shifts than Shewhart control charts. A prevailing problem in control charts is the property of not responding quickly to process shifts, that is, showing statistical control of the process while a shift has occurred in the process parameter(s). This property of control charts, which is referred to as “inertia”, is an important issue in control charting and has been a major concern to engineers and statisticians. This study surveys the inertial properties of EWMA control charts in detail. First, the distribution of EWMA chart statistic and signal resistance probability (SRP) are studied for many different cases when there are undetected transient shifts. All measures are calculated and evaluated via a Markov chain approach. Then, an optimal scheme is proposed to minimize the out-of-control average run length (ARL) for a specified shift, subject to SRP constraints. The results reveal that the inertia can be sometimes a serious problem in EWMA control schemes that should not be overlooked. It is shown that an appropriate scheme based on both ARL and SRP measures could be useful for processes that may have sustained and/or transient out-of-control states.

Optimal statistical design of the double sampling np chart based on expected median run length

Double sampling (DS) control charts are widely regarded as an effective process monitoring tool owing to their remarkable properties, such as the ability to detect small and moderate process shifts efficiently with the reduced sample size. Since the shape of the run length distribution is highly right-skewed for the process small shift size and becomes almost symmetric when the process shift size is large, the use of median run length (MRL) as a performance measure is therefore more representative. Existing works on the DS np chart construction were performed by taking an approach that the shift size of the process fraction nonconforming is assumed to be known. However, the shift size of the fraction nonconforming is usually unknown by the quality practitioners in practice. Herein, to address this issue, the expected median run length (EMRL) has been suggested as a performance measure for the unknown shift size. This paper suggests an optimal design procedure for the DS np chart based on the EMRL criterion. An example is provided to illustrate the construction of the EMRL-based DS np chart. The DS np chart is compared with a competing chart based on the EMRL criterion. Findings obtained reveal that when the shift size is unknown, the EMRL is an alternative performance measure for the DS np chart, with greater sensitivity observed for the DS np chart in contrast to the standard np chart for detecting a wide range of shifts.

An enhanced sum of squares generally weighted moving average chart based on auxiliary information for process monitoring

The AIB-SSEWMA chart is an auxiliary information-based (AIB) sum of squares exponentially weighted moving average (SSEWMA) chart using correlated auxiliary information to effectively monitor the shifts in the process mean and/or variability of a normally distributed process. The main focus of this study is proposed to combine an AIB sum of squares generally weighted moving average (AIB-SSGWMA) chart with the properties of the GWMA chart into an AIB-SSEWMA chart. Numerical simulations indicate that the AIB-SSGWMA chart based on average run lengths (ARLs) performs uniformly better than its counterparts, such as the AIB-SSEWMA, SSGWMA, and SSEWMA charts in detecting small process mean and/or variability shifts. In addition, the proposed chart is sensitive to small upward shifts in the mean as well as variability, as compared to the existing AIB-MaxGWMA chart. An example is used to illustrate the efficiency of the proposed AIB-SSGWMA chart in detecting small process shifts.

Optimal design of an improved X¯ and R control chart for joint monitoring of process location and dispersion

Enhancing the detection power of control charts for detecting small to moderate process changes is always the focus of attention in academia. To improve the detection ability of conventional [Formula: see text] and R control charts, an improved joint [Formula: see text] and R chart, which combines the ordinary [Formula: see text] and R charts with runs rules of the type ‘ r out of m’, is proposed to monitor the process location and dispersion simultaneously. A finite Markov chain imbedding approach is employed to develop the resulting control scheme. A comparative study is conducted to investigate the performance of the proposed chart in terms of the out-of-control average run length. The statistical performance of the suggested chart when the process parameters are estimated is also evaluated. The numerical results indicate that (1) the proposed chart improves the detection ability of traditional [Formula: see text] and R charts in detecting small to moderate process shifts; (2) the suggested scheme performs better than the EWMA and CUSUM schemes in detecting large process fluctuations. Furthermore, when specific values of r and m are selected, the statistical performance of the proposed chart for detecting small shifts is close to or even better than that of its competitors; (3) the run length performance of the proposed chart is greatly affected by parameter estimation, especially for small process shifts.

The combined Shewhart-CUSUM sign charts

A Shewhart control chart is highly effective for detecting large process shifts, however, it is relatively less sensitive to the small shifts. A CUSUM chart is more efficient than a Shewhart chart for detecting small process shifts but it is inferior to that for detecting the large ones. This paper proposes the nonparametric combined Shewhart-CUSUM (CSC) control charts based on the sign statistic. By appropriately choosing the design parameters, a CSC chart exhibits a trade-off statistical performance between that of the Shewhart and CUSUM sign charts. That is, its performance lies between the performances of the Shewhart and CUSUM sign charts for detecting a process shift of any size. The expressions for the zero-state and steady-state average run lengths of the CSC chart are obtained using a Markov chain approach. An example illustrating the implementation of this chart is provided.

One-sided 4-out-of-5 Run Rules Charts for the Multivariate Coefficient of Variation in the Finite Horizon Process

Quality improvement has been receiving great attention in industries. In recent years, the finite horizon process is commonly encountered in industries due to flexible manufacturing production. Past research works on finite horizon process monitoring are still limited. Because of this, one-sided 4-out-of-5 run rules charts are proposed to monitor the multivariate coefficient of variation in a finite horizon process. The performance measures of the proposed charts are derived using the Markov-chain approach. The proposed schemes can serve as a framework for practitioners who wish to perform process monitoring easily and efficiently. Numerical comparisons between the proposed and existing charts have been made, in terms of the truncated average run length and the expected truncated average run length criteria. The findings reveal that the proposed charts outperform the existing charts for detecting small and moderate process shifts in the finite horizon process.

Performance assessment of surface-guided radiation therapy and patient setup in head-and-neck and breast cancer patients based on statistical process control.

To assess the effectiveness of SGRT in clinical applications through statistical process control (SPC). Taking the patients' positioning through optical surface imaging (OSI) as a process, the average level of process execution was defined as the process mean. Setup errors detected by cone-beam computed tomography (CBCT) and OSI were extracted for head-and-neck cancer (HNC) and breast cancer patients. These data were used to construct individual and exponentially weighted moving average (EWMA) control charts to analyze outlier fractions and small process shifts from the process mean. Using the control charts and process capability indices derived from this process, the patient positioning-related OSI performance and setup error were analyzed for each patient. Outlier fractions and small shifts from the process mean that are indicative of setup errors were found to be widely prevalent, with the outliers randomly distributed between fractions. A systematic error of up to 1.6 mm between the OSI and CBCT results was observed in all directions, indicating a significantly degraded OSI performance. Adjusting this systematic error for each patient using setup errors of the first five fractions could effectively mitigate these effects. Process capability analysis following adjustment for systematic error indicated that OSI performance was acceptable (process capability index Cpk = 1.0) for HNC patients but unacceptable (Cpk < 0.75) for breast cancer patients. SPC is a powerful tool for detecting the outlier fractions and process changes. Our application of SPC to patient-specific evaluations validated the suitability of OSI in clinical applications involving patient positioning.

Using the Quality Control to Determine the Factors of Failure Operation in Cement Sector

Quality control technic is an important method of designing a strategic plan for many productive industries. The Shewhart control chart is that it uses only the information observation. Cumulative sum (CUSUM) and Exponentially weighted moving average (EWMA) two very effective alternatives to the Shewhart control chart may be used when small process shifts are of interest. This paper discusses data on failure time of five cement mills in Sulaimani Mass cement factories, used, the reliability methods for analysis the failure time. The quality of the products manufactured in this factory has been estimated according to a quality control process through the use of specific control chart one of the chart Exponentially Weighted Moving Average (EWMA) chart. Whereas reliability concerns functioning under specified time. So, it can be said that the reliability is a relation between production with expected period time in quality. This study investigates the implementation of reliability and quality control. The findings indicate that factors that affecting the function of mills which will increase the failure rate of mills and lower their life span, through which quality of products will be affected.

Auxiliary information‐based maximum generally weighted moving average chart for simultaneously monitoring process mean and variability

AbstractAn auxiliary information‐based (AIB) maximum exponentially weighted moving average (MaxEWMA) chart has been proposed to simultaneously monitor both increases and decreases in the process mean and/or variability, called the AIB‐MaxEWMA chart, which is superior to the existing MaxEWMA chart. In this paper, we propose the AIB maximum generally weighted moving average chart, called the AIB‐MaxGWMA chart, to further enhance the sensitivity of the AIB‐MaxEWMA chart. Numerical simulation studies indicate that the AIB‐MaxGWMA chart is sensitive to small shifts in the process mean and/or variability. The performance of the AIB‐MaxGWMA chart based on average run lengths (ARLs) also outperforms than its counterparts including AIB‐MaxEWMA, MaxGWMA and MaxEWMA charts. An example is used to illustrate the efficiency of the proposed AIB‐MaxGWMA chart in detecting small process shifts.

Quality Control of Labelstock Using Fuzzy Exponentially Weighted Moving Average (FEWMA) Control

Production development in the industrial era sues the company to continue creating the best product for consumer society. Product quality is the main consideration for the consumer in selecting products. This is certainly driving the company to maintain the quality of its products. Therefore, companies need to control the quality of production so their products can fulfill the standards set. One of the ways that can be used to control quality is using the control chart. The most frequently used control chart is the Shewhart type control chart. However, the Shewhart control chart can only be used for crisp data, while for data containing ambiguity, a fuzzy control chart can be applied. In this research, the thickness of the label stock glue quality on HVS P 60 is monitored using the fuzzy control chart. The type of fuzzy control chart used in this study is the FEWMA (Fuzzy Exponentially Weighted Moving Average) control chart. This control chart was chosen because it can monitor data that contains ambiguity and data with small process shifts. In this research, rigorous inspection (α-cuts) was used to detect shifting data. Based on the analysis, it was found that the weight (λ) 0.1 is the optimum weight value in detecting a process shift in the thickness of the label stock glue. Through the cause and effect diagram, four factors that cause the out of control data was found, namely machine, method, man, and material.

