Monitoring Process Mean Research Articles

A new omnibus SPRT chart for monitoring process mean and variability based on the average number of observations to signal

The recent development of the omnibus sequential probability ratio test (OSPRT) chart marks a significant contribution to the advancement of joint monitoring schemes. As the OSPRT chart is a variable-sample-size control chart, practitioners often wish to understand its inspection efficiency, i.e. the number of observations it samples before producing a signal. In this article, we propose two enhanced optimization designs for the OSPRT chart based on the average number of observations of signal (ANOS) and expected value of the ANOS (EANOS) metrics under deterministic and unknown shift sizes, respectively. The ANOS metric is central to our design as it perfectly combines both the average run length (ARL) and the average sample number. A comparative analysis reveals that the OSPRT chart outperforms four benchmarking control charts in terms of the ANOS and EANOS metrics. Finally, an implementation of the OSPRT chart is presented with a ball shear test dataset.

Sensitivity and reliability comparisons of EWMA mean control chart based on robust scale estimators under non‐normal process: COVID data application

AbstractRobust control charts are getting vital importance in statistical process control theory as they are insensitive to the departure from normality. Therefore, the main objective of current work is to determine the effects of non‐normal process on the Exponentially Weighted Moving Average (EWMA) control chart. To achieve this goal, the sensitivity and reliability comparisons are made under the non‐normal process by comparing five robust M‐scale estimators, suggested in literature to modify the EWMA control limits for monitoring process mean and on the basis of percentile bootstrap estimator. The paper addresses the run length (RL) distribution of a robust EWMA control chart under the non‐normal process for which the exponential distribution is used as non‐normal process. The standard deviation of RL, out‐of‐control average run length (ARL), and shift detection probabilities are examined to assess the sensitivity and reliability of robust EWMA control charts for mean of monitoring process. The results of this research indicate that the classical EWMA control chart's performance is substantially impacted by the non‐normal distribution and the proposed EWMA control charts show higher sensitivity than classical one in terms of having smaller values of out‐of‐control ARLs. A real‐life example from the medical sciences field is provided the practical usage of the proposed control charts. The simulation analysis and practical example have shown that the suggested control charts are effective in quickly monitoring the out‐of‐control process.

New extended exponentially weighted moving average control chart for monitoring process mean

In this article, we develop a new control chart based on the Exponentially Weighted Moving Average (EWMA) statistic, termed the New Extended Exponentially Weighted Moving Average (NEEWMA) statistic, designed to recognize slight changes in the process mean. We derive expressions for the mean and variance of the NEEWMA statistic, ensuring an unbiased estimation of the mean, with simulation results showing lower variance compared to traditional EWMA charts. Evaluating its performance using Average Run Length (ARL), our analysis reveals that the NEEWMA control chart outperforms EWMA and Extended EWMA (EEWMA) charts in swiftly recognizing shifts in the process mean. Illustrating its operational methodology through Monte Carlo simulations, an illustrative example using practical data is also provided to showcase its effectiveness.

Statistical Design for Monitoring Process Mean on Modified EWMA Control Chart based on Autocorrelated Data

This research endeavor is focused on establishing explicit formulas for the computation of the average run length (ARL) within the context of a moving average process characterized by exogenous variables, denoted as MAX(q,r), and subjected to exponential white noise. Additionally, we aim to conduct a comparative analysis of their performance against the exponentially weighted moving average (EWMA) and the modified exponentially weighted moving average (modified EWMA) methodologies. The evaluation of their performance will be based on metrics such as the absolute percentage relative error (APRE) and the relative mean index (RMI). Furthermore, we undertake a rigorous assessment of the accuracy of these explicit formulas in relation to ARL by considering CPU time, utilizing the numerical integral equation (NIE) method derived through the application of the Gauss-Legendre quadrature rule. This comparative evaluation is carried out for both control chart methodologies. To ascertain the efficacy of our explicit formulas approach, we apply it to two distinct datasets. The first dataset pertains to the closing price of natural gas, with the crude oil WTI price serving as the exogenous variable. The second dataset encompasses the closing stock price of KTB Public Company Limited, with daily foreign exchange rates for USD/JPY and EUR/USD as the exogenous variables. The results of applying the ARL based on the explicit formulas to these two datasets demonstrate that, under these conditions, the modified EWMA control chart outperforms the EWMA control chart.

