Cumulative Sum Charts Research Articles

13. Risk Adjusted Cumulative Sum chart methodology to monitor of free flap failure rates in the QOMS national audit

13. Risk Adjusted Cumulative Sum chart methodology to monitor of free flap failure rates in the QOMS national audit

RTK ramp faults detection and exclusion by the hybrid control chart

For real-time kinematic (RTK) positioning in intelligent transportation systems (ITS), the slow-growing faults detection and exclusion (FDE) in carrier phase measurements with time-correlated satellite navigation data poses a significant challenge. In response, we propose the short-baseline RTK Receiver Autonomous Integrity Monitoring (RTK-RAIM), which utilizes a hybrid control chart with a colored Kalman filter for detecting small yet persistent faults. The hybrid control chart incorporates the windowed multivariate homogeneously weighted moving average and dual multivariate cumulative sum charts to accelerate fault detection. The fault exclusion is conducted using the solution separation. Experimental validation using static data and dynamic data in suburban and urban areas demonstrates the efficacy of RTK-RAIM in detecting ramp faults with time-correlated noise. Results show that Colored KF can attenuate the detection metrics in the fault-free case when measurements are time-correlated. The hybrid control chart, operating in an open environment, has the ability to detect carrier phase slope faults with a high probability, even when the slope is as small as 0.01cycle/s. It can also detect carrier-phase ramp faults whose gradient are 0.1cycle/s in an urban area. By enhancing the detection ability of FDE in RTK, this hybrid-control-chart-based RAIM promotes safer and more dependable performance in future ITS applications.

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

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

A Weibull process monitoring with AEWMA control chart: an application to breaking strength of the fibrous composite

In recent times, there has been a growing focus among researchers on memory-based control charts. The Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) charts and the adaptive control charting approaches got the attention. Control charts are commonly employed to oversee processes, assuming the monitored variable follows a normal distribution. However, it's worth noting that this assumption does not hold true in many real-world situations. The use of the algebraic expression for normalization, which can be used for all kinds of skewed distributions with a closed-form distribution function, using the proposed continuous function to adapt a smoothing constant, motivates this study. In the present manuscript, we design an EWMA statistic-based adaptive control chart to monitor the irregular variations in the mean of two parametric Weibull distribution and use Hasting approximation for normalization. The adaptive control charts are used to update the smoothing constant according to the estimated shift. Here we use the proposed continuous function to adapt the smoothing constant. The average run length and standard deviation of run length are calculated under different parameter settings. The effectiveness of the proposed chart is argued in terms of ARLs over the considered EWMA chart through Monte-Carlo (MC) simulation method. The proposed chart is examined, followed by a real data set to demonstrate the design and application procedures.

A new phase Ⅱ risk-adjusted CUSUM chart for monitoring surgical performance

In recent years, the use of risk-adjusted control charts for monitoring surgical performance has gained significant attention among researchers. However, many existing monitoring methods only consider patient risk factors that impact surgical performance, and fail to account for other risk factors, such as the surgeon's level of experience. This study presents a new phase II risk-adjusted cumulative sum (CUSUM) chart based on the score test statistic, which includes a risk-adjusted mortality model with dummy variables. This new control chart not only monitors shifts in location and scale parameters related to surgical performance, but also accounts for changes in the risk distribution of the patient population by using dynamic probability control limits (DPCLs). The proposed method is further elaborated and validated through simulations in a practical context, and simulation results indicate that this method is more sensitive to small abnormal changes.

Inspecting the quality of care: a comparison of CUSUM methods for inter hospital performance

During the past 14 years, a clinical audit has been used in the Netherlands to provide hospitals with data on their performance in colorectal cancer care. Continuous feedback on the quality of care provided at each hospital is essential to improve patient outcomes. It is unclear which methods should be used to generate most informative output for the identification of potential quality issues. Our aim is to compare the commonly employed funnel plot with existing cumulative sum (CUSUM) methodology for the evaluation of postoperative survival and hospital stay outcomes of patients who underwent colorectal surgery in the Netherlands. Data from the Dutch ColoRectal Audit on 25367 patients in the Netherlands who underwent surgical resection for colorectal cancer in 71 hospitals between 2019 and 2021 is used to compare four methods for the detection of deviations in the quality of care. Two methods based on binary outcomes (funnel plot, binary CUSUM) and two CUSUM charts based on survival outcomes (BK-CUSUM and CGR-CUSUM) are considered. A novel approach for determining hospital specific control limits for CUSUM charts is proposed. The ability to detect deviations as well as the time until detection are compared for the four methods. Charts were constructed for the inspection of both postoperative survival and hospital stay. Methods using survival outcomes always yielded faster detection times compared to approaches employing binary outcomes. Detections between methods mostly coincided for postoperative survival. For hospital stay detections varied strongly, with methods based on survival outcomes signalling over half the hospitals. Further pros and cons as well as pitfalls of all methods under consideration are discussed. Methodology for the continuous inspection of the quality of care should be tailored to the specific outcome. Properly understanding how the mechanism of a control chart functions is crucial for the correct interpretation of results. This is particularly true for CUSUM charts, which require the choice of a parameter that greatly influences the results. When applying CUSUM charts, consideration of these issues is strongly recommended.

