Cumulative Sum Charts Research Articles

CUSUM charts utilizing reparametrized Birnbaum-saunders model for fault detection and process control

Statistical process control is always intrigued by the design of effective control charts for monitoring production processes and determining assignable causes of variations. It can be challenging to keep track of a positive asymmetric response variable while considering the impact of the input variables. The current work incorporates the Reparametrized Birnbaum Saunders (RBS) model to develop more effective cumulative sum (CUSUM) control charts for analyzing the mean of such a process. We perform a simulation study to evaluate the effectiveness of existing and derived approaches in terms of run length characteristics. The findings showed that when the underlying process distribution is positively asymmetric, the proposed charts provide stronger protection against process alterations as compared to existing methods. Moreover, the suggested control charts are implemented using actual data from a combined cycle power plant.

Comparison of risk-adjusted cumulative quality control charts compared with standardized mortality ratios in critical care.

The optimal method for monitoring intensive care unit (ICU) performance is unknown. We sought to compare process control charts using standardized mortality ratio (SMR), p-charts, and cumulative sum (CUSUM) charts for detecting increases in risk-adjusted mortality within ICUs. Using data from 17 medical-surgical ICUs that included 29,592 patients in Ontario, Canada, we created risk-adjusted p-charts and SMRs on monthly intervals and CUSUM charts. We defined positive signals as any data point that was above the 3-sigma limit (approximating a 99% confidence interval [CI]) on a p-chart, any data point whose 95% CI did not include 1 for the SMR charts, and when a data point exceeded control limits for an odds ratio of 1.5 for CUSUM charts. We simulated increases in mortality of 10%, 30%, and 50% for each ICU to determine the sensitivity of each method. We calculated sensitivity as the number of positive signals divided by the number of ICUs (equal to number of simulated events). Cumulative sum charts generated 31 signals in 12 different ICUs, while p-charts and SMR agreed in 10 and 6 of these signals, respectively, followed by 21 signals from p-charts across 14 ICUs (agreement in 10 of these signals for both CUSUM and SMR) and 15 signals from SMR charts across eight ICUs (agreement from p-charts and CUSUM in 10 and six signals, respectively). The p-chart had a sensitivity of 88% (95% CI, 73 to 104) for a 50% simulated increase in ICU mortality followed by CUSUM at 71% (95% CI, 49 to 102) and SMR at 59% (95% CI, 35 to 82). Performance with lower simulated increases was poor for all three methods. P-charts created with risk-adjusted mortality at monthly intervals are potentially useful tools for monitoring ICU performance. Future studies should consider usability testing with ICU leaders and application of these methods to additional clinical domains.

QC Constellation: a cutting-edge solution for risk and patient-based quality control in clinical laboratories.

Clinical laboratories face limitations in implementing advanced quality control (QC) methods with existing systems. This study aimed to develop a web-based application to addresses this gap, and improve QC practices. QC Constellation, a web application built using Python 3.11, integrates various statistical QC modules. These include Levey-Jennings charts with Westgard rules, sigma-metric calculations, exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, and method decision charts. Additionally, it offers a risk-based QC section and a patient-based QC module aligning with modern QC practices. The codes and the web application links for QC Constellation were shared at https://github.com/hikmetc/QC_Constellation, and http://qcconstellation.com, respectively. Using synthetic data, QC Constellation demonstrated effective implementation of Levey-Jennings charts with user-friendly features like checkboxes for Westgard rules and customizable moving averages graphs. Sigma-metric calculations for hypothetical performance values of serum total cholesterol were successfully performed using allowable total error and maximum allowable measurement uncertainty goals, and displayed on method decision charts. The utility of the risk-based QC module was exemplified by assessing QC plans for serum total cholesterol, showcasing the application's capability in calculating risk-based QC parameters including maximum unreliable final patient results, risk management index, and maximum run size andoffering risk-based QC recommendations. Similarly, the patient-based QC and optimization modules were demonstrated using simulated sodium results. In conclusion, QC Constellation emerges as a pivotal tool for laboratory professionals, streamlining the management of quality control and analytical performance monitoring, while enhancing patient safety through optimized QC processes.