Efficient signed-rank based EWMA and HWMA repetitive control charts for monitoring process mean with and without auxiliary information

Control charts are powerful tools to observe the presentation of the manufacturing process. Mostly, when the data in industries come from the process may follow non-normal or unknown distributions. So, the distribution-free control charts are useful in practice when the possibility model of the process productivity is unknown. In such situations, the correct selection of the sampling mechanism is beneficial for process examination. This paper proposes a nonparametric exponentially weighted moving average signed-rank (EWMA-SR) and also proposed a homogeneously weighted moving average Signed-Rank (HWMA-SR) control charts for examining the small shift in process with the help of an auxiliary variable (in the form of a regression estimator) by using an efficient plan, namely, a repetitive sampling plan. The proposal’s presentation is evaluated and matched with its complements for different symmetric distributions by using some famous run length properties including average run length, median run length, and standard deviation of run length.

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.

AUXILIARY INFORMATION BASED GENERALLY WEIGHTED MOVING AVERAGE FOR PROCESS MEAN

The univariate mean process monitoring is only used the information from the study variable. One of the univariate control chart that used to monitor the mean process is GWMA control chart. But, in this research, we need to monitor process mean using the information from the study variable and information on the adding or auxiliary variable. The enhanced control chart in this research named AIB-GWMA control chart. In this research, we also made a comparison between the GWMA and AIB-GWMA to know the sensitivity and effectiveness of these control chart. The comparison is used to know the effect of the auxiliary variable in process monitoring. The performance of these control chart is evaluated using Average Run Length with help of Monte Carlo simulation. The result of this study is AIB-GWMA has a smaller ARL than the GWMA control chart. It showed that AIB-GWMA is faster to detect a shift in mean process. In further study, we recommended to enhance the performance of the AIB-GWMA by extending the current work to the AIB-MaxGWMA, so it is possible to monitor process mean and variance simultaneously.

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.

Robust Shewhart-CUSUM design for monitoring process mean using repetitive sampling

The present study initiates the use of repetitive sampling (RS) for CUSUM type statistics discussed by Riaz et al. (2017) and couples it with the Shewhart chart (termed as RS-SEC-TCC) by targeting two objectives, i.e. robustness to non-normality and detection of small to large mean shifts quickly. The dominance of the RS-SEC-TCC over its competitors has been established using both individual and overall performance metrics. The results indicate that the RS-SEC-TCC excels in identifying small to large mean shifts in both directions for symmetric and skewed distributions. The use of asymmetric decision intervals ensures that the RS-SEC-TCC is robust to skewed process distributions by eliminating the average run length (ARL) biased problem. The RS-SEC-TCC has also surmounted the weakness of the mixed EWMA-CUSUM TCC by enabling earlier detection of the larger shift. In terms of overall performance metrics, the RS-SEC-TCC is adopted as a benchmark chart. By producing more out-of-control signals than its competitors in a real-world application, the RS-SEC-TCC proves its usefulness in practice. Consequently, the proposed RS-SEC-TCC will be a useful process monitoring tool that can be relied upon by quality and industrial engineers.

A phase II run sum chart for monitoring process mean and variability

ABSTRACT This article proposes a run sum Max chart for monitoring a process and detecting changes in mean and variability simultaneously. A Markov chain method is applied to evaluate the statistical performance of the chart by using both average run length (ARL) and expected average run length (EARL) criteria. The numerical analysis demonstrates an improved performance of the run sum Max control chart over the usual Max chart. In addition, a numerical comparison with the Max-EWMA control chart as well as with the Max chart supplemented with runs rules, reveals that the run sum Max chart outperforms these charts in the detection of moderate to large shifts in both process parameters. Furthermore, we provide practical guidance for the selection of the appropriate charting procedure, while the use of the proposed run sum Max chart in practice is illustrated via a numerical example.

