CUSUM Control Chart Research Articles

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.

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).

Using the CUSUM control chart to monitor the reported deaths of COVID-19 in Egypt.

Using the CUSUM control chart to monitor the reported deaths of COVID-19 in Egypt.

Enhanced Process Monitoring for the Maxwell Process via the CUSUM Control Chart and Its Application to the Carbon Fiber Industry

Enhanced Process Monitoring for the Maxwell Process via the CUSUM Control Chart and Its Application to the Carbon Fiber Industry

Approximating the ARL of Changes in the Mean of a Seasonal Time Series Model with Exponential White Noise Running on a CUSUM Control Chart

Control charts comprise an excellent statistical process control tool for monitoring industrial processes. Especially, the CUSUM control chart is very sensitive to small-to-moderate process parameter changes. The proposed approach utilizes the numerical integral equation (NIE) method to approximate the average run length (ARL) of changes in the mean of a seasonal time series model with underlying exponential white noise running on a CUSUM control chart. This was achieved by solving a system of linear equations and integration through partitioning and summation using the area under the curve of a function obtained by applying the Gauss-Legendre quadrature. A numerical study was conducted to compare the capabilities of the ARL derivations obtained using the NIE method and explicit formulas to detect changes in the mean of a long-memory model with exponential white noise running on a CUSUM control chart. The results reveal that the performances of both were comparable in terms of the accuracy percentage, which was greater than 95%, meaning that the ARL values were highly consistent. Thus, the NIE method can be used to validate ARL results for this situation.

Adaptive sampling and monitoring of partially observed images

Image-based monitoring techniques have achieved great success in many engineering applications. However, most existing image monitoring methods require fully observed images to implement modeling/monitoring. This requirement limits the application of these techniques for images with large size and/or cameras with limited scanning area. In this article, we propose to solve this issue by splitting the large image into multiple sub-images and using partially observed sub-images to implement monitoring of the whole large image. More specifically, the two-dimensional multivariate functional principal component analysis (2D-MFPCA) is proposed to model the cross-and-within correlation among sub-images, which facilitates the information augmentation from partially observed sub-images. The asymptotic properties of the 2D-MFPCA estimators are investigated to justify the use of MFPC scores as the monitoring statistics, which are fed into a multivariate CUSUM control chart to implement adaptive sampling and monitoring of image data. The developed chart can dynamically select locations of partially observed sub-images and adaptively focus on the most suspicious sub-images. The proposed method is validated and compared with various benchmark methods in both numerical and case studies. The results demonstrate the proposed method can achieve superior monitoring performance for large images when only partially observed sub-images are available.

A CUSUM control chart for gamma distribution with guaranteed performance

AbstractEven though most control chart developments have revolved around the normal distribution, productive operations, in fact, often use non‐normal data, and some even use skewed distributions. This occurs with cycle times and many processes with a single specification limit. Under these conditions, gamma distributions often offer a better characterization where CUSUM schemes provide optimal performance to detect changes of a known in‐control (IC) parameter. In practice, gamma parameters have to be estimated, and limited phase I samples have undesirable effects on the phase II average run length (ARL) that has not been examined. To address this situation, this study uses Markovian models to assess the ARL of a CUSUM developed to monitor scale changes when IC parameters are estimated. This paper discusses the conditional ARL performance and proposes an adaptation of a stochastic estimation algorithm to guarantee a minimum performance. IC and out‐of‐control performance is compared with the conditional performance of a traditional approach where no corrections are made to guarantee a specific behavior. To demonstrate the practical application of this new approach, an implementation was made in a packaging process using multihead weighing machines. Practitioners interested in using reliable monitoring schemes will find, in this proposal, several implementation guidelines such as algorithms and look up tables to facilitate their implementations.

An optimization method for change-point monitoring in finite samples sequence

This article proposes a method of optimizing control chart (sequential test) to detect an abnormal change in a sequence of finite or even small samples with the unknown change-point and the unknown post-change probability distribution. We not only introduced a performance measure for a given charting statistic to evaluate the detection effect of a control chart, but also constructed an optimal control chart under the measure. The effect of optimization method was illustrated by numerical simulations of three optimized Shewhart, CUSUM and EWMA control charts, and a real data example.

