Performance Of Control Charts Research Articles

A comparative analysis of mean charts assuming Weibull and generalized exponential distributions

This study discusses Shewhart control charts to monitor the mean of non-normally distributed data using extensive Monte Carlo simulations. In particular, Weibull, exponential, and generalized exponential distributions are used to conduct a systematic study. Different parameters settings are considered to evaluate the effectiveness of the Shewhart charts based on the normal approximation. The results show significant differences between the charts using generalized exponential and Weibull distributions. In particular, the generalized exponential distribution based chart achieves the desired average run length of 370 with a single threshold value across a wide range of shape parameter combinations. On the other hand, the Weibull distribution requires different threshold values depending on its shape parameter. These findings highlight the significance of the two most commonly used distributions in reliability studies and their impact on control chart performance.

Robustness of Moving Average-Exponential Weighted Moving Average Control Chart with the Light-Tailed Distribution

Control charts are the most significant statistical process control tools for ensuring industrial process reliability and efficiency. This research uses moving average – exponentially weighted moving average (MA-EWMA) control charts to investigate the dispersion characteristics. The control chart performance compares the arithmetic mean of run length (AMRL) and standard deviation of run length (SDRL) profiles of MA-EWMA and synthetic charts. Student's t-distributions are compared for dispersion processes. Finally, we present a case to show how essential control charts are in practice.

Unique exploration method of electronic component failure time and yield strengths of circular tubes under complete flexible model.

The aim of this study is to develop new exponential weighted moving average control charts based on a flexible model. These control charts created through least square and weighted least square estimators of the shape parameter of the new Kumaraswamy Pareto distribution. Exponential weighted moving average control charts based on least square and weighted least square estimators are compared for checking the performance of control charts. The results were not only explored through numerical values but also explored through half a dozen plots. The numerical results and plots exposed that the exponential weighted moving average control chart based on weighted least square estimator has better performance than the other proposed chart. Some key findings are discussed which are obtained from the comparative analysis of EWMA control charts. The simulation study of proposed charts is also reported in detail. The two data sets further demonstrate the effectiveness of the proposed charts. The reported results, for real data sets, are not only displayed in normal plots but also displayed in three-dimension plots. We recommend that the proposed method can be adapted for different types of distributions, and also suggest some future research directions. The concluding remarks are reported at the end of this manuscript.

A new control chart based on proportional hazards and frailty regression models for monitoring high‐quality processes with censored observations

AbstractImproving quality and reducing defects in various processes have led to the design of numerous control charts for monitoring count data. These charts are characterized by a large number of zero defects and are modeled with zero‐inflated distributions. Besides, it is important to consider the influence of key factors on the number of defects in some processes. This paper presents three monitoring scenarios that utilize cumulative sum (CUSUM) control charts in Phase II. These scenarios are valuable for monitoring high‐quality processes, particularly with censored observations. The first scenario uses a zero‐inflated Poisson (ZIP) distribution while the second one employs a proportional hazards regression model to account for observed variables. The third scenario combines the proportional hazards and frailty regression models to consider both observed and unobserved variables. The performance of all three control charts is evaluated by applying shifts to both parameters of the ZIP distribution separately and simultaneously. Extensive simulation studies are conducted and the effects of low, moderate, and high censoring rates are thoroughly studied. The results highlight the importance of considering influential variables for detecting early shifts, as neglecting them significantly impairs the control chart performance. Finally, a real case study, involving defect counts in printed rolls at a label printing factory, has been provided and discussed to show the application of the monitoring procedures.

Effects of measurement errors on semicircle control chart

In recent years, the impacts of measurement errors on the performance of various control charts have been well evaluated. The existing semicircle (SC) control chart has been proposed based on the assumption that there are no measurement errors. In this paper, we investigated the effect of measurement errors using the linear covariate error model with constant variance and linearly increasing variance on the performance of the SC chart. We used simulation to evaluate the performance of the SC chart, in terms of average run length (ARL), standard deviation of the run length (SDRL), median run length (MDRL), and expected average run length (EARL) metrics. The results obtained indicate that measurement errors negatively affect the performance of the SC chart and taking multiple measurements on each item or/and increasing the slope coefficient of the covariate error model can effectively reduce the adverse impact of errors on the chart’s performance. Finally, an illustrative real life example is provided to demonstrate the undesired impact of measurement errors on the detection capability of the SC chart.

Explicit Formulas of Average Run Length for Triple Moving Average Control Chart to Monitor Changes in Mean Parameter of Normal and Non-normal Process

In this research, a formula is presented for calculating the average run length of a triple moving average (TMA) control chart, which is used to measure control chart performance and determine control chart width. To apply appropriately to data in various processes, a TMA control chart is used to detect small changes in a process by finding the average value of the data over a specified period of time (w). However, determining measure control chart performance and control chart width is difficult because the formula for calculation is not created. The performance of the control charts is measured using the standard normal distribution probability properties and compared with the moving average (MA) control charts and the double moving average (DMA) control charts. The analysis results show that TMA is very effective at detecting small changes, when w is set to have a small value. The study determines that the data within the process are normally and non-normally distributed. Detecting changes on real data by TMA charts has the best detection performance compared to MA and DMA.

Transforming healthcare performance monitoring - A cutting-edge approach with generalized additive profiles: GAMs for healthcare quality monitoring.

Recent findings indicate a growing trend in data analysis within healthcare using statistical process control. However, the diversity of variables involved necessitates the expansion of new process control methodologies. This study examined control chart applications in cardiology by using generalized additive models (GAMs) to construct profiles while involving multiple healthcare variables (08). Two distinct statistics: deviation (D), and Hotelling (T2) were employed for constructing control charts: a commonly used single-variable statistic for nonparametric profiles and an innovative multivariate statistic that assesses the contribution of each element to process changes. These statistics were tested for monitoring ischemic and hemorrhagic strokes in 1-year acute stroke (369) patients at the Faisalabad Institute of Cardiology. Demographic parameters (age, gender), vascular risk factors (diabetes, family history, sleep), socioeconomic variables (smoking, location), and blood pressure are included in the model. The research includes the computation of zero-state average run length (ARL) for assessing the performance of control charts. The characteristics of the proposed profile were analyzed, such as the T2 control chart, performing better than the D chart for medium-to-large shifts (δ ≥ 0.50). On the other hand, for small δ = 0.25, the D control chart produces smaller ARL values but more significant standard deviations. While both statistics contribute to profile monitoring, T2 is more effective at identifying and tracing medium and large shifts. In conclusion, such handy tools may aid healthcare performance monitoring, especially for complicated predictor-response relationships. Monitored profiles demonstrated that GAMs are useful for healthcare analysis and process monitoring.

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.

An adaptive multivariate functional EWMA control chart

In many modern industrial scenarios, measurements of the quality characteristics of interest are often required to be represented as functional data or profiles. This motivates the growing interest in extending traditional univariate statistical process monitoring (SPM) schemes to the functional data setting. This article proposes a new SPM scheme, which is referred to as adaptive multivariate functional EWMA (AMFEWMA), to extend the well-known exponentially weighted moving average (EWMA) control chart from the univariate scalar to the multivariate functional setting. The proposed method distinguishes itself by adaptively selecting the weighting parameter in the calculation of the EWMA statistic to enhance the sensitivity of the AMFEWMA control chart across a spectrum of potential out-of-control scenarios. Such adaptability is essential in industrial processes, where multivariate functional quality characteristics are also subject to varying degrees of change. The favorable performance of the AMFEWMA control chart over existing methods is assessed via an extensive Monte Carlo simulation. Its practical applicability is demonstrated through a case study in monitoring the quality of a resistance spot welding (RSW) process in the automotive industry through online observations of dynamic resistance curves, which are associated with multiple spot welds on the same car body and are recognized as highly representative of the RSW process quality. The proposed method is implemented in the R package funcharts, available online on CRAN.

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.

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.

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.

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.