Monitoring surgical quality: the cumulative sum (CUSUM) approach.

The monitoring of processes is a vital mechanism for ensuring that such processes remain safe and under control. The present research aims to solve problems associated with correlated data by applying the Box-Jenkins method integrated with statistical process control (SPC) tools, namely the Shewhart chart, the moving average chart, the cumulative sum (CUSUM) chart, and the exponentially weighted moving-average (EWMA) chart. The efficiency of the four SPC tools was also compared in terms of the false alarm rate (FAR) and the missed detection rate (MDR). The findings indicated that the EWMA chart was the most effective in detecting anomaly, the Shewhart chart and the moving average chart produced high MDR, and the CUSUM chart suffered the highest FAR.

The cumulative sum (CUSUM) chart is a very effective control charting procedure used for the quick detection of small‐sized and moderate‐sized changes. It can detect small process shifts missed by the Shewhart‐type control chart, which is sensitive mainly to large shifts. To further enhance the sensitivity of the CUSUM control chart at detecting very small process disturbances, this article presents CUSUM control charts based on well‐structured sampling procedures, double ranked set sampling, median‐double ranked set sampling, and double‐median ranked set sampling. These sampling techniques significantly improve the overall performance of the CUSUM chart over the entire process mean shift range, without increasing the false alarm rate. The newly developed control schemes do not only dominate most of the existing charts but are also easy to design and implement as illustrated through an application example of real datasets. The control schemes used for comparison in this study include the conventional CUSUM chart, a fast initial response CUSUM chart, a 2‐CUSUM chart, a 3‐CUSUM chart, a runs rules‐based CUSUM chart, the enhanced adaptive CUSUM chart, the CUSUM chart based on ranked set sampling (RSS), and the single CUSUM and combined Shewhart–CUSUM charts based on median RSS. Copyright © 2014 John Wiley & Sons, Ltd.

Control charts applied to simulated sow herd datasets

Statistical process control (SPC) is the method that monitors process quality characteristics. Through control charts, one can detect whether the present process malfunction. However, some annoyances may arise while the engineers need to choose appropriately control chart under different levels of process variation. The Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely used for monitoring semiconductor manufacturing processes. Generally weighted moving average (GWMA) control chart is a new method of SPC, which was proposed by Sheu and Lin (2003). The main objective of this research is using step-by-step procedures to present a comparative study of the monitoring performance for Shewhart, CUSUM, EWMA and GWMA control charts. According to a specified in-control average run length (ARL), we determine the parameters of each control chart based on the Monte Carlo numerical simulation. The setting parameters in each control chart sre displayed and tabulated. While the process means or the process standard deviations are changing in different levels, the performance of each weighted control chart can be then compared by using the ARL. A rule of thumb for selecting better control schemes is provided as a truthfully reference to help engineers in choosing the more appropriate control charts immediately when the assignable causes occurred.

The cumulative sum (CUSUM) chart is known to be effective at detecting sustained shifts in the process mean. Unfortunately, its performance deteriorates when the process observations are autocorrelated. To eliminate the effect of autocorrelation in monitoring changes in the mean, the CUSUM chart is typically applied on the residuals of the chosen time-series model for the process observations. As an alternative, we develop a CUSUM scheme for detecting a step change in the process mean that directly utilizes the autocorrelated process observations. Analysis shows that the performance of the proposed scheme is very competitive when compared with the Shewhart and CUSUM charts based on residuals.

Monitoring Weibull time between event (TBE) processes is essential to avoid deterioration of quality characteristics in various reliability analysis problems. Statistical process monitoring (SPM) charts are widely used to monitor the possible decreasing mean shift. For monitoring such data, many control charts have been proposed in the literature, such as the Weibull exponentially weighted moving average (EWMA) chart, the Weibull cumulative sum (CUSUM) chart, and Mixed EWMA–CUSUM (MEC) chart and Mixed Hybrid EWMA–CUSUM (MHEC) chart. The current investigation revisits their efficacy and compares them with a CUSUM chart based on the generally weighted moving average (GWMA) statistic, labelled as the Mixed GWMA–CUSUM (MGC) chart, to monitor the decreasing mean shift in Weibull TBEs processes. We offer some numerical results based on the Monte‐Carlo simulation, such as average run length (ARL), the standard deviation of the run length (SDRL) and the relative mean index (RMI). Our findings show that the MGC chart often outperforms the existing control charts in detecting small downward shifts. Finally, an illustrative example is given to display the application of the MGC chart for Weibulll data.

Given the low early revision rate after total hip arthroplasty (THA) and total knee arthroplasty (TKA), hospital performance is typically compared using 3 years of data. The purpose of this study was to assess how much earlier worsening hospital performance in 1-year revision rates after THA and TKA can be detected. All 86,468 THA and 73,077 TKA procedures performed from 2014 to 2016 and recorded in the Dutch Arthroplasty Register were included. Negative outlier hospitals were identified by significantly higher O/E (observed divided by expected) 1-year revision rates in a funnel plot. Monthly Shewhart p-charts (with 2 and 3-sigma control limits) and cumulative sum (CUSUM) charts (with 3.5 and 5 control limits) were constructed to detect a doubling of revisions (odds ratio of 2), generating a signal when the control limit was reached. The median number of months until generation of a first signal for negative outliers and the number of false signals for non-negative outliers were calculated. Sensitivity, specificity, and accuracy were calculated for all charts and control limit settings using outlier status in the funnel plot as the gold standard. The funnel plot showed that 13 of 97 hospitals had significantly higher O/E 1-year revision rates and were negative outliers for THA and 7 of 98 hospitals had significantly higher O/E 1-year revision rates and were negative outliers for TKA. The Shewhart p-chart with the 3-sigma control limit generated 68 signals (34 false-positive) for THA and 85 signals (63 false-positive) for TKA. The sensitivity for THA and TKA was 92% and 100%, respectively; the specificity was 69% and 51%, respectively; and the accuracy was 72% and 54%, respectively. The CUSUM chart with a 5 control limit generated 18 signals (1 false-positive) for THA and 7 (1 false-positive) for TKA. The sensitivity was 85% and 71% for THA and TKA, respectively; the specificity was 99% for both; and the accuracy was 97% for both. The Shewhart p-chart with a 3-sigma control limit generated the first signal for negative outliers after a median of 10 months (interquartile range [IQR] = 2 to 18) for THA and 13 months (IQR = 5 to 18) for TKA. The CUSUM chart with a 5 control limit generated the first signal after a median of 18 months (IQR = 7 to 22) for THA and 21 months (IQR = 9 to 25) for TKA. Monthly monitoring using CUSUM charts with a 5 control limit enables earlier detection of worsening 1-year revision rates with accuracy so that initiatives to improve care can start earlier.

Three statistical control chart methods were investigated to determine the one with the highest detection probability and the best average run length (ARL). The three control charts include the Shewhart control chart of count data, cumulative sum (CUSUM) analysis of count data (Poisson CUSUM), and CUSUM analysis of time-interval (time difference between two consecutive radiation pulses) data (time-interval CUSUM). The time-interval CUSUM (CUSUMti) control chart was compared with the Poisson CUSUM (CUSUMcnt) and the Shewhart control charts with experimental and simulated data. The experimental data were acquired with a DGF-4C (XIA, Inc.) system in list mode. Simulated data were obtained by using Monte Carlo techniques to obtain a random sampling of a Poisson process. All statistical algorithms were developed using R (R Development Core Team). Detection probabilities and ARLs for the three methods were compared. The time-interval CUSUM control chart resulted in a similar detection probability as that of the Poisson CUSUM control chart but had the shortest ARL at relatively higher radiation levels; e.g., about 40% shorter than the Poisson CUSUM at 10.0 counts per second (cps) (five times above the background count rate). Both CUSUM control charts resulted in a higher detection probability than that of the Shewhart control chart; e.g., 100% greater than the Shewhart control method at 4.0 cps (two times above the background count rate). In addition, when time-interval information was used, the CUSUM control chart coupled with a modified runs rule (mrCUSUMti) showed the ability to further reduce the time needed to respond to changes in radiation levels and keep the false positive rate at a required level.

Cumulative Sum Curves and Their Prediction Limits

A neural network-based procedure for the monitoring of exponential mean

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.

This paper considers the problem of monitoring the mean of a normally distributed process variable when the objective is to effectively detect both small and large shifts in this mean. The performance of a generalized likelihood ratio (GLR) control chart is evaluated, where the likelihood ratio is based on a moving window of past observations. The performance of the GLR chart is compared with the performance of other options, such as combinations of Shewhart and cumulative sum (CUSUM) charts and an adaptive CUSUM chart, that have been proposed for detecting a wide range of shift sizes. Performance is evaluated for sustained shifts, transient shifts, and drifts in the mean. It is shown that the overall performance of the GLR chart is at least as good as these other options. These other options have multiple control-chart parameters that allow for the charts to be tuned to be more sensitive to certain shifts that may be of interest. However, the GLR chart does not require users to specify the values of any control-chart parameters other than the size of the window and the control limit. We recommend a specific window size and provide a table of control limits corresponding to specified values of the false-alarm rate, so it is very easy to design the GLR chart for use in applications. Simulating the performance of the GLR chart is time consuming, but approximating the GLR chart with a set of CUSUM charts provides a much faster way of evaluating the performance of the GLR chart for research purposes.

In the chemical and biochemical industries, batch processes play an important role in producing high-quality and value-added specialty products. The variables measured in such processes often have periodic trajectories with varying batch duration and fixed operational stages. The measured value of a process variable provides only part of the information about process conditions, while the process monitoring and operation activities mostly rely on the trends and trajectories of these variables. It is necessary to construct a trend-monitoring statistic to detect an abnormality in a batch process variable trajectory to provide operation decision support and guarantee product quality. In this paper, a new trend cumulative sum (CUSUM) chart is introduced as a way to detect the deviation of batch process variable trends, which may be caused by abnormal operations. This method relies on the extraction of variable trend features as a combination of derivatives through a functional description of variable trajectories. This then leads to the construction of an individual trend CUSUM chart and a multiple-trend CUSUM chart. The multiple-trend CUSUM chart, the sum of the trend CUSUM charts of all process variables, aims to improve the monitoring efficiency by combining the trend deviations of all variables in a single chart. The potential of these novel univariate control charts is demonstrated using the batch manufacture of polypropylene (PP). When several simulated and actual batches are studied, the results show that the trend CUSUM chart is capable of capturing trend abnormalities. We also show, by comparison, that alarms can be triggered in the trend CUSUM chart before the measured process variables exceed the control limits of their Shewhart individuals charts, allowing for the corrections to be made at an early stage of an abnormal situation.

Control charts (CCs) are one of the main tools in Statistical Process Control that have been widely adopted in manufacturing sectors as an effective strategy for malfunction detection throughout the previous decades. Measurement errors (M.E's) are involved in the quality characteristic of interest, which can effect the CC's performance. The authors explored the impact of a linear model with additive covariate M.E on the multivariate cumulative sum (CUSUM) CC for a specific kind of data known as compositional data (CoDa). The average run length is used to assess the performance of the proposed chart. The results indicate that M.E's significantly affects the multivariate CUSUM-CoDa CCs. The authors have used the Markov chain method to study the impact of different involved parameters using six different cases for the variance-covariance matrix (VCM) (i.e., uncorrelated with equal variances, uncorrelated with unequal variances, positively correlated with equal variances, positively correlated with unequal variances, negatively correlated with equal variances and negatively correlated with unequal variances). The authors concluded that the error VCM has a negative impact on the performance of the multivariate CUSUM-CoDa CC, as the increases with an increase in the value of the error VCM. The subgroup size m and powering operator b positively impact the proposed CC, as the decreases with an increase in m or b. The number of variables p also has a negative impact on the performance of the proposed CC, as the values of increase with an increase in p. For the implementation of the proposal, two illustrated examples have been reported for multivariate CUSUM-CoDa CCs in the presence of M.E's. One deals with the manufacturing process of uncoated aspirin tablets, and the other is based on monitoring the machines involved in the muesli manufacturing process.

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.