An improved Hotelling's T2 chart for monitoring a finite horizon process based on run rules schemes: A Markov‐chain approach

AbstractQuality improvement has been receiving great attention in industries. In recent years, the finite horizon process is commonly encountered in industries due to flexible manufacturing production. Past research works on finite horizon process monitoring are still limited. Because of this, three run rules Hotelling's T2 charts are proposed to monitor a finite horizon process. The performance measures of the proposed charts are derived using the Markov‐chain approach. The proposed schemes can serve as a framework for quality engineers who wish to perform process monitoring easily and efficiently. Numerical comparisons between the proposed and existing Shewhart (SH) T2 charts have been made. The statistical performance measures were investigated in this article. The findings reveal that the proposed charts outperform the SH T2 chart for detecting small and moderate process shifts in a finite horizon process. The illustration of the run rules (RR) T2 chart is shown on a real manufacturing dataset in a finite horizon process.

A New Sum of Squares Exponentially Weighted Moving Average Control Chart Using Auxiliary Information

The concept of control charts is based on mathematics and statistics to process forecast; which applications are widely used in industrial management. The sum of squares exponentially weighted moving average (SSEWMA) chart is a well-known tool for effectively monitoring both the increase and decrease in the process mean and/or variability. In this paper, we propose a novel SSEWMA chart using auxiliary information, called the AIB-SSEWMA chart, for jointly monitoring the process mean and/or variability. With our proposed chart, the attempt is to enhance the performance of the classical SSEWMA chart. Numerical simulation studies indicate that the AIB-SSEWMA chart has better detection ability than the existing SSEWMA and its competitive maximum EWMA based on auxiliary information (AIB-MaxEWMA) charts in view of average run lengths (ARLs). An illustrated example is used to demonstrate the efficiency of the proposed AIB-SSEWMA chart in detecting small process shifts.

A hybrid homogeneously weighted moving average control chart for process monitoring

AbstractSeveral modifications and enhancements to control charts in increasing the performance of small and moderate process shifts have been introduced in the quality control charting techniques. In this paper, a new hybrid control chart for monitoring process location is proposed by combining two homogeneously weighted moving average (HWMA) control charts. The hybrid homogeneously weighted moving average (HHWMA) statistic is derived using two smoothing constants λ1 and λ2. The average run length (ARL) and the standard deviation of the run length (SDRL) values of the HHWMA control chart are obtained and compared with some existing control charts for monitoring small and moderate shifts in the process location. The results of study show that the HHWMA control chart outperforms the existing control charts in many situations. The application of the HHWMA chart is demonstrated using a simulated data.

A Deep Learning Approach for the Identification of Small Process Shifts in Additive Manufacturing using 3D Point Clouds

Additive manufacturing (AM) refers to a family of manufacturing technologies that fabricate parts by joining materials layer by layer. It has a high level of flexibility in design and manufacturing, which provides a unique opportunity for producing parts with complex geometries that are not feasible using conventional subtractive manufacturing. Due to the sensitivity of AM to machine settings and process conditions, process shifts are oftentimes incurred in AM, which introduce defects and impact the quality and reliability of AM products. As such, it is critical to identify AM process shifts, especially at the incipient stage, for quality assurance. Most existing approaches, however, are limited in their ability to detect small AM process shifts. In this study, a structured light scanner is used to capture 3D point clouds from printed surfaces. A deep learning framework is introduced to extract useful information from point cloud data to delineate geometric variations of the printed surface and detect process shifts. The research methodology is evaluated and validated using both simulation studies and real-world applications. Experimental results have shown that the deep learning approach is with remarkable ability in detecting small process shifts and it outperforms convolutional neural network models when large amounts of training samples are not available. The proposed framework has a strong potential to be used for in-situ layer-wise monitoring of AM processes for quality control and the detection of cyber-physical attacks.

Enhanced generally weighted moving average variance charts for monitoring process variance with individual observations

AbstractThe generally weighted moving average variance (GWMAV) chart is effective in detecting increases in process variance when only individual observations are available. Recently, the combination of exponentially weighted moving average and cumulative sum (CUSUM) charts for the effective detection of small process shifts has emerged. Inspired by the features, we propose the mixed GWMAV‐CUSUM chart and its reverse order CUSUM‐GWMAV to enhance the detection ability of the GWMAV chart and compare with the existing counterparts. Numerical simulation revealed that the mixed GWMAV‐CUSUM and mixed CUSUM‐GWMAV charts are sensitive to small upward shifts in the process variance and efficient structures compared with their prototypes and their separate charts, that is, GWMAV and CUSUM charts. An industrial dataset was used to illustrate the application of the proposed mixed charts.