Control charts to establish and monitor proficiency in the detection of pulmonary B-lines with Point of Care Ultrasound

Objective: Point of care ultrasound (POCUS) is a widely used clinical tool. This operator-dependent technique requires methods to establish individual benchmarks and to monitor the learning process. We present the use of the learning curve standard cumulative summation (LC-CUSUM) and CUSUM control charts to establish and monitor, respectively, the proficiency of a physician to detect pulmonary B-lines with POCUS. Materials and Methods: A training course for general practitioners was conducted to detect plasma leakage using POCUS. The trainees and an expert radiologist identified the number of pulmonary B-lines in the POCUS images of 53 hospitalized patients. The interpretation of one trainee was compared to that of the expert radiologist using LC-CUSUM and CUSUM considering image quality and anatomical site. Results and Discussion: We found that image quality was better in the apices than the bases of the lungs. The trainee learning curve differed by anatomical site and the results of LC-CUSUM and CUSUM differed when only high-quality (first scenario) or all images (second scenario) were included in the analysis. Conclusion: The LC-CUSUM and CUSUM control charts were useful to evaluate the learning curve in this case and to identify image quality as an important factor in the evaluation process. They warrant further study as graphical tools for real-time monitoring of POCUS training.

Optimized control charts using indifference regions

In statistical process monitoring, the CUSUM and EWMA control charts have received considerable attention because of their remarkable ability to detect small sustained shifts. In practice, small process variation and shifts are anticipated beforehand in many processes, so the focus should be on detecting a moderate to a large shift. The aforementioned charts identify minor changes in population parameters as out-of-control scenarios; thus, “small” and potentially practically insignificant shifts are producing signals. To counteract this, both charts are amended to accommodate an indifference region by optimizing the detection of a shift at the outer boundaries of the indifference region. The results show that the adapted CUSUM and EWMA monitoring schemes yield comparable results. On nearly all occasions, the CUSUM chart outperforms the EWMA chart, yet the EWMA chart seems more robust and is easier to interpret. Furthermore, we provide two practical examples to illustrate the use-case of optimized charts to mitigate small (unimportant) variations, such as seasonality and modest temporary shifts. Overall, this work provides a general approach tailored to practice in quality control, e.g., as prescribed by ISO standards. It also answers a recent call in statistical process monitoring literature to reconsider the design of control charts.

HYBRID DOUBLE EXPONENTIALLY WEIGHTED MOVING AVERAGE (HDEWMA) CONTROL CHART FOR INVERSE RAYLEIGH DISTRIBUTION

In this paper, we proposed a Hybrid Double Exponentially Weighted Moving Average HDEWMA control chart. The proposed control chart is based on Inverse Rayleigh Distributed lifetimes using simple random sampling (SRS) and ranked set sampling (RSS). Out-of-control-Average Run Length (ARL1) is used to evaluate the performance of the proposed control chart. The HDEWMA control chart is compared with traditional/simple EWMA and CUSUM control charts. The performance of the control chart is evaluated using out of control average run length (ARL1). A simulated example is used to compare the proposed HDEWMA, traditional/simple EWMA chart and CUSUM control chart. It is observed that the proposed HDEWMA control chart performs simple EWMA and CUSUM control charts. The HDEWMA control chart can be used for efficient monitoring of the production process in manufacturing industries where the data is coming from inverse Rayleigh Distribution. Keywords: Hybrid, EWMA, CUSUM, DEWMA, average run length (ARL).

A bivariate CUSUM control chart based on exceedance statistics

AbstractIn manufacturing systems, statistical process control (SPC) is used to detect unusual observations in the process. Most control charts are composed based on the normality assumptions of the observations. However, checking the normality assumption in multivariate control systems cannot be practical in real‐life applications. As a result, we propose a nonparametric bivariate cumulative sum control chart (CUSUM) based on exceedance statistics for detecting the shifts in location parameters. Since the proposed chart (BCUSUM‐EX) relied on exceedance statistics and is nonparametric, the use of the chart is straightforward and practical for users. Moreover, due to the nature of CUSUM charts, the proposed chart contains information about historical and current observations. The performance of the BCUSUM‐EX chart is compared with the spatial sign CUSUM (SS‐CUSUM) control chart under some well‐known bivariate distributions such as bivariate normal, t, and gamma. The BCUSUM‐EX chart's performance is better than the SS‐CUSUM control chart regarding run length characteristics. Lastly, to show the importance of the proposed control chart, the BCUSUM‐EX chart has been applied to the aluminium electrolytic capacitor manufacturing process.

