Performance Of Chart Research Articles

Monitoring paired observations with complete, missing and censored data by control charts

This study analyzes the performance of control charts using statistics to monitor the stability of the mean in paired data, in the presence of missing or censored data. To determine the control limits, extensive simulations of paired data with a normal distribution are conducted to establish an empirical distribution under different correlation scenarios, sample sizes, and percentages of censored or missing data. After calculating the control limits, additional simulations are carried out to assess the out of control average run length to detect changes in the mean. We employ the paired t-test and the paired Wilcoxon test when the population is normal as they obtain similar results, however if they differ significantly, thus it is an indication of a potential violation of the hypothesis of normality in the data. Additionally, we evaluated some proposals to minimize the negative effect of data displaying censoring and missing values. We found that the results using parametric and non-parametric approaches are practically similar when the data is complete; the non-parametric approach being more affected by missing and censored data. A practical example monitoring the most-streamed songs in the US illustrates the proposed procedure.

Multiple ‘memory-based’ schemes for monitoring Maxwell distributions with measurement errors

In many industrial applications, Maxwell is used as a life distribution to describe the life characteristics of a product. However, the accuracy of the life test results is usually affected by factors such as the way the operator operates and the accuracy of the measuring instrument, which in turn affects the reliability of the test results. Measurement errors can adversely affect the inspection results. In this paper, we focus on solving the problem of measurement error when Maxwell distribution is used as a lifetime distribution. This paper focuses on Shewhart, double exponentially weighted moving average (DEWMA) and homogeneously weighted moving average (HWMA), exponentially weighted moving average (EWMA), and generally weighted moving average (GWMA) control charts with measurement error models are presented, respectively. In addition, corresponding control charts corrected for multiple measurements are provided to minimize the effects of measurement errors and ensure that the Maxwell distribution's lifetime characteristics are accurately monitored. Sometimes, relying only on good zero-state run length metrics can be misleading. Therefore, we used a variety of metrics to assess the performance differences between these control charts, including multiple zero-state run length metrics and conditional delay expectations (CED). Meanwhile, through Monte Carlo simulations, we investigate the effects of relevant parameters on the performance of the control charts. Finally, the effectiveness of these control charts in practical applications is further verified through two real examples.

Enhanced Designs for the Multi‐Region Run Sum X¯${{\bar{X}}}$ Control Chart Based on the Median Run Length Metric

ABSTRACTExtensive research has focused on the multi‐region run sum control chart, a sophisticated procedure for monitoring process mean shifts, particularly utilising the average run length (ARL) metric. Nevertheless, the skewed nature of the run‐length distribution can render the ARL metric misleading, and occasionally ineffective, when assessing a control chart's performance. The employment of the ARL metric in designing the run sum chart can erode practitioners’ confidence. This might be due to its complexities and difficulties in interpreting the complicated statistical concepts involved. To address this issue, the median run length (MRL) metric is proposed in this paper, which has been endorsed by various researchers due to its robustness towards skewness in the run‐length distribution. We design two novel optimal run sum charts utilising MRL and expected MRL (EMRL) metrics, under the assumptions of deterministic and unknown shit‐size scenarios, respectively. Specifically, the performances of the 4‐region and 7‐region run sum charts in both the zero‐state and steady‐state scenarios are developed using the Markov chain approach. Our comparative studies reveal that the proposed MRL‐ and EMRL‐optimal run sum charts surpass the optimal Shewhart and exponentially weighted moving average (EWMA) charts in terms of their average detection speeds, especially for moderate to large levels of process mean shifts. Practical examples from different industries are demonstrated using the proposed optimal run sum chart.

The Efficiency of the New Extended EWMA Control Chart for Detecting Changes Under an Autoregressive Model and Its Application

Control charts are frequently used instruments for process quality monitoring. Another name for the NEEWMA control chart is the new extended exponentially weighted moving average (new extended EWMA) control chart. The lower control limit (LCL) and upper control limit (UCL) are equally spaced from the center line, giving it a symmetrical design. Because of its symmetry, the NEEWMA chart is very good at identifying even the tiniest changes in operation by detecting deviations from the target in both upward and downward directions. This study derives an explicit formula for the average run length (ARL) of the NEEWMA control chart based on the autoregressive (AR) model with exponential white noise. The focus is on the zero-state performance of the NEEWMA control chart, which is derived using explicit formulas. Banach’s fixed-point theorem was used to prove existence and uniqueness of this formula. The accuracy of this formula is validated by comparing it to the numerical integral equation (NIE) method using percentage accuracy (%Acc). The results show that the NEEWMA control chart is more efficient than the ARL evaluated by the NIE method, particularly regarding computation time. The performance of the NEEWMA control chart is compared with the EWMA and extended EWMA control charts by evaluating both the ARL and standard deviation run length (SDRL). The NEEWMA control chart outperforms the others in detection performance, followed by the extended EWMA and EWMA control charts. Further verification of its superior performance is provided through comparisons using the average extra quadratic loss (AEQL) and the performance comparison index (PCI), which confirm that it outperforms both the EWMA and extended EWMA control charts across various parameters and shift sizes. Finally, an illustrative example using real-life economic data demonstrates its efficiency.

Supply chain risk transmission monitoring based on graphic evaluation and review technique.

In the supply chain context, risk events can accumulate, amplify, and mutate as they spread through the supply chain network structure. This can lead to significant losses for supply chains and global businesses. Therefore, monitoring supply chain risk is crucial to ensure the smooth operation of the supply chain. To address this issue, our study focuses on the DongNan automobile manufacturing supply chain and examines the monitoring of lead time risk. We use the graphic evaluation and review technique (GERT) to characterize the topology of the risk transmission network in the supply chain and construct a supply chain risk transmission model. We then use the change-point control chart to monitor risk factors, specifically delayed lead time. Our study includes a case study that demonstrates the effectiveness of the change-point control chart in signaling and accurately estimating the change point and out-of-control stage in terms of performance indices. We also investigate the impact of mis-specified risk function parameters on the chart's performance, finding that it remains relatively stable. Overall, the change-point control chart is an effective tool for monitoring supply chain risk, and its monitoring effect is relatively stable.

Covariance monitoring of multimode multivariate IoT devices data

This study introduces a novel multimode online monitoring approach that employs a covariance test for the analysis of multimode, high-dimensional, and non-normally distributed data from Internet of Things (IoT) devices. The methodology involves estimating the covariance matrix using a linear shrinkage estimation method, followed by the calculation of a sparse principal eigenvalue test statistic based on the estimated covariance matrix. Additionally, an Exponentially Weighted Moving Average (EWMA) control chart is designed, incorporating a sliding window and a mode transition constraint parameter, referred to as the MMEWMA chart. To evaluate the performance of the MMEWMA control chart, Monte Carlo simulations are conducted under various conditions, including dimensionality, data distribution, drift size, in-control sample size, and mode transition parameters. The results demonstrate that the proposed MMEWMA control chart significantly outperforms other covariance test-based control charts, particularly in scenarios characterized by substantial drift and non-normally distributed data. Furthermore, the method’s effectiveness is validated through the analysis of real IoT device data sourced from wind turbines.

Designing a variable control chart for a two-stage production process

In this paper, a variable chart has been proposed to study a two-stage serial production process. Measurements of quality characteristics of products processed at each stage are assumed to be independent and follow normal distribution. In order to evaluate performance of the control chart, two cases of equal shifts in both the stages and unequal shifts were considered and results were presented accordingly. The necessary measures are given to calculate the average run length (ARL) for shifted processes. The tables of ARLs are presented for equal and different sample sizes at first- and second- stage. Performance of the proposed control chart is presented using a simulation study.

Adaptive Risk‐Adjusted Weighted CUSUM Chart for Monitoring Surgical Performance

ABSTRACTDetecting changes in surgical performance early is important to improve the quality of surgery. In recent years, numerous risk‐adjusted control charts have been applied to monitor surgical performance. The conventional risk‐adjusted cumulative sum (CUSUM) charts need to be preset with the out‐of‐control odds ratio, and the performance of the control charts can be significantly affected by the actual change level. To effectively monitor changes in surgical performance, this paper proposes a novel adaptive risk‐adjusted weighted cumulative sum (RA‐WCUSUM) chart for monitoring binary surgical outcomes, where a weighting function based on standardized residuals is applied to the log‐likelihood ratio statistic. The proposed method is compared with several competing charts through simulation, and the simulation results show the superiority of the proposed method. A cardiac surgery dataset is used to demonstrate the application of the proposed method.

A Control Chart for the Joint Monitoring of Mean and Variance With Klein's Supplementary Rule

ABSTRACTSupplementary run rules have been employed since the 1950s to enhance the performance of control charts, such as the control chart, which aims to control the process mean, or control chart, which aims to control the process variance. One simple, effective, and popular suggestion is Klein's 2‐of‐2, which signals an out‐of‐control process only when two sequential sample averages are observed above the upper control limit or below the lower control limit. We propose to implement Klein's 2‐of‐2 for a more complex control chart, the joint control chart, which aims to simultaneously monitor the mean and the variance of a process. Compared with the traditional control chart, using this rule for the control chart reduces the average run length (ARL) and standard deviation of the run length (SDRL) for detecting small process shifts while maintaining high applicability owing to the ease of use in employing the 2‐of‐2 rule in practical environments. Klein's run rule was implemented in the control chart through a 15‐state Markov chain, and its performance was compared with the basic control chart as well as the exponentially weighted moving average (EWMA) chart, known to have excellent capabilities in detecting small process average shifts at the cost of a more complex control scheme. The newly proposed Klein control chart demonstrated superior performance compared to the traditional control chart and competitive performance even against the more complex joint EWMA control chart.

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.

Comparison of stability analysis methods for safe design of volcanic rock slope

The performance of the stability chart (SC), limit equilibrium (LE), and finite element (FE) methods for stability analysis of weathered volcanic rock slopes under static and earthquake loads is not fully understood. This research aimed to evaluate the performance of the SC, LE, and FE methods for slope stability analyses by studying a case of a weathered volcanic rock slope at the Leuwikeris Dam diversion tunnel in Indonesia. Site characterisations were carried out to obtain the input parameters for the static and pseudostatic slope stability analyses. The results showed that using various search methods of failure surface and the suggested optimum number of finite elements, multiple non-circular failure surfaces were predicted from the LE and FE methods that were not anticipated in the initial slope design based on the SC method. The location and shape of the failure surfaces from the LE method agreed with those from the FE method. The difference between the Fs values from the static LE analysis and those from the static FE analyses was less than 14%, but the discrepancy increased up to 78% in the pseudostatic analyses. This study highlights the importance of validating the results from one method with the other methods to prevent slope failures.

Sum of defects (SOD) chart for joint monitoring of the two parameters of a zero-inflated Poisson process

Rapid technological advancements and automation in today's world have led to many high quality manufacturing processes, where most of the products are free from defects. The defects data from high quality processes are commonly modeled by twoparameter zero- inflated Poisson (ZIP) distribution. Most of the existing control charting procedures for ZIP processes are developed assuming that all the manufactured units are inspected one by one, and most often separate control charts are proposed for monitoring the two parameters of a ZIP process. However, joint monitoring of the two parameters in a single chart can offer significant operational advantages because one needs to focus on a sole chart and a single charting statistic. Again, in many manufacturing set ups 100% inspection may not always be feasible. Recently, a few one-chart schemes with group inspection of small samples are reported in literature, and all these schemes require estimation of the two parameters based on accumulated samples till the current sampling stage for computation of the monitoring statistics. This accumulation of samples introduces several limitations in these schemes. In this paper, probability mass function and the cumulative distribution function (cdf) of the sum of defects (SOD) in a sample of size are defined, and a control chart for SOD is proposed. Both the parameters of a ZIP process can be jointly monitored using the SOD chart. Again, since no accumulation of the samples is required for application of the SOD chart, it is free from all limitations of the existing one-chart schemes with group inspection. Two case studies based on past data are presented. The performance of the SOD chart is found to be very encouraging.

Novel color vision assessment tool: AIM Color Detection and Discrimination.

Color vision assessment is essential in clinical practice, yet different tests exhibit distinct strengths and limitations. Here we apply a psychophysical paradigm, Angular Indication Measurement (AIM) for color detection and discrimination. AIM is designed to address some of the shortcomings of existing tests, such as prolonged testing time, limited accuracy and sensitivity, and the necessity for clinician oversight. AIM presents adaptively generated charts, each a N×M (here 4×4) grid of stimuli, and participants are instructed to indicate either the orientation of the gap in a cone-isolating Landolt C optotype or the orientation of the edge between two colors in an equiluminant color space. The contrasts or color differences of the stimuli are adaptively selected for each chart based on performance of prior AIM charts. In a group of 23 color-normal and 15 people with color vision deficiency (CVD), we validate AIM color against Hardy-Rand-Rittler (HRR), Farnsworth-Munsell 100 hue test (FM100), and anomaloscope color matching diagnosis and use machine learning techniques to classify the type and severity of CVD. The results show that AIM has classification accuracies comparable to that of the anomaloscope, and while HRR and FM100 are less accurate than AIM and an anomaloscope, HRR is very rapid. We conclude that AIM is a computer-based, self-administered, response-adaptive and rapid tool with high test-retest repeatability that has the potential to be suitable for both clinical and research applications.

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.

Performance evaluation of extended EWMA control chart in the presence of measurement error

In any manufacturing or service industry, substantial effort is made to keep a process under control. However, factors such as measurement error are bound to create distortions. Many researchers have studied the effect of measurement error on various types of control charts including the EWMA control chart. In this paper, we study the effect of measurement error on the competency of the extended EWMA control chart. We examine the performance of the chart in the case of a shift in mean taking into account the model with linear covariates. The consequence of making multiple measurements on each sampled unit is also investigated. Last but not the least, we examine the case of linearly increasing variance. Through a simulation study, we demonstrate that the performance of the chart for detecting a shift in the mean is substantially reduced in the presence of measurement error. The important finding, however, is that, in spite of the existence of measurement error, the EEWMA control chart performs better than the EWMA control chart. A practical example is provided to elucidate this finding.

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.