Evaluating multivariate charts: A first‐to‐signal criterion approach

AbstractThis study advances the application of the first‐to‐signal (FTS) concept to evaluate the effectiveness of multivariate charts when detecting shifts in the mean vector of a multivariate normally distributed process. Using Monte Carlo simulations, we estimate steady‐state average run‐length profiles and the probabilities of multivariate charts being the FTS an out‐of‐control state. Notably, our findings indicate that while the multivariate cumulative sum (MCUSUM) chart serves as a viable alternative to the multivariate exponentially weighted moving average (MEWMA) chart when detecting small shifts in the process mean vector, the latter surpasses the former in detecting moderate‐to‐large shifts. In addition, the Hotelling's chart outperforms the MEWMA and MCUSUM charts when detecting large shifts.

A weighted dual cumulative sum chart for monitoring the process mean

AbstractThe cumulative sum (CUSUM) charts are well‐structured and widely used for detecting small‐to‐moderate changes in the process parameters. However, their performance can be limited when the shift size is unknown or varies over time. Various methods have been developed to address this issue, including dual CUSUM (DCUSUM), adaptive CUSUM, adaptive EWMA, and weighted CUSUM charts, all of which offer better sensitivity compared to traditional CUSUM charts. In this study, we propose a new weighted DCUSUM chart designed to effectively detect the mean shifts in a normally distributed process. Monte Carlo simulations are used to estimate the zero‐state and steady‐state average run‐length (ARL) profiles of the control charts. The ARL performances of the control charts are evaluated in terms of expected relative ARL (ERARL) and expected weighted run‐length (EWRL). Our results show that the proposed chart may outperform existing counterparts in terms of the ARL, ERARL, and EWRL measures, indicating superior performance in detecting a range of the mean shift sizes. Finally, we apply the existing and proposed charts to a real dataset, showcasing their practical utility in process monitoring.

Efficient ARL estimation for general control charts using censored run lengths

The average run length (ARL), the average number of in-control signals before an out-of-control signal occurs, is a critical measure of the performance of a control chart. Various methods have been explored for estimating the ARL, including Markov chain-based approximation, integration method, and the Monte Carlo method, especially for time-dependent charting statistics. Although computationally expensive, the Monte Carlo method is generic and applicable to all control charts. Typically, it involves choosing the maximum run length in advance and discarding iterations that fail to produce out-of-control signals to accommodate some unusually lengthy runs. However, these discarded runs provide information for estimating the run length. This paper introduces a new Monte Carlo approximation that retains failed iterations as Type I censored observations for ARL estimation. Our approach relies on the memoryless expectation of the run length distribution to have a simple and efficient ARL estimator. This assumption is necessary for mean estimation in Type I censored data and aligns with existing ARL approximations used in popular control charts like Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts. Numerical simulations demonstrate our method’s computational and statistical efficiency across the mean, median, EWMA, and CUSUM charts.

The Learning Curve for Holmium Laser Enucleation of the Prostate: A Single-Center Analysis of Surgical And Functional Outcomes.

Background: To report the surgical and functional outcomes of the holmium laser enucleation of the prostate (HoLEP) surgical program implemented at a high-volume tertiary referral center and to estimate the learning curve (LC) duration for this surgical procedure. Methods: Data of all consecutive patients undergoing HoLEP at the University of Verona between June 2022 and April 2024 were retrieved from a prospectively maintained institutional database of patients undergoing benign prostatic hyperplasia (BPH) surgical treatment. The primary endpoint was functional outcomes evaluation during the surgeons' LC. The secondary endpoint was to define the surgical LC for HoLEP. A multivariable test of means was performed to compare functional outcomes at different time points. After adjusting for potential confounders (age, preoperative pharmacotherapy, and prostate volume), multivariable linear regression models were fitted to evaluate the effect of experience on operative time (OT) and enucleation efficiency. To assess LCs for HoLEP surgery, the non-risk-adjusted cumulative sum (CUSUM) method was used. Results: A statistically significant improvement in International Prostate Symptoms Score (IPSS) score, delta% IPSS score, IPSS quality of life (IPSS-QoL) score, and delta% IPSS-QoL score was observed over the study period. Furthermore, the incidence of irritative symptoms (p < 0.001) and stress incontinence (p = 0.01) significantly decreased over time, with a 12-month incidence of 8.4% and 9.5%, respectively. A statistically significant association between experience and both OT and enucleation efficiency was observed in multivariable linear regression analysis. The CUSUM chart for OT and enucleation efficiency showed a steep initial upward/downward trend of ∼50 cases each, and a plateau until ∼100 procedures are reached, where the breakpoint is recognized for both variables and where the CUSUM curve goes below the locally weighted scatterplot smoothing curve in the corresponding observed-expected CUSUM plot. Conclusions: HoLEP represents an effective treatment for BPH, demonstrating significant improvement in BPH-related symptoms over the study period, despite the considerable LC of ∼50 cases associated with the procedure.

