Showing papers by "William H. Woodall published in 2017"

An overview and perspective on social network monitoring

Abstract: In this expository article we give an overview of some statistical methods for the monitoring of social networks. We discuss the advantages and limitations of various methods as well as some relevant issues. One of our primary contributions is to give the relationships between network monitoring methods and monitoring methods in engineering statistics and public health surveillance. We encourage researchers in the industrial process monitoring area to work on developing and comparing the performance of social network monitoring methods. We also discuss some of the issues in social network monitoring and give a number of research ideas.

A head-to-head comparative study of the conditional performance of control charts based on estimated parameters

Abstract: Implementation of the Shewhart, CUSUM, and EWMA charts requires estimates of the in-control process parameters. Many researchers have shown that estimation error strongly influences the performance of these charts. However, a given amount of estimation error may differ in effect across charts. Therefore, we perform a pairwise comparison of the effect of estimation error across these charts. We conclude that the Shewhart chart is more strongly affected by estimation error than the CUSUM and EWMA charts. Furthermore, we show that the general belief that the CUSUM and EWMA charts have similar performance no longer holds under estimated parameters.

Dynamic probability control limits for risk‐adjusted CUSUM charts based on multiresponses

Abstract: For a patient who has survived a surgery, there could be several levels of recovery. Thus, it is reasonable to consider more than two outcomes when monitoring surgical outcome quality. The risk-adjusted cumulative sum (CUSUM) chart based on multiresponses has been developed for monitoring a surgical process with three or more outcomes. However, there is a significant effect of varying risk distributions on the in-control performance of the chart when constant control limits are applied. To overcome this disadvantage, we apply the dynamic probability control limits to the risk-adjusted CUSUM charts for multiresponses. The simulation results demonstrate that the in-control performance of the charts with dynamic probability control limits can be controlled for different patient populations because these limits are determined for each specific sequence of patients. Thus, the use of dynamic probability control limits for risk-adjusted CUSUM charts based on multiresponses allows each chart to be designed for the corresponding patient sequence of a surgeon or a hospital and therefore does not require estimating or monitoring the patients' risk distribution. Copyright © 2017 John Wiley & Sons, Ltd.

Dynamic Probability Control Limits for Lower and Two‐Sided Risk‐Adjusted Bernoulli CUSUM Charts

Abstract: Because of its advantages of design, performance, and effectiveness in reducing the effect of patients' prior risks, the risk-adjusted Bernoulli cumulative sum (CUSUM) chart is widely applied to monitor clinical and surgical outcome performance. In practice, it is beneficial to obtain evidence of improved surgical performance using the lower risk-adjusted Bernoulli CUSUM charts. However, it had been shown that the in-control performance of the charts with constant control limits varies considerably for different patient populations. In our study, we apply the dynamic probability control limits (DPCLs) developed for the upper risk-adjusted Bernoulli CUSUM charts to the lower and two-sided charts and examine their in-control performance. The simulation results demonstrate that the in-control performance of the lower risk-adjusted Bernoulli CUSUM charts with DPCLs can be controlled for different patient populations, because these limits are determined for each specific sequence of patients. In addition, practitioners could also run upper and lower risk-adjusted Bernoulli CUSUM charts with DPCLs side by side simultaneously and obtain desired in-control performance for the two-sided chart for any particular sequence of patients for a surgeon or hospital. Copyright © 2016 John Wiley & Sons, Ltd.