The optimal CUSUM control chart with a dynamic non-random control limit and a given sampling strategy for small samples sequence

This article proposes a performance measure to evaluate the detection performance of a control chart with a given sampling strategy for finite or small samples sequence and prove that the CUSUM control chart with dynamic non-random control limit and a given sampling strategy can be optimal under the measure. Numerical simulations and real data for an earthquake are provided to illustrate that for different sampling strategies, the CUSUM chart will have different monitoring performance in change-point detection. Among the six sampling strategies that take only a part of samples, the numerical comparing results illustrate that the uniform sampling strategy (uniformly dispersed sampling strategy) has the best monitoring effect.

Enhancing Cryptocurrency Price Forecasting Accuracy: A Feature Selection and Weighting Approach With Bi-Directional LSTM and Trend-Preserving Model Bias Correction

A cryptocurrency is a digitized, encrypted, and decentralized virtual currency, which is impossible to counterfeit or double-spend. It is one of the very popular investment instruments and traded in blockchain based crypto exchanges on ever growing volume. It is quite volatile due to imbalance of supply and demand, government regulations, investor sentiment and above all media hype. Cryptocurrency price forecasting is an active area of research and several approaches have been proposed recently. This study proposed a price forecasting model based on three vital characteristics (i) a feature selection and weighting approach based on Mean Decrease Impurity(MDI) features. (ii) Bi-directional LSTM and (iii) with a trend preserving model bias correction (CUSUM control charts for monitoring the model performance over time) to forecast Bitcoin and Ethereum values for long and short term spans. The data for both currencies were analyzed in three different intervals: (i) April 01, 2013 to April 01, 2016 (ii) April 01, 2013 to April 01, 2017 and (iii) April 01, 2013 to December 31, 2019. Extensive series of experiments were performed and evaluated on Root Mean Square Errors (RMSE). Comparing with the prevalent forecasting models we report a new state of the art in cryptocurrency forecasting.

Design and properties of the predictive ratio cusum (PRC) control charts

In statistical process control/monitoring (SPC/M), memory-based control charts aim to detect small/medium persistent parameter shifts. When a phase I calibration is not feasible, self-starting methods have been proposed, with the predictive ratio cusum (PRC) being one of them. To apply such methods in practice, one needs to derive the decision limit threshold that will guarantee a preset false alarm tolerance, a very difficult task when the process parameters are unknown and their estimate is sequentially updated. Utilizing the Bayesian framework in PRC, we will provide the theoretic framework that will allow to derive a decision-making threshold, based on false alarm tolerance, which along with the PRC closed-form monitoring scheme will permit its straightforward application in real-life practice. An enhancement of PRC is proposed, and a simulation study evaluates its robustness against competitors for various model type misspecifications. Finally, three real data sets (normal, Poisson, and binomial) illustrate its implementation in practice. Technical details, algorithms, and R-codes reproducing the illustrations are provided as supplementary material.

MONITORING INVERSE RAYLEIGH DISTRIBUTED LIFETIMES USING DEWMA CONTROL CHART

In this paper, we proposed a Double Exponentially Weighted Moving Average DEWMA control chart. The proposed control chart is based on Inverse Rayleigh Distributed lifetimes using simple random sampling. Out-of-control-Average Run Length (ARL1) is used to evaluate the performance of the proposed control chart. The DEWMA control chart is compared with traditional/simple EWMA and CUSUM control charts. A simulated example is used to compare the proposed DEWMA, traditional/simple EWMA chart control chart. It is observed that the proposed DEWMA control chart performs simple EWMA control charts. The DEWMA control chart can be used for efficient monitoring of the production process in manufacturing industries where the data is coming from inverse Rayleigh Distribution. Keywords: EWMA, CUSUM, DEWMA, average run length (ARL).

The extended Erlang-truncated exponential distribution under CUSUM control charts for one sided

The extended Erlang-truncated exponential distribution under CUSUM control charts for one sided

Mill condition monitoring based on instantaneous identification of specific force coefficients under variable cutting conditions