Cumulative sum (CUSUM) analysis: A 10 year experience of outcome monitoring in a regional burn centre

IntroductionOutcome monitoring can identify fluctuations in healthcare. Cumulative sum (CUSUM) analysis can detect when mortality deviates from expected, allowing early intervention through targeted audit. We present a 10-year experience of the prospective use of CUSUM methodology in a regional burn centre. MethodProspective outcome monitoring was conducted for all admissions to the intensive care unit between 2012 and 2022. The revised Baux score was used for mortality risk prediction. Risk-adjusted CUSUM charts tracked mortality against that predicted by the revised Baux score. Deviations from expected outcomes triggered detailed structured analysis. Learning outcomes were identified from internal and external governance groups. ResultsCUSUM analysis was triggered on eight occasions: one paediatric (excess deaths), six adult (four excess survivors, two excess deaths) and one elderly (excess survivors). Detailed analysis identified areas for continuous improvement and positive themes from excess survivors. ConclusionThe use of CUSUM as an early warning trigger stimulates assessment of practice and critical appraisal of factors contributing to unexpected mortality or survival. The revised Baux score at its foundation needs to be carefully considered but remains a valid model. One benefit is positive reinforcement of team cohesion and morale during periods of care excellence leading to excess survivors.

Pneumovesical vesicovaginal fistula repair: Lessons learned from an initial series of 25 patients.

This study aims to share the experiences and outcomes of laparoscopic pneumovesical repair for vesicovaginal fistulas (VVF). A retrospective review of medical records from a single institution over 10 years was conducted. The focus was on patients who underwent VVF repair using a pneumovesical approach with three 5 mm laparoscopic ports. The study evaluated perioperative parameters, postoperative outcomes, and complication rates to assess the efficacy and safety of this surgical method. Cumulative sum (CUSUM) analysis was used to determine the learning curve based on operative time. Of the 26 patients with VVF, 23 (88.5%) had successful fistula closure after the first surgery. One patient required open surgery conversion due to challenges in maintaining pneumovesicum, and two experienced recurrences, although successful repairs were achieved in subsequent surgeries. The average patient age was 47.4 years, with a mean operative time of 99.9 min. The postoperative hospital stay averaged 9.1 days, and catheterization lasted about 11 days. The CUSUM chart indicated a learning curve, with fluctuations until the 19th case, followed by a consistent upward pattern. Laparoscopic pneumovesical VVF repair is an effective and safe technique, especially suitable for fistulas near the ureteral orifice or deep in the vaginal cavity. The method demonstrates favorable outcomes with minimal complications and allows for easy reoperation if necessary.

Less invasive replacement of aortic root, ascending aorta and hemiarch via partial upper sternotomy: a propensity-score-matched comparison with full sternotomy.

