Should Observations Be Grouped for Effective Process Monitoring?

This study considers the construction of control charts when outliers could occur in the data. Simply increasing the width of control limits will make it more difficult to detect an out-of-control signal. This study aims to determine weights for each observation by measuring their respective distances to the average. The study proposes a retrospective weighted average and weighted inter-quartile range (WIQR) control chart based on the normal distribution that accounts for the false alarm rate, special causes, outliers, and a combination of special causes and outliers that might exist within the process. In addition to validating the detection effectiveness of the proposed control charts, this study also compares various average-type and range-type control charts for detecting the outliers and special causes. The proposed control charts show superior detection effectiveness in four tested scenarios compared to other types of control charts. Finally, the study also illustrates the practical application of the control charts for measuring the tensile strength of a deformed bar in coil. [Received 10 February 2014; Revised 21 August 2015; Revised 3 November 2015; Accepted 14 December 2015]

Background Although benchmarks and control charts are basic quality improvement tools, few surgeons use them to monitor surgical site infection (SSI). Obstacles to widespread acceptance include: (1) small denominators, (2) complexities of adjusting for patient risk and (3) scepticism about their true purpose (cost cutting, surgical privilege determination or improving outcomes). Methods The application of benchmark charts (using US national SSI rates as limits) and control charts (using facility rates as limits) was studied in 51 hospitals submitting data to the AICE National Database Initiative. SSI rates were risk adjusted by calculating a new statistic, the standardized infection ratio (SIR), based on the risk index suggested by the Centers for Disease Control National Nosocomial Infection Surveillance Study. Fourteen different types of control chart were examined and 115 suspiciously high or low monthly rates were flagged. Participating hospital epidemiologists investigated and classified each flag as ‘a real problem’ (potentially preventable) or ‘not a problem’ (beyond the control of personnel at this facility). Results None of the standard, widely recommended, control charts studied showed practical value for identifying either preventable rate increases or outbreaks (clusters due to a single organism). On the other hand, several types of risk-adjusted control chart based on the SIR correctly identified most true opportunities for improvement. Sensitivity, specificity and receiver–operator characteristic (ROC) analysis revealed that the XmR chart of monthly SIRs would be useful in hospitals with smaller surgical volumes (ROC area = 0·732, P = 0·001). For larger hospitals, the most sensitive and robust SIR chart for real-time monitoring of surgical infections was the mXmR chart (ROC area = 0·753, P = 0·0005).

Knowing when a process has changed would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process engineers. Much of the literature on change point models and techniques for statistical process control applications consider processes well modelled by the normal distribution. However, the Poisson distribution is commonly used in industrial quality control applications for modelling attribute-based process quality characteristics (e.g., counts of non-conformities). Some commonly used control charts for monitoring Poisson distributed data are the Poisson cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts. In this paper, we study the effect of changes in the design of the control chart on the performances of the change point estimators offered by these procedures. In particular, we compare root mean square error performances of the change point estimators offered by the Poisson CUSUM and EWMA control charts relative to that achieved by a maximum likelihood estimator for the process change point. Results indicate that the relative performance achieved by each change point estimator is a function of the corresponding control chart design. Relative mean index plots are provided to enable users of these control charts to choose a control chart design and change point estimator combination that will yield robust change point estimation performance across a range of potential change magnitudes.

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.

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.

The adaptive exponentially weighted moving average (AEWMA) control charts are the advanced form of classical memory control charts used for efficiently monitoring small-to-large shifts in the process parameters (location and/or dispersion). These AEWMA control charts estimate the unknown shifts using exponentially weighted moving average (EWMA) or cumulative sum (CUSUM) control charts statistics. The hybrid EWMA (HEWMA) control chart is preferred over classical memory control charts to detect early shifts in process parameters. So, this study presents a new auxiliary information-based (AIB) AEWMA (IAEWMAAIB) control chart for process location that estimates the unknown location shift using HEWMA statistic. The objective is to develop an unbiased location shift estimator using HEWMA statistic and then adaptively update the smoothing constant. The shift estimation using HEWMA statistic instead of EWMA or CUSUM statistics boosts the performance of the proposed IAEWMAAIB control chart. The Monte Carlo simulation technique is used to get the numerical results. Famous performance evaluation measures like average run length, extra quadratic loss, relative average run length, and performance comparison index are used to evaluate the performance of the proposed chart with existing counterparts. The comparison reveals the superiority of the proposed control chart. Finally, two real-life applications from the glass manufacturing industry and physicochemical parameters of groundwater are considered to show the proposed control chart’s implementation procedure and dominance.

In many cases, a $\overline X $ control chart based on a performance variable is used in industrial fields. Typically, the control chart monitors the measurements of a performance variable itself. However, if the performance variable is too costly or impossible to measure, and a less expensive surrogate variable is available, the process may be more efficiently controlled using surrogate variables. In this paper, we present a model for the economic statistical design of a VSI (Variable Sampling Interval) $\overline X $ control chart using a surrogate variable that is linearly correlated with the performance variable. We derive the total average profit model from an economic viewpoint and apply the model to a Very High Temperature Reactor (VHTR) nuclear fuel measurement system and derive the optimal result using genetic algorithms. Compared with the control chart based on a performance variable, the proposed model gives a larger expected net income per unit of time in the long-run if the correlation between the performance variable and the surrogate variable is relatively high. The proposed model was confined to the sample mean control chart under the assumption that a single assignable cause occurs according to the Poisson process. However, the model may also be extended to other types of control charts using a single or multiple assignable cause assumptions such as VSS (Variable Sample Size) $\overline X $ control chart, EWMA, CUSUM charts and so on.

Control charts applied to simulated sow herd datasets

The magnificent seven statistical process control (SPC) tools are commonly used to monitor the variation in the process. Control charts are the most efficient and real‐time monitoring tool from the SPC toolkit. A control chart visually differentiates the effect of special or inherent cause variations and indicates the process as out‐of‐control when such a special cause exists. For single occasion problems, simple random sampling (SRS) is used as a sampling design. When the quality of a product is assessed at regular intervals, then modified successive sampling (MSS) is chosen as the preferred sampling mechanism. Hence, this paper intends to propose EWMA‐MSS(S) and CUSUM‐MSS(S) charts under MSS schemes to monitor moderate to small shifts in the location parameter of a process. We presented the performance evaluation of EWMA‐MSS(S) and CUSUM‐MSS(S) charts in terms of run length metrics and compared them with the Shewhart‐MSS(S) control chart. The outcomes show that the EWMA‐MSS(S) perform amazingly well as compared to the Shewhart‐MSS(S) and CUSUM‐MSS(S) control charts. Further, illustration of the proposed charts on the QSAR aquatic toxicity dataset is also used to demonstrate the application of the proposed charts.

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are used to detect smaller shifts in process parameters. The usual EWMA and CUSUM charts depend on the normality assumption for a better detection ability. This study proposes an efficient EWMA control chart based on the spirit of Tukey control chart, especially designed for skewed distributions. The performance of the proposed and the competing charts is measured using different length properties such as average run length (ARL), standard deviation of run length (SDRL), and median run length (MDRL). We have observed that the proposed chart is quite efficient at detecting process shifts of smaller magnitude, especially for skewed distributions. For practical considerations, the proposed chart is implemented at aerospace manufacturing data on industrial production index.

6579 Background: Collecting electronic patient reported outcomes (ePROs) reduces the burden of cancer and prevents acute care hospitalizations. However, broad implementation in the routine care setting remains challenging, partly because the optimal implementation strategies – actions that are most likely to encourage adoption and use – are not known. Since 2019, the SIMPRO Consortium has deployed an ePRO-based symptom management program (eSyM) across 6 community-based cancer centers. Methods: We used statistical process control (SPC) charts to identify variation due to special versus common causes (random variation) for one key performance indicator (KPI) – the weekly ePROs response rate. All 6 SIMPRO sites contributed data for this analysis: 3 for chemotherapy patients and 3 for surgery patients. Sites had to have at least 18 months of KPI data; information from the first 4 months after eSyM rollout were excluded to account for program ramp-up. The KPI was calculated as the number of patients who submitted an ePRO questionnaire divided by the number eligible to submit a questionnaire each week. The upper and lower confidence limits were set at +/- 2 sigma to allow for 95% of observations to fall within the limits. Three rules were applied to identify special cause variation: 1) astronomical points (outside sigma limits), 2) shifts (8 or more points above or below a center line), and 3) trends (6 or more points consecutively ascending or descending). Implementation strategies that mapped to special cause variations were selected as those most likely to impact the KPI. Results: Across the 6 sites that deployed eSyM, the mean KPI performance ranged from 19.7%-35.7%. SPC charts detected multiple special cause variations in the KPI at all 6 sites, though the patterns varied by site. All sites demonstrated positive and negative astronomical variations as well as positive and negative shifts. Three sites demonstrated negative trends; no sites demonstrated positive trends. Direct patient outreach was the implementation strategy most frequently associated with special cause variation, followed by changes in promoting the ePRO program to clinical staff. Positive changes were associated with strategy initiation; negative changes were associated with strategy discontinuation. Conclusions: Applying SPC charts to a KPI from the eSyM deployment highlighted the effect of personal communication with patients and providers, suggesting that these implementation strategies could offer value to other sites deploying eSyM. The absence of positive trends early in eSyM program deployment underscores the need to identify better implementation strategies and allocate more resources to foster program adoption and sustainability. Applying SPCs to other KPIs, such as symptom severity and healthcare utilization, could improve eSyM deployment and impact.

Control chart (CC) is used to monitor the special causes that arise during the process monitoring. These special causes produce continual shifts in the process parameters that last until it is identified and removed. There is a need for such techniques, which present the true representation of the entire process. Rational subgrouping is an essential concept in Statistical Process Control (SPC) which is seldom overlooked by the practitioner. Hence, most of the manufacturing, engineering, and production processes give output products in the form of batches over smaller intervals of time. The aim of this study is to provide a median based design for Tukey and Tukey-EWMA control charts under subgrouping. It will use the idea of boxplot to monitor the process behavior. This study also provides a brief discussion regarding selecting and forming subgroups from the process data. The performance of the median based Tukey and Tukey-EWMA charts are judged using Average, Median and Standard-Deviation run-length as performance measures. We have considered subgroup sizes of m=1,5 &10 at pre-specified ARL0 equal to 370. To real-life applications of the median based tukey designs are also presented to show their implementation in food manufacturing and hard-bake processes.

A general fuzzy-statistical clustering approach for estimating the time of change in variable sampling control charts

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 the quality of new or ongoing surgical activities is a necessity. Several Statistical Process Control (SPC) tools are available to professionals. Among them, Shewhart charts and cumulative sum charts (CUSUM charts) are useful methods to provide visual feedback before significant quality issues arise. In this paper, we discuss both methods based on our current approach. On Shewhart charts, one variable value is plotted on a time-series line. This method provides information about every single determination. Random variations of the values appear and by adjusting the adequate control limits it is possible to know whether those variations are random or out-of-control. Although large variations are easily detected, small but relevant changes are not. On the contrary, CUSUM charts have the capability of detecting small changes quickly. CUSUM is defined as a statistical tool that graphically represents the sequential monitoring of cumulative performance of any dichotomized or continuous variable under assessment. It emphasizes failures penalizing them against the correct performance when individual risk is adjusted. This makes CUSUM especially sensitive to negative changes. CUSUM can be created without the need of a specific sample size and grow with every new case included. Besides the variable under control (with specific definitions of acceptable and unacceptable outcomes), the type I and II errors for the defined parameter and the individual risk of acceptable or unacceptable outcomes must be included in the chart. Graphical representation of these three parameters is easy and intuitive to read making CUSUM graphs a reliable tool to understand the trending of the parameter under control. If performance is considered inadequate: analysis, discussion and implementation of agreed measures should be taken. Despite its limitations, CUSUM analysis is considered the best tool for quality control in health care domain.