An equivalence between multivariate cumulative sum control charts

ABSTRACT We show that an auxiliary information based (AIB) cumulative sum (CUSUM) chart is equivalent to a special case of the multivariate CUSUM control chart proposed by J. D. Healy. Due to this equivalence, the limitations and restrictions of the AIB-CUSUM chart also apply to Healy’s multivariate CUSUM chart.

A self-starting non-restarting CUSUM chart for monitoring Poisson count data with time-varying sample sizes

Many studies have focused on monitoring the incidence rate of Poisson count data with time-varying sample sizes, with control charts being widely used. However, almost all of the existing reports mainly focus on solving the problem of time-varying sample sizes. Rare attention is paid to the real-life problems where the data cannot restart. Besides, these studies aim at Phase II with the in-control parameters known, which is unrealistic in real applications. As far as we know, there is no research on the non-restarting and unknown in-control parameters control charts, but it is essential and critical for extending applications of control charts. To address these limitations, this study offered two self-starting non-restarting cumulative sum (CUSUM) control charts based on the modified test to monitor the incidence rate of non-restarting Poisson data with time-varying sample sizes. The methods can be applied to other control charts and take into account both Phase I and Phase II without assumptions of time-varying sample sizes. Moreover, the monitor can be carried out with small Phase I samples. Simulation results show that the second control chart proposed in this study (SSNR-CUSUM-P2) is optimal compared to the common non-restarting control chart (E) and the first control chart proposed in this study (SSNR-CUSUM-P1). The SSNR-CUSUM-P2 chart has the highest similarity to the control chart with known parameters (T) in both post-outbreak false alarm rate and outbreak time point set. Finally, a dataset on German measles patients and a dataset on US employment are used to illustrate the application of the methods.

Methylene blue sentinel lymph node biopsy for breast cancer learning curve in the COVID-19 era: How many cases are enough?

Background: Sentinel lymph node biopsy (SLNB) is now the gold standard for early breast cancer with clinically negative lymph nodes (N0). According to the Indonesian Board-Certified oncologist surgeon, the learning curve for evaluating fellow breast surgeons to achieve this competency could have been shorter due to the COVID-19 pandemic. This study aims to see if the learning curve for sentinel lymph node (SLN) identification can be shortened. Methods: Trainee breast surgeons were taught to perform SLNB on breast cancer patients. Intraoperative assessment and completion of axillary lymph node dissection (ALND) were performed in the first setting for standardization with the attending surgeon. Sentinel lymph node identification was plotted on cumulative sum chart (CUSUM) limitations for evaluating the variability competency between the attending and trainee surgeons based on a target identification rate of 85%. Results: We concluded that CUSUM charts are the best tools currently available for assessing psychomotor learning SLNB. According to a CUSUM chart based on a reasonable set of parameters, the learning curve for SLNB using methylene blue dye is reached after 4-5 consecutive positively detected SLN. Conclusion: CUSUM Chart showed that experienced breast surgeons have completed the SLNB learning curve after 4-5 successful methylene blue attempts. In the future, this learning curve analysis can be applied to trainee breast surgeons by utilizing a proxy measure for failure, such as failure to identify the SLN.

A variable sampling interval one-sided CUSUM control chart for monitoring the multivariate coefficient of variation

Monitoring techniques based on the multivariate coefficients of variation (MCV) have received a great deal of attention in quality control. Numerous studies have shown that adaptively changing the charting parameters based on the past sample information can improve the performance of a chart in detecting process changes. In view of the performance benefits of adaptive strategies, two one-sided cumulative sum (CUSUM) charts are proposed to monitor the MCV and a variable sampling interval (VSI) strategy is incorporated into these charts. By using the Markov chain method, the formulas for calculating the average and standard deviation of time to signal measures of the VSI CUSUM MCV control charts are derived. Then for the known and unknown shift sizes, the optimization algorithms for obtaining the charting parameters are presented. The superiority of the proposed control charts is confirmed by comparing their performance with two existing MCV charts. Finally, an example using real investment data demonstrates the practical application of the proposed charts.