Less invasive surgery has emerged as an option for aortic pathologies. The current study compared our experience on early postoperative results of patients with aortic surgery between partial upper sternotomy (PUS) and full sternotomy (FS). We performed a retrospective analysis of the data of patients undergoing aortic root surgery with concomitant ascending aorta and hemiarch replacement. Exclusion criteria were type A aortic dissection and other concomitant major cardiac surgery. After propensity score matching, we compared the perioperative outcomes of patients undergoing surgery with PUS versus FS. A total of 161 patients operated on between January 2013 and September 2022 met the inclusion criteria (PUS: n = 22, FS: n = 139). Propensity score matching yielded 22 pairs with a balanced distribution of propensity scores and covariates between the compared groups. There was no evidence that PUS affects cardiopulmonary bypass [108 (67-119) vs 113 (87-148) min, P = 0.154; PUS vs FS] and circulatory arrest duration [9 (7-10) vs 9 (8-13) min, P = 0.264; PUS vs FS]. There was a reduced cross-clamp duration in the PUS group [88 (58-96) vs 92 (71-122) min, P = 0.032]. Cumulative sum charts have shown consistently low cross-clamp and circulatory arrest duration for 2 experienced surgeons who performed 20 of the procedures in the PUS group (10 each). Perioperative mortality and morbidity were low, with no in-hospital mortality in the PUS group [0 vs 1(4.5%), P > 0.999] and absence of strokes in both groups. In summary, our initial experience suggests that less invasive aortic root, ascending aorta and hemiarch replacement via PUS could be performed in our patient cohort as safely as via full sternotomy. Advantages for the patient are reduced surgical trauma, improved cosmetic results and-presumably-less pain.

Leveraging dynamic power benchmarks and CUSUM charts for enhanced fault detection in distributed PV systems

Faults in photovoltaic (PV) systems are common during their operational lifetime. Existing PV fault detection methods, which are primarily designed for large-scale PV fields, struggle with distributed systems due to their reliance on on-site weather sensors and inability to handle complex local shading effects on PV performance in the built environment. This paper presents a fault detection scheme specifically applicable to distributed PV systems that solely relies on monitored AC output and remote weather sources. Without requiring additional equipment or detailed information on the PV configuration and local shading conditions, the proposed method consists of two steps. First, historical monitoring data is used in a bootstrap fashion to develop machine learning models that establish baselines for normal PV output and corresponding estimation uncertainty. Then, a dynamic PV power benchmark constructed based on the 3-sigma rule, and cumulative sum (CUSUM) control charts are employed simultaneously to detect system malfunctions. Through experimental verification on actual distributed PV systems, the effectiveness of the proposed method is assessed for four categories of frequently observed malfunctions. The comprehensive experimental results indicate the considerable efficiency of the proposed sensorless method in detecting both serious PV malfunctions and minor faults with a severity as small as 4.2%.

Proficiency in performing radiofrequency ablation procedure for non-functioning benign thyroid nodules: a qualitative rather than quantitative matter.

Radiofrequency ablation (RFA) is an emerging non-surgical treatment for benign thyroid nodules (BTN). Despite its proven safety profile, data on the learning curve (LC) required to achieve proficiency are still lacking. The first 179 RFA procedures performed by a single operator in patients with non-functioning BTN were retrospectively analyzed. Six-month nodule volume reduction rate (VRR) ≥ 50% was regarded as reflection of proficiency. Multiple linear regression analysis has been performed to determine the relationship between the VRR and clinical variables. Cumulative sum (CUSUM) charts were plotted to assess LCs for all consecutive procedures and in relation to basal nodule size. In details, Group 1 (G1): 57 patients with small nodules (<10 ml); Group 2 (G2): 87 patients with intermediate nodules (10 - 25 ml); Group 3 (G3): 35 patients with large size (> 25 ml). LC of all 179 procedures showed 3 phases: initial learning (1-39 procedures); consolidation (40-145 procedures); and experienced period (146-179 procedures). For G1 and G2 proficiency is achieved starting from the 10th procedure within the group (or 37th considering consecutively all procedures) and from the 59th procedure within the group (or 116th considering consecutively all procedures), respectively. LC of G3 did not detect operator proficiency. Specific LCs exist concerning the basal size of the nodule treated with RFA. In nodules with baseline volume > 25 ml suboptimal VRR has to be expected. Previously achieved experience on small-intermediate nodules does not seem to provide advantages in terms of higher VRR in the treatment of large nodules. Other potential and non-modifiable factors likely play a key role in the final volume reduction independently from the increased skill of the operator.

A robust cusum control chart for median absolute deviation based on trimming and winsorization.

