Economic Design of CUSUM Control Charts

In statistical process control, control charts are one tool for monitoring the control status of a process. One such type of chart is the cumulative sum (CUSUM) chart which has advantages over other styles of control chart. A study of the economic design of CUSUM control charts is undertaken via a comparative study of long-run hourly cost (LRHC) and a computational search algorithm is used to minimize LRHC for a CUSUM chart using nine parameters confined to their respective feasible parameter spaces as defined by the chart designer. Savings over similarly designed two stage Xbar charts are discovered and presented.  M.A

Development and Evaluation of Special Control Charts for Quality Data Generated from a First Order Response Process

This research is concerned with the development and evaluation of special control charting techniques for quality data generated from a first order response process. The primary objectives are to present methodology for constructing the control limits of these special control charts using a conditional distribution and to use computer simulation to determine the average run length of these charts. Several SAS programs are used in the study to determine the average run length for a particular scenario. Modifications of the programs are then done to facilitate the determination of the average run length for other scenarios. Comparisons of these average run lengths with those of other control charts commonly used on continuous flow processes are then made. A FORTRAN program is also coded to calculate the control limits of these special control charts. It is found that the special control charts are capable of monitoring the mean and/or dispersion of a first order response process.Industrial Engineering and Managemen

Control Charts to Enhance Quality

Control charts are important tools of statistical quality control to enhance quality. Quality improvement methods have been applied in the last few 10 years to fulfill the needs of consumers. The product has to retain the desired properties with the least possible defects, while maximizing profit. There are natural variations in production, but there are also assignable causes which do not form part of chance. Control charts are used to monitor production; in particular, their application may serve as an “early warning” index regarding potential “out-of-control” processes. In order to keep production under control, different control charts which are prepared for dissimilar cases are established incorporating upper and lower control limits. There are a number of control charts in use and are grouped mainly as control charts for variables and control charts for attributes. Points plotted on the charts may reveal certain patterns, which in turn allows the user to obtain specific information. Patterns showing deviations from normal behavior are raw material, machine setting or measuring method, human, and environmental factors, inadvertently affecting the quality of product. The information obtained from control charts assists the user to take corrective actions, hence opting for specified nominal values enhancing as such quality

Acquired brain injury and evaluation of intensive training of attention in early neurorehabilitation : statistical evaluation and qualitative perspectives

Attention dysfunction is a cardinal symptom after an acquired brain injury (ABI) sometimes leading to life-long consequences that affect learning skills, daily functioning and social and emotional life. Attention may be successfully improved by structured training within rehabilitation programs, with the Attention Process Training (APT) as practice standard in the chronic stage after ABI. Practice recommendations in an earlier stage after ABI are less conclusive, possibly due to difficulties in distinguishing treatment effect from individual trajectories of spontaneous recovery. A randomized controlled trial (RCT) was performed at a university department of rehabilitation medicine. Patients with attention dysfunction after stroke or traumatic brain injury received 20 hours of attention training added to their individual rehabilitation program. The patients were randomized to one of two interventions of attention training: APT or activity-based attention training. The thesis focuses on the effect of attention training within four months post-injury. In Study I, the strict inclusion and exclusion criteria common to interventions trials in clinical research decimated patient recruitment, ultimately leading to an inclusion of < 10 % of admitted patients with stroke or TBI. Sampling bias was identified within the group of patients meeting all criteria. Eligible patients participating in the intervention study were more likely to be in a relationship and had a higher education. Strict inclusion and exclusion criteria prolonged data collection rendering the study group potentially less representative. We advocate the use of broader inclusion criteria and common data elements in future studies. Study II evaluated the feasibility of time-series measurements using statistical process control (SPC) for detecting change in an evolving process. SPC identified if, and when change occurred and the results described three patterns of performance: rapid improvement, steady improvement and stationary performance showing no improvement. By providing information about when change occurs, SPC enables adjustment of individual treatment response in early cognitive rehabilitation. In Study III, we applied SPC to explore the intervention effect of two methods of attention training: APT and activity-based attention training, within four months post injury. Although substantial improvement of attention was confirmed for both intervention groups, APT lead to an increased robustness of improvement, and resulted in a higher number of improved patients reaching change in performance at a faster rate. Study IV explored the experience of managing attention difficulties in daily life 2-4 years after brain injury and APT. Fourteen interviews were analyzed according to grounded theory and lead to the development of a model of attention management. The attention management emerged as a dynamic process where adjustment and refinement of management strategies increased with awareness and deepened application of applied knowledge, regulated by situation-dependent factors. Self-awareness and the detailed identification of dysfunction derived problem areas, including tenacious self-training with specific goal-setting, were promoted by APT. In conclusion, attention training is a promising intervention in the early stage after ABI with APT potentially boosting the improvement process as seen both during intervention and in the experience of attention management over time. SPC enables us to identify if, when and how change occurs in an evolving process. It may be used on both individual and group level

Monitoring Hospital Safety Climate Using Control Charts of Non-harm Events in Reporting Systems

The primary aim of this thesis is to design an approach and demonstrate a methodology to supplement safety culture assessment efforts. The framework affords an enhanced understanding of hospital safety climate, specifically reporting culture, through the use of control charts to monitor non-harm patient safety events documented in reporting systems. Assessing safety culture and climate remains difficult. One of the most common methods to assess safety culture is a self-report survey administered annually. Surveys assess safety climate, because they are a snapshot of the management\u27s and front-line staff\u27s perceptions of safety within their settings. One component of safety culture is reporting culture, which is assessed by survey questions targeting the total number and frequency of events reported by individuals. Surveys use subjective data to measure outcome variables with regard to patient safety event reporting. Relying on subjective data when organizations also collect data on actual reporting rates may not be optimal. Additionally, the time lag limits management\u27s ability to efficiently assess the need for, and the effect of improvements. Strategic interventions may result in effective change, but annual summary data may mask the effects. Additionally, there are advantages to focusing on non-harm events, and capturing non-harm event reporting rates may aid safety climate assessment. Despite the limitations of reporting systems, incorporating actual data may allow organizations to gain a more accurate depiction of the safety climate and reporting culture. With the increased prevalence of reporting systems in healthcare organizations, the data can be used to track and trend reporting rates of the organization. Incorporating control charts can help identify expected non-harm event reporting rates, and can be used to monitor trends in reporting culture. Data in reporting systems are continuously updated allowing quicker assessment and feedback than annual surveys. The methodology is meant to be prescriptive and uses data that hospitals typically collect. Hospitals can easily follow the summarized approach: check for underlying data assumptions, construct control charts, monitor and analyze those charts, and investigate special cause variation as it arises. The methodology is described and demonstrated using simulated data for a hospital and three of its departments

MULTIVARIATE STATISTICAL PROCESS CONTROL FOR CORRELATION MATRICES

Measures of dispersion in the form of covariance control charts are the multivariate analog to the univariate R-chart, and are used in conjunction with multivariate location charts such as the Hotelling T2 chart, much as the R-chart is the companion to the univariate X-bar chart. Significantly more research has been directed towards location measures, but three multivariate statistics (|S|, Wi, and G) have been developed to measure dispersion. This research explores the correlation component of the covariance statistics and demonstrates that, in many cases, the contribution of correlation is less significant than originally believed, but also offers suggestions for how to implement a correlation control chart when this is the variable of primary interest.This research mathematically analyzes the potential use of the three covariance statistics (|S|, Wi, and G), modified for the special case of correlation. A simulation study is then performed to characterize the behavior of the two modified statistics that are found to be feasible. Parameters varied include the sample size (n), number of quality characteristics (p), the variance, and the number of correlation matrix entries that are perturbed. The performance and utility of the front-running correlation (modified Wi) statistic is then examined by comparison to similarly classed statistics and by trials with real and simulated data sets, respectively. Recommendations for the development of correlation control charts are presented, an outgrowth of which is the understanding that correlation often does not have a large effect on the dispersion measure in most cases

Some new nonparametric distribution-free control charts based on rank statistics

Ph.DDOCTOR OF PHILOSOPH

STATISTICAL ASPECTS OF FETAL SCREENING

This thesis discusses the current screening algorithm that is used to detect fetal Down's syndrome. The algorithm combines a model for predicting age related risks and a model for appropriately transformed serum concentrations to produce estimates of risks. A discriminant analysis is used to classify pregnancies as either unaffected or Down's syndrome. The serum concentrations vary with gestational age and the relationship between serum concentrations and gestational age is modelled using regression. These models are discussed and alternative models for these relationships are offered. Concentration values are generally expressed in terms of multiples of the medians for unaffected pregnancies, or MoM values, which involves grouping the concentrations into weekly bins. Transformations of the MoM values are used in the model for predicting risks. The transformed values are equivalent to the residuals of the fitted regression models. This thesis directly models the residuals rather than converting the data to MoM values. This approach avoids the need to group gestational dates into completed weeks. The performance of the algorithm is assessed in terms the detection rates and false positive rates. The performance rates are prone to considerable sampling error. Simulation methods are used to calculate standard errors for reported detection rates. The bias in the rates is also investigated using bootstrapping techniques. The algorithm often fails to recognize abnormalities other than Down's syndrome and frequently associates them with low risks. A solution to the problem is offered that assigns an index of atypicality to each pregnancy, to identify those pregnancies that are atypical of unaffected pregnancies, but are also unlike Down's syndrome pregnancies. Nonparametric techniques for estimating the class conditional densities of transformed serum values are used as an alternative to the conventional parametric techniques of estimation. High quality density estimates are illustrated and these are used to compute nonparametric likelihood ratios that can be used in the probability model to predict risks. The effect of errors in the methods of recording gestational dates on the parameter estimates that are used in the discriminant analysis is also considered.Johnson & Johnson Clinical Diagnostics Lt