Uniportal video-assisted thoracoscopic surgery for lobectomy: the learning curve.

Prior reported learning curves for uniportal video-assisted thoracoscopic lobectomy were predominantly based on surgery duration, whilst reports on complications are limited. Therefore, our study assessed the learning curve based on both technique-related complications and surgery duration. We retrospectively collected data from patients who underwent uniportal video-assisted thoracoscopic lobectomy, between 2015 and 2020. Exclusion criteria were concomitant procedures other than ipsilateral wedge resection, discontinued procedures, or lost to follow-up (<30 days). Learning curves were constructed per surgeon who performed over 20 procedures using non-risk adjusted cumulative sum analysis for technique-related complications and cumulative sum analysis for surgery duration. Based on the literature, an acceptable complication rate was set at 30%, an unacceptable complication rate at 45%, and a mean surgery duration of 145 minutes. Learning curves were constructed for three thoracic surgeons and one fellow who performed 324 uniportal video-assisted thoracoscopic lobectomies in total. Each surgeon was experienced in multiportal video-assisted thoracoscopic lobectomy, the fellow was familiar with basic multiportal video-assisted thoracoscopic procedures. Cumulative sum charts of three surgeons reached a statistically significant technique-related complication rate below 30% between 50 to 96 procedures. Regarding surgery duration, typical learning curves were observed for three surgeons with a transition point between 14 to 26 procedures. Learning of uniportal video-assisted thoracoscopic surgery for lobectomy is safe without unacceptable complication rates and has a declining surgery duration over time for thoracic surgeons with experience in multiportal video-assisted thoracoscopic lobectomies. However, it remains unknown when the different stages of mastery are completed.

Cumulative Sum Chart as Complement to Objective Assessment of Graduating Surgical Resident Competency: An Exploratory Study.

Rater-based assessment and objective assessment play an important role in evaluating residents' clinical competencies. We hypothesize that a cumulative sum (CUSUM) chart of operative time is a complement to the assessment of chief general surgery residents' competencies with ACGME Milestones, aiding residency programs' determination of graduating residents' practice readiness. We extracted ACGME Milestone evaluations of performance of operations and procedures (POP) and 3 objective metrics (operative time, case type, and case complexity) from 3 procedures (cholecystectomy, colectomy, and inguinal hernia) performed by 3 cohorts of residents (N = 15) during their PGY4-5. CUSUM charts were computed for each resident on each procedure type. A learning plateau was defined as at least 4 cases consistently locating around the centerline (target performance) at the end of a CUSUM chart with minimal deviations (range 0 to 1). All residents reached the ACGME graduation targets for the overall POP by the end of chief year. A total of 2,446 cases were included (cholecystectomy N = 1234, colectomy N = 507, and inguinal hernia N = 705), and 3 CUSUM chart patterns emerged: skewed distribution, bimodal distribution, and peaks and valleys distribution. Analysis of CUSUM charts revealed surgery residents' development processes in the operating room towards a learning plateau vary, and only 46.7% residents reach a learning plateau in all 3 procedures upon graduation. CUSUM charts of operative time complement the ACGME Milestones evaluations. The use of both may enable residency programs to holistically determine graduating residents' practice readiness and provide recommendations for their upcoming career/practice transition.

Dynamic CUSUM Chart With an Integrated Indicator for Bearing Condition Monitoring

The operation status of bearings plays a critical role in the mechanical systems. Current models for condition monitoring of bearings tend to overlook the complex properties of the process, including its non-Gaussian, nonlinear, and dynamic characteristics. To address these issues, this paper proposes a novel approach for condition monitoring based on a novel dynamic cumulative sum (CUSUM) chart with an integrated indicator. The integrated indicator accounts for the non-Gaussian, nonlinearity, and dynamic properties of the process by utilizing optimal components that are decomposed via independent component analysis (ICA) and its extended versions. The developed dynamic CUSUM chart can adapt to the variation of the process. The proposed condition monitoring strategy is validated using the simulation and experiment data of bearings. Results demonstrate that the proposed method yields a significant improvement in hit rates and a reduction in false alarms compared to conventional methods.

Anastomotic time was associated with postoperative complications: a cumulative sum analysis of thoracoscopic repair of tracheoesophageal fistula in a single surgeon's experience.