On the Performance of the Extended EWMA Control Chart for Monitoring Process Mean Based on Autocorrelated Data

The extended exponentially weighted moving average (EEWMA) control chart is an instrument for detection. It can quickly identify small shifts in the process. The benchmark for the control chart's performance is the average run length (ARL). In this paper, we present the efficiency of the EEWMA control chart to detect tiny shifts when the observations are autocorrelated with exponential residuals through the explicit formulas of the ARL. The accuracy of the solution was verified with the numerical integral equation (NIE) method. After that, the ARL effectiveness of the ARL on the EEWMA control chart was expanded to compare with the traditional EWMA control chart. Finally, using two real datasets that indicate the percentages of internet users using Windows 7 and iOS, the applicability of the offered method is shown. Our findings support the notion that the EEWMA control chart performs better when using autocorrelated data to track tiny changes.

A new npCEV chart for monitoring process mean shifts based on an attribute inspection

Due to the simplicity and low cost of attribute inspection, several control charts have been proposed for employing attribute inspection to monitor the mean shifts. But these charts usually require a larger sample size to perform well as the chart. In this paper, a new npCEV chart is proposed to monitor process mean shifts based on attribute inspection in which the conditional expected value (CEV) weight method is adopted to take full advantage of the censored observations obtained from attribute inspection. The optimal design of the proposed chart is derived from optimizing average run length (ARL) properties. Several numerical experiments are conducted to investigate the performance of the proposed chart. The results demonstrate that the proposed chart is always superior to npx chart by reducing the sample size by 70% to 97% while achieving the same ARL as npx chart. In addition, the proposed chart always achieves a smaller ARL 1 than chart. Furthermore, the proposed chart outperforms chart as it achieves the same ARL as that of chart with a lower inspection cost. Finally, an industry example is given to illustrate how to simply apply the proposed chart to the manufacturing process.

Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information

The classical cumulative SUM (CUSUM) chart is commonly used to monitor a particular size of the mean shift. In many real processes, it is assumed that the shift level varies within a range, and the exact level of the shift size is mostly unknown. For detecting a range of shift size, the dual-CUSUM (DC) and dual-Crosier CUSUM (DCC) charts are used to provide better detection ability as compared to the CUSUM and Crosier CUSUM (CC) charts, respectively. This paper introduces a new mixed exponentially weighted moving average (EWMA)-DCC (EDCC) chart to monitor process mean. In addition, AIB-based EWMA-DC (EDC) and EDCC charts (namely, AIB-EDC and AIB-EDCC charts) are suggested to detect shifts in the process mean level. Monte Carlo simulations are used to compute the run length (RL) characteristics of the proposed charts. A detailed comparison of the proposed schemes with other competing charts is also provided. It turns out that the proposed chart provides better performance than the counterparts when detecting a range of mean shift sizes. A real-life application is also presented to illustrate the implementation of the existing and proposed charts.

Monitoring process mean and variability with one triple EWMA chart

Control charts are very popular quality tools used to detect and control industrial process deviations in Statistical Process Control. In the current paper, we propose a new single memory-type control chart, called the maximum triple exponentially weighted moving average chart (referred as Max-TEWMA chart), that simultaneously detects both upward and downward shifts in the process mean and/or process dispersion. The run length performance and the diagnostic ability of the Max-TEWMA control chart are compared with that of the Max-EWMA, Max-DEWMA and Max-GWMA charts, through Monte-Carlo simulations. The comparisons reveal that the proposed chart is more efficient, than the competing ones, in detecting shifts in the process mean and variability simultaneously. Furthermore, the Max-TEWMA chart provides a satisfactory overall performance for identifying a wide range of shifts in the process mean and variability. Finally, two illustrative examples are presented to explain the application of the Max-TEWMA control chart.