Statistical quality control is concerned with the analysis of production and manufacturing processes. Control charts are process control techniques, commonly applied to observe and control deviations. Shewhart control charts are very sensitive and used for large shifts based on the basic assumption of normality. Cumulative Sum (CUSUM) control charts are effective for identifying that may have special causes, such as outliers or excessive variability in subgroup means. This study uses a CUSUM control chart problems structure to evaluate the performance of robust dispersion parameters. We investigated the design structure features of various control charts, based on currently defined estimators and some new robust scale estimators using trimming and winsorization in different scenarios. The Median Absolute Deviation based on trimming and winsorization is introduced. The effectiveness of CUSUM control charts based on these estimators is evaluated in terms of average run length (ARL) and Standard Deviation of the Run Length (SDRL) using a simulation study. The results show the robustness of the CUSUM chart in observing small changes in magnitude for both normal and contaminated data. In general, robust estimators MADTM and MADWM based on CUSUM charts outperform in all environments.

Designing Bayesian paradigm-based CUSUM scheme for monitoring shape parameter of the Inverse Gaussian distribution

Bayesian Control charts have gained prominence as highly effective statistical instruments in overseeing manufacturing processes and ensuring adept management of process variability. The Bayesian methodology proves especially adept in managing uncertainties related to parameters within the manufacturing sector. In this research endeavor, our focus lies in establishing the threshold for monitoring the shape parameter of the Inverse Gaussian distribution (IGD) in phase-II based on cumulative sum (CUSUM) chart in classical and Bayesian frameworks using a variety of loss functions for enhancing their utility and applicability and have compared them with the Shewhart and EWMA control charts. We have also compared the proposed IGD-based CUSUM charts with the Lomax-based CUSUM charts. The evaluation of the proposed approach hinges on performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MDRL). Through simulation, the study showcases the efficiency of the Bayesian approach-based CUSUM charts, highlighting their superiority over the conventional classical setup-oriented CUSUM charts. Additionally, the proposed approach is employed in practical scenarios using real-data case studies from the aerospace manufacturing sector. The outcomes derived from real-data analysis substantiate and reinforce the conclusions drawn from the simulated results.

A Method for Continuous Surgeon Improvement in Rectal Cancer: Risk-Adjusted Cumulative Sum.

To develop and analyze a risk-adjusted cumulative sum (RA-CUSUM) chart as a potential method to monitor individual surgeon performance in robotic total mesorectal excision (TME) for rectal cancer. Currently, surgeons lack real-time tools to monitor and enhance their performance beyond residency completion. While national quality programs exist, granular, individual-level data is crucial for continuous improvement. Previous studies suggest CUSUM charts hold promise in identifying performance trends and outliers. This retrospective study analyzed data from 640 robotic TME cases performed by 12 surgeons at two institutions. RA-CUSUM charts were generated for three outcomes: complications, operative time, and length of stay. The overall RA-CUSUM curves for operative time and complications showed an initial learning phase followed by a plateau or downward slope, indicating proficiency or improvement. However, individual surgeon curves revealed significant heterogeneity. Three surgeons consistently excelled in operative time, while five minimized complications most effectively. Potential quality improvement could be implemented to drive performance toward positive outliers. No differences were found in unadjusted outcomes, including conversion, number of lymph nodes harvested, and positive circumferential margins. The RA-CUSUM chart is a promising method for identifying individual surgeon performance in robotic TME. It could help surgeons, teams, and leaders identify improvement areas and benchmark themselves against positive outliers. Further studies are needed to explore the potential of RA-CUSUM for implementing interventions to improve surgical quality.