This study aimed to evaluate the learning curve of thoracoscopic repair of tracheoesophageal fistula (TEF) by a single surgeon using a cumulative sum (CUSUM) analysis. Prospective clinical data of consecutive Gross type-C TEF repairs performed by a pediatric surgeon from 2010 to 2020 were recorded. CUSUM charts for anastomosis and operating times were generated. The learning curves were compared with the effect of accumulation based on case experience. For 33 consecutive cases, the mean operative and anastomosis times were 139 ± 39min and 3137 ± 1110s, respectively. Significant transitions beyond the learning phase for total operating and anastomosis times were observed at cases 13 and 17. Both the total operating time and anastomosis time were significantly faster in the proficiency improvement phase than in the initial learning phase. Postoperative complications significantly decreased after the initial anastomosis learning phase but not after the initial total operating learning phase. Thoracoscopic repair of TEF is considered safe and feasible after 13 cases, where the surgeon can improve their proficiency with the total operation procedure, and 17 cases, which will enable the surgeon to achieve proficiency in anastomosis. Postoperative complications significantly decreased after gaining familiarity with the anastomosis procedure through the learning phase.

Likelihood ratio-based CUSUM charts for real-time monitoring the quality of service in a network of queues

Queuing networks (QNs) are widely used stochastic models for service systems include healthcare systems, transportation systems, and computer networks. While existing literature has extensively focused on modeling and optimizing resource allocation in QNs, very little research has been done on developing systematic statistical monitoring methods for QNs. This paper proposes cumulative sum (CUSUM) control charts that monitor the queuing information collected in real-time from the QN. We compare the proposed methods with existing statistical monitoring methods to demonstrate their ability to quickly detect a change in the service rate of one or more queues at the nodes in the QN. Simulation results show that the proposed CUSUM charts are more effective than existing statistical monitoring methods. The motivation for this research comes from the need to monitor the performance of a hospital emergency department (ED) with the goal of monitoring delays experienced by patients visiting the ED. A case study using the data from the ED of a large academic medical center shows that proposed methods are a promising tool for monitoring the timeliness of care provided to patients visiting the ED.

Design of adaptive EWMA control charts using the conditional false alarm rate

AbstractDynamic control limits can be useful in designing control charts, especially when sample sizes, risk scores, or other covariate values change over time. Computer simulation can be used to control the conditional false alarm rate and thus the in‐control run length properties. We show that this approach can be useful in designing adaptive exponentially weighted moving average (AEWMA) control charts for which the control chart smoothing parameter at a given time point depends on the observed value at that time point. We use AEWMA charts as examples, but the approach can be applied to the adaptive cumulative sum (CUSUM) chart and other types of adaptive charts.

Integrated Optimization Model for Maintenance Policies and Quality Control Parameters for Multi-Component System

The practical applications of integrated maintenance policies and quality for a multi-component system are more complicated, still rare, and incomplete to meet the requirements of Industry 4.0. Therefore, this work aims to extend the integration economic model for optimizing maintenance policies and quality control parameters by incorporating the Taguchi loss function for a multi-component system. An optimization model is developed based on preventive maintenance, corrective maintenance policies, and quality control parameters with the CUSUM (Cumulative Sum) chart, which is widely used for detecting small shifts in the process mean. The model was developed to minimize the expected total cost per unit of time and to obtain the optimal values of decision variables: the size of samples, sample frequency, decision interval, coefficient of the CUSUM chart, and preventive and corrective maintenance intervals. The solution steps were employed by selecting a case study in the Alahlia Mineral Water Company (AMWC). Then, the design of experiments based on one-factor-at-a-time was used to evaluate the effect of selected decision variables on the expected total cost. Finally, sensitivity analysis was performed on the selected decision variables to demonstrate the robustness of the developed model. A predictive maintenance plan was developed based on the optimal value of preventive maintenance interval, and the results showed that the performance of the maintenance plan realizes the full potential of the integrated model. In addition, the case study results indicate that the extended integrated model for multicomponent is the new standard for the quality production of multi-component systems in future works.

Comprehensive Learning Curve Analysis of a Long-Term Experience With Thoracic Endovascular Aneurysm Repair

Purpose: To analyze the learning curve for thoracic endovascular aortic repair (TEVAR) in a single center over a period of 25 years. Materials and Methods: In total, 390 consecutive standard TEVAR procedures undertaken between 1996 and 2021 were included in a retrospective, observational, single-center study. Cumulative sum charts were elaborated for the entire center experience (primary outcome) as well as for the first and second implanting physicians. Data on procedural variables (contrast volume, operative and fluoroscopy time), 30-day major adverse events (MAEs) and clinical success, and endoleak and reintervention rates were secondary outcomes and subdivided into 4 quartiles of experience (Q1–Q4) or presented as first 2 versus latest 2 quartiles (Q1–Q2 vs Q3–Q4). Results: The mean follow-up was 4.3±4.0 years. The center’s learning curve was achieved after 75 procedures, and it was similar for the first implanting physician. The surgeon coming thereafter had a significantly shorter curve (10 TEVARs). Comparing Q1–Q2 with Q3–Q4, 30-day MAEs (16.1 vs 11.3%, p=0.164), 30-day mortality (11.4% vs 3.6%, p=0.003), and intraoperative additional maneuvers (21.5% vs 13.3%, p=0.033) were reduced along with an improvement in clinical success (85.9% vs 90.3%, p=0.190). From Q1 to Q4, operative time (139.8±65.5 to 76.7±43.7 min, p=0.001), fluoroscopy time (15.1±8.8 to 7.1±5.1 min, p<0.001), and contrast volume (244.0±112.1 to 104.3±46.1 mL, p<0.001) showed a considerable reduction. Late endoleak and aortic-related mortality declined significantly from Q1–Q2 to Q3–Q4 (24.1% to 15.5%, p=0.033 and 18.6% vs 8.2%, p=0.006, respectively). Operative time (p=0.021), contrast volume (p=0.016), and fluoroscopy time (p=0.004) were independent risk factors for endoleak, causing a 1.3-fold risk increase for both each 60 minutes of additional operative time (p=0.021) and every 100 mL of additional contrast medium (p=0.016). Each 10-minute increase in fluoroscopy time determined a 1.4-fold risk increment (p=0.004). Conclusion: The learning curve shortened significantly over time with non-negligible clinical outcome improvements, suggesting that specific endovascular training is mandatory to become an effective TEVAR performer. Clinical Impact For the first time in literature, the standard TEVAR’s learning curve has been evaluated at a single vascular surgery center over a period of 25 years. The learning curve for the center and the first physician historically undertaking TEVAR was achieved at the 75th treated patient. The learning curve of the surgeons coming thereafter was significantly shorter (10 cases). This quarter-century demonstrated that intraoperative learning-related variables were associated with long-term clinical outcomes and all have improved over time. Centers approaching TEVAR for the first time and training program providers could use these data to aim to offer better clinical outcomes.

On efficient change point detection using a step cumulative sum control chart

Control charts are widely used to monitor the stability of processes and Shewhart is the most commonly used type of chart because of the simplicity of its structure. To improve the performance, there are several modifications on control chart suggested since its proposal like cumulative sum and exponentially weighted moving average control charts. The cumulative sum chart accumulates all the deviations from target mean higher than a specific design parameter which can be used to controls the sensitivity of this chart. The optimal choice of this design parameter is half of the target shift size. This results into an optimal performance in terms of quick detection of shift that is equal to the target shift size. For shift sizes other than target, the cumulative sum chart loses its performance and becomes inferior to other control charts in terms of average run length. Since we rarely know the process shift size that is going to occur in future, this study proposes a revision in the structure of cumulative sum chart. The adjusted cumulative sum chart is shown to be very flexible for a wide range of shifts, when designed against a target shift size. The proposed adjusted cumulative sum control chart is compared with cumulative sum, exponentially weighted, combined Shewhart-CUSUM, progressive mean, double progressive mean and mixed EWMA-CUSUM control charts in terms of zero- and steady-state average run lengths. The superiority zones are identified and the results are supported by a real-life implementation of the proposed scheme.

Efficient CUSUM control charts for monitoring the multivariate coefficient of variation

Monitoring the coefficient of variation (CV) is of interest when there is a constant proportion between the varying standard deviation and the varying mean in the process. In a multivariate process, monitoring the multivariate CV (MCV) is useful to assess the relative variability of the process. With the aim to improve the existing MCV charts’ performance, this paper develops two one-sided cumulative sum (CUSUM) charts for monitoring the MCV. Based on the Markov chain model, some run length (RL) measures are evaluated and used to show the superiority of the proposed charts over the competing MCV charts under the deterministic shift. Moreover, when the shift size is unknown in practice, the performance of the proposed CUSUM MCV charts is evaluated. Finally, an example is provided to show the implementation of the proposed CUSUM MCV charts.