Multivariate control charts for monitoring process mean vector of individual observations under regularized covariance estimation

ABSTRACT Multivariate control charts are generally used in industries for monitoring and diagnosing processes characterized by several process variables. The applications of charts assume that the in-control process parameters are known and the charts’ limits are obtained from the known parameters. The parameters are typically unknown in practice, and the charts’ limits are usually based on estimated parameters from some historical in-control datasets in the Phase I study. The performance of the charts for monitoring future observation depends on efficient estimates of the process parameters from the historical in-control process. When only a few historical observations are available, the performance of the charts based on the empirical estimates of the process mean vector and covariance matrix have been shown to deviate from the desired performance of the charts based on the true parameters. We investigate the performance of the multivariate Shewhart control charts based on several shrinkage estimates of the covariance matrix when only a few in-control observations are available to estimate the parameters. Simulation results show that the control charts based on the shrinkage estimators outperform the charts based on existing classical estimators. An example involving high-dimensional monitoring is provided to illustrate the performance of the proposed Shrinkage-based Shewhart chart.

THEORETICAL AND EXPERIMENTAL INVESTIGATION OF ESTIMATING CHANGE POINT IN MULTIVARIATE PROCESSES VIA SIMULTANEOUS COVARIANCE MATRIX AND MEAN VECTOR

The identification of change points in statistical process control (SPC) data is the critical criterion for multivariate techniques when output is out-of-control condition. Therefore, monitoring all independent variables is essential and demands targeted attention to avoid errors at the systems control stage. However, estimating change-point in multivariate control charts is the main problem when these correlated quality characteristics monitor together. Therefore, we proposed a combination of an ensemble learning-based model of artificial neural networks with support vector machines to monitor process mean vector and covariance matrix shifts simultaneously to estimate the change point in a multivariable system. The performance of the final model indicated an estimated changing point with one sample over 6,000 simulated cases with a probability of 98 percent, which is a significantly high accuracy rating. Finding suggests the outcome of the project confirms that the proposed model can provide a precise estimating the change point by monitoring the mean vector and the covariance matrix simultaneously and, helps to identify those variable(s) responsible for an out-of-control condition. For further validation of the model, the performance of the proposed model has been compared with previous reported which confirms a better performance of the proposed model. Finally, the model was applied to monitor the performance of the solar hydrogen production system and the model identify the variables which have negative effects on the performance of the system.

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

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

Monitoring process mean and dispersion with one double generally weighted moving average control chart

Control charts are widely known quality tools used to detect and control industrial process deviations in Statistical Process Control. In the current paper, we propose a new single memory-type control chart, called the maximum double generally weighted moving average chart (referred as Max-DGWMA), that simultaneously detects shifts in the process mean and/or process dispersion. The run length performance of the proposed Max-DGWMA chart is compared with that of the Max-EWMA, Max-DEWMA, Max-GWMA and SS-DGWMA charts, using time-varying control limits, through Monte–Carlo simulations. The comparisons reveal that the proposed chart is more efficient than the Max-EWMA, Max-DEWMA and Max-GWMA charts, while it is comparable with the SS-DGWMA chart. An automotive industry application is presented in order to implement the Max-DGWMA chart. The goal is to establish statistical control of the manufacturing process of the automobile engine piston rings. The source of the out-of-control signals is interpreted and the efficiency of the proposed chart in detecting shifts faster is evident.

Design and Application of a Modified EWMA Control Chart for Monitoring Process Mean

The modified exponentially weighted moving average (modified EWMA) control chart is an improvement on the performance of the standard EWMA control chart for detecting small and abrupt shifts in the process mean. In this study, the effect of varying the constant and exponential smoothing parameters for detecting shifts in the mean of an autoregressive process with exogenous variables (ARX(p,r)) with a trend and exponentially distributed white noise on the standard and modified EWMA control chart was investigated. The performances of the two control charts were compared via their average run lengths (ARLs) computed by using explicit formulas and the numerical integrated equation (NIE) technique. A comparative study of the two ARL methods on the modified and traditional EWMA control charts shows that the modified schemes had better detection ability at all levels of shift size. Finally, two examples using real datasets on gold and silver prices are given to illustrate the applicability of the proposed procedure. Our findings advocate that the modified EWMA chart is excellent for monitoring ARX(p,r) processes with exponentially distributed white noise

Adaptive Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean Under Ranked Set Sampling Schemes

Adaptive Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean Under Ranked Set Sampling Schemes