Following the necessity of increased performance and availability requirements for manufacturing systems, research is becoming more and more attracted by monitoring solutions for cutting tools. In this paper, a robust unsupervised strategy for milling tool wear monitoring under variable process parameters and lubrication conditions is presented. The proposed method is completely unsupervised, thus not requiring any kind of training procedure, and is validated on different machine tools. The solution is based upon the online estimation of specific force coefficients (SFC) from instantaneous cutting forces in high-feed milling of Ti6Al4V workpiece. This avoids the need for continuously variable feed per tooth during cutting tests, necessitated for the application of reference literature approach. For this purpose, a novel high-feed mill mechanistic model was conceived and developed. Five run-to-failures were performed in different lubrication conditions – cryogenic and traditional lubrication – with different cutting speeds (50 m/min, 70 m/min and 125 m/min) on two different machine tools. Principal Component Regression was introduced in order to deal with the variability of the estimated coefficients. Self-starting tabular cusum control charts were implemented and demonstrated high accuracy and reliability in the prediction of notch wear phenomena as well as chipping of tool cutting edges for all the cases considered. The solution detected an out-of-control conditions ranging from 166μm to 499μm of maximum flank wear for the analysed tests. The mean prediction error with respect to the 600μm threshold is of −45% with a peak of −72%, whereas reference literature algorithms reach −57% and −66%, respectively. A sensitivity analysis of control chart threshold was performed with reference to the maximum flank wear at the detection point. In a supervised scenario, the threshold can be increased to obtain a less conservative approach: for instance, a mean prediction error of −41% was reached by doubling the threshold.

Diagnosing and quantifying post-COVID-19 fluctuations in the architecture billings indices

PurposeThe purpose of this paper is to understand the post-COVID-19 fluctuations in the building construction demand from various angles at the national, regional, and sectoral levels. Despite the significant impact of COVID-19 on the building construction industry, a detailed quantitative analysis of the COVID-19 impact on the building construction demand is still lacking. The current study aims to (1) establish a statistical approach to quantify the COVID-19 impact on the building construction demand; (2) investigate the post-COVID-19 fluctuations in the construction demand of different building services, regional markets, and building sectors using the historical time series of the architecture billings index (ABI); and (3) identify vulnerable market and sector and discuss the post-COVID-19 recovery strategies.Design/methodology/approachThe research methodology follows four steps: (1) collecting national, regional, and sectoral ABIs; (2) creating seasonal autoregressive integrated moving average models; (3) illustrating cumulative sum control charts to identify significant ABI deviations; and (4) quantifying the post-COVID-19 ABI fluctuations.FindingsThe results show that all the ABIs experienced a statistically significant decrease after COVID-19. The project inquiries index reduced more but recovered faster than billings and design contracts indices. The midwest billings index decreased the most among the regional ABIs and the commercial/industrial billing index dropped the most among the sectoral ABIs.Originality/valueThis study is unique in the way that it utilized the ABI data and the approach using SARIMA models and CUSUM control charts to assess the post-COVID-19 building construction demand represented by ABI fluctuations.

PSXII-20 Use of Statistical Process Control to Evaluate the Effect of Isoquinoline Alkaloids Supplementation on Productive Performance of Growing-Finishing Pigs

Abstract Statistical process control (SPC) is a statistical method that can be used to evaluate the production variation in swine operations, thus facilitating decision making. The objective of this study was to evaluate the effect of plant-derived isoquinoline alkaloids (IQs) supplementation on production performance of growing-finishing pigs by using SPC.The experiment was carried out in a commercial swine integration in Spain. Historical control (calibration) data was compiled from 2017 to June 2020. During this period, all animals received a standard commercial diet. During the treatment period, which started in July 2020 and lasted until February 2021, all pigs were fed the standard diet supplemented with 1 kg/t feed of a plant-based IQ product (Phytobiotics Futterzusatzstoffe GmbH, Eltville, Germany), from day 70 of life until slaughter. Data recorded during both, historical control and treatment periods included feed conversion ratio (FCR), average daily gain (ADG, g/d), average daily feed intake (ADFI, g/d), cost of medicines (Euro/pig), runts (%) and mortality rate (%). SPC tools were used to monitor the previously described performance parameters. CUSUM control charts were obtained for all parameters and for each nutritional and health cluster to show the evolution or the changes of each parameter. The results showed that pigs supplemented with IQs had a lower FCR, increased ADG and reduced cost in medications as compared to the control period (p ≤ 0.05; Table 1). SPC methods were successfully implemented to evaluate the effect of IQs supplementation on growth performance of grow-finish pigs. The results of the study indicated that IQs supplementation improved FCR and ADG, whereas the cost of medication was significantly reduced. Therefore, IQs supplementation in pigs from day 70 of life until slaughter could be a good strategy to improve the efficiency and profitability of the production system.