Coating process control in lithium-ion battery manufacturing using cumulative sum charts

Coating process control in lithium-ion battery manufacturing using cumulative sum charts

Assessment of climate change induced rainfall trend and variability with non-parametric and linear approach for Sirajganj district, Bangladesh

The monthly and annual trends and variance of rainfall have been studied for five stations in an economically important Bangladeshi district named Sirajganj since 1965 to 2021. Natural disasters have prevalent in Sirajganj which is indispensable to assess. But, several researchers have been normally focused on river bank management and flood risk assessment. However, no extensive research has been conducted on Sirajganj based on non-normally distributed time series meteorological data such as rainfall time series so the current study is very important. In this study, the non-parametric Mann-Kendall and Sen's methods have been used to determine the statistical significance of a positive or negative trend in rainfall data. Also, cumulative sum charts and bootstrapping, one-way ANOVA, Tukey's range tests, and linear regression have been used to discover the incidence of abrupt changes, compare the significant difference in monthly and annual rainfall data, multiple comparisons amidst mentioned stations to find changes, and to investigate the changeover on dry and rainy days, respectively. The analysis showed a statistically significant decreasing trends in monthly and annual rainfall series. As well, changes from positive to negative direction have been recognized in the February, May, July, September, and annual rainfall time sequence. Besides, ANOVA and Tukey's range tests revealed a statistically substantial difference in all monthly and annual rainfall volume excluding January, March, and June. Additionally, these two tests demonstrated momentous differences in all monthly and annual frequency of rainfall categories excepting January and April. However, Linear regression analysis revealed that the number of dry days gradually reduced at the end of the dry winter, though the number of rainy days decreased during the rainy season. As in, the number of rainy days replaces the number of dry days during the dry season and vice versa during the rainy season. Even though, with very few exceptions, the volume of rainfall decreases throughout the year. The outcomes of this research might helpful for implementing the planning and evaluating hydrological projects on Sirajganj district.

Parametric and nonparametric versions of adaptive CUSUM charts for monitoring the location of individual measurements

Control charts are customarily developed under the assumption of normal quality characteristics to be monitored. However, in many real dataset applications, the normality assumption is not easy to hold. The in-control (IC) robustness of the charting schemes has significant importance for the valid out-of-control (OOC) performance. This article intends to investigate the IC robustness of the unbiased-function-based adaptive cumulative sum (ACUSUM) chart and nonparametric ACUSUM (NPACUSUM) chart against the non-normal process distributions including symmetrical, skewed, and contaminated normal distributions. The OOC run length profiles of the ACUSUM and the proposed NPACUSUM charts for the individual measurements against the non-normal distributions are also a part of this study. The run length profiles of the proposed charting schemes have been computed using the Monte Carlo simulation method. The artificial datasets have been taken from some symmetric and skewed distributions to implement the proposals. An electrical engineering dataset has also been taken for the implementation of the proposal on a real dataset.

A likelihood-based adaptive CUSUM for monitoring linear drift of Poisson rate with time-varying sample sizes

Several weighted cumulative sum (CUSUM) and adaptive CUSUM (ACUSUM) control charts have been developed to address the challenge of time-varying sample sizes in detecting the incidence rates of Poisson count data. However, the known post-drift parameters in the CUSUM chart make it less realistic. Additionally, the adaptive component in the ACUSUM chart cannot integrate with time-varying sample sizes naturally. Furthermore, the existing charts predominantly address step drift, neglecting linear drift. Hence, this study introduces a Poisson ACUSUM chart that considers both linear drift and integration issues. Detailed comparisons are made among the proposed control chart, CUSUM control charts, and other ACUSUM control charts. Results demonstrate the proposed method's superior robustness and ability to effectively detect small drifts. Finally, the empirical results of the mortality data are employed to further validate the effectiveness of the proposed method.

Cumulative sum control charts for monitoring zero‐inflated COM‐Poisson processes

AbstractThe zero‐inflated Conway‐Maxwell Poisson (ZICMP) distribution models count data with many zero observations. ZICMP model has been developed assuming that zero observations exist with probability and the number of non‐conformities in a product unit follows the Conway‐Maxwell Poisson (COM‐Poisson) distribution with location parameter and dispersion parameter . This article presents four kinds of cumulative sum (CUSUM) charts for monitoring upward shifts in a ZICMP process. Three CUSUM schemes, namely ‐CUSUM, ‐CUSUM, and ‐CUSUM, have been designed to detect shift only in one parameter assuming that the other two are fixed and one CUSUM scheme, namely ‐CUSUM, has been designed to detect shifts in all the parameters. The performance of the proposed charts has been evaluated in terms of the average run‐length (ARL). Finally, a numerical example is given to demonstrate the application of the proposed charts.