Reduction of the Effect of Estimation Error on In‐control Performance for Risk‐adjusted Bernoulli CUSUM Chart with Dynamic Probability Control Limits

Abstract: The in-control performance of any control chart is highly associated with the accuracy of estimation for the in-control parameter(s). For the risk-adjusted Bernoulli cumulative sum (CUSUM) chart with a constant control limit, it had been shown that the estimation error could have a substantial effect on the in-control performance. In our study, we examine the effect of estimation error on the in-control performance of the risk-adjusted Bernoulli CUSUM chart with dynamic probability control limits (DPCLs). Our simulation results show that the in-control performance of risk-adjusted Bernoulli CUSUM chart with DPCLs is also affected by the estimation error. The most important factors affecting estimation error are the specified desired in-control average run length, the Phase I sample size, and the adverse event rate. However, the effect of estimation error is uniformly smaller for the risk-adjusted Bernoulli CUSUM chart with DPCLs than for the corresponding chart with a constant control limit under various realistic scenarios. In addition, we found a substantial reduction in the mean and variation of the standard deviation of the in-control run length when DPCLs are used. Therefore, use of DPCLs has yet another advantage when designing a risk-adjusted Bernoulli CUSUM chart. Copyright © 2016 John Wiley & Sons, Ltd.

Improved implementation of the risk-adjusted Bernoulli CUSUM chart to monitor surgical outcome quality.

Abstract: Methodology issue The traditional implementation of the risk-adjusted Bernoulli cumulative sum (CUSUM) chart for monitoring surgical outcome quality requires waiting a pre-specified period of time after surgery before incorporating patient outcome information. Proposed solution We propose a simple but powerful implementation of the risk-adjusted Bernoulli CUSUM chart that incorporates outcome information as soon as it is available, rather than waiting a pre-specified period of time after surgery. Evaluation A simulation study is presented that compares the performance of the traditional implementation of the risk-adjusted Bernoulli CUSUM chart to our improved implementation. We show that incorporating patient outcome information as soon as it is available leads to quicker detection of process deterioration. Advice to practitioners Deterioration of surgical performance could be detected much sooner using our proposed implementation, which could lead to the earlier identification of problems.

Monitoring foreclosure rates with a spatially risk-adjusted Bernoulli CUSUM chart for concurrent observations

Abstract: Frequently in process monitoring, situations arise in which the order that events occur cannot be distinguished, motivating the need to accommodate multiple observations occurring at the same time, or concurrent observations. The risk-adjusted Bernoulli cumulative sum (CUSUM) control chart can be used to monitor the rate of an adverse event by fitting a risk-adjustment model, followed by a likelihood ratio-based scoring method that produces a statistic that can be monitored. In our paper, we develop a risk-adjusted Bernoulli CUSUM control chart for concurrent observations. Furthermore, we adopt a novel approach that uses a combined mixture model and kernel density estimation approach in order to perform risk-adjustment with regard to spatial location. Our proposed method allows for monitoring binary outcomes through time with multiple observations at each time point, where the chart is spatially adjusted for each Bernoulli observation's estimated probability of the adverse event. A simulation stud...

Using the predictive distribution to determine control limits for the Bayesian MEWMA chart

Abstract: Bayesian control charts have been proposed for monitoring multivariate processes with the multivariate exponentially weighted moving average (MEWMA) statistic. It has been suggested that we use limits based on the predictive distribution of the MEWMA statistic. This analysis, however is based on the erroneous result that the average run length (ARL) is a function of the exceedance probability, that is, the probability that the first point exceeds the control limit. We show how this result can be corrected and we discuss how the Bayesian MEWMA chart with limits based on the predictive distribution compares with other multivariate control chart procedures.

An Evaluation of Wheeler's Method for Monitoring the Rate of Rare Events

Abstract: Its wide application in practice makes the monitoring of the rate of rare events a popular research topic. Recently a researcher proposed plotting the counts between events on an individuals X-chart with an upper control limit to detect process improvement and plotting the reciprocals of the counts on an X-chart to detect process deterioration. He also used the median as the center line and the median moving range to obtain control limits in both control charts to address the problem of the standard deviation estimate inflation caused by extreme values. In our paper, we investigated the statistical performance of the four proposed approaches using simulation. We find using the mean results in a high proportion of ineffective control limits, while using the median avoids the issue of ineffective control limits but produces an unacceptably high proportion of false alarms. Copyright © 2016 John Wiley & Sons, Ltd.