Stefan H. Steiner

EWMA CONTROL CHARTS WITH TIME-VARYING CONTROL LIMITS AND FAST INITIAL RESPONSE

The control limits of an exponentially weighted moving average (EWMA) control chart should vary with time, approaching asymptotic limits as time increases. However, previous analyses of EWMA charts consider only asymptotic control limits. In this articl..

An Overview of Phase I Analysis for Process Improvement and Monitoring

We provide an overview and perspective on the Phase I collection and analysis of data for use in process improvement and control charting. In Phase I, the focus is on understanding the process variability, assessing the stability of the process, investigating process-improvement ideas, selecting an appropriate in-control model, and providing estimates of the in-control model parameters. In our article, we review and synthesize many of the important developments that pertain to the analysis of process data in Phase I. We give our view of the major issues and developments in Phase I analysis. We identify the current best practices and some opportunities for future research in this area.

Risk-Adjusted Monitoring of Binary Surgical Outcomes

A graphical procedure suitable for prospectively monitoring surgical performance is proposed. The approach is based on accumulating evidence from the outcomes of all previous surgical patients in a series using a new type of cumulative sum chart. Cumulative sum procedures are designed to “signal” if sufficient evidence has accumulated that the surgical failure rate has changed substantially. In this way, the chart rapidly detects deterioration (or improvement) in surgical performance while not overreacting to the expected fluctuations due to chance. Through the use of a likelihood-based scoring method, the cumulative sum procedure is adapted so that it adjusts for the surgical risk of each patient estimated preoperatively. The procedure is therefore applicable in situations where it is desirable to adjust for a mix of patients. Signals of the chart lead to investigations of the cause and to the timely introduction of remedial measures designed to avoid unnecessary future failures.

Monitoring the Evolutionary Process of Quality: Risk-Adjusted Charting to Track Outcomes in Intensive Care

OBJECTIVE To present graphical procedures for prospectively monitoring outcomes in the intensive care unit. DESIGN Observational study: risk-adjusted control chart analysis of a case series. SETTING Tertiary referral adult intensive care unit: Princess Alexandra Hospital, Brisbane, Australia. PATIENTS A total of 3398 intensive care unit admissions from January 1, 1995, to January 1, 1998. CONCLUSIONS Risk-adjusted process control charting procedures for continuous monitoring of intensive care unit outcomes are proposed as quality management tools. A modified Shewhart p chart and cumulative sum process control chart, using the Acute Physiology and Chronic Health Evaluation III model mortality prediction for risk adjustment, are presented. The risk-adjusted p chart summarizes performance at arbitrary intervals and plots observed against predicted mortality rate to detect large changes in risk-adjusted mortality. The risk-adjusted cumulative sum procedure is a likelihood-based scoring method that adjusts for estimated risk of death, accumulating evidence from outcomes of all previous patients. It formally tests the hypothesis of a change in the odds of death. In this application, we detected a decrease from above to predicted risk-adjusted mortality. This was temporally related to increased senior staffing levels and enhanced ongoing multidisciplinary review of practice, quality improvement, and educational activities. Formulas and analyses are provided as appendices.

Risk-adjusted survival time monitoring with an updating exponentially weighted moving average (EWMA) control chart

Monitoring medical outcomes is desirable to help quickly detect performance changes. Previous applications have focused mostly on binary outcomes, such as 30-day mortality after surgery. However, in many applications the survival time data are routinely collected. In this paper, we propose an updating exponentially weighted moving average (EWMA) control chart to monitor risk-adjusted survival times. The updating EWMA (uEWMA) operates in a continuous time; hence, the scores for each patient always reflect the most up-to-date information. The uEWMA can be implemented based on a variety of survival-time models and can be set up to provide an ongoing estimate of a clinically interpretable average patient score. The efficiency of the uEWMA is shown to compare favorably with the competing methods.

Monitoring paired binary surgical outcomes using cumulative sum charts

Correlated binary data are encountered in many areas of medical research, system reliability and quality control. For monitoring failures rates in such situations, simultaneous bivariate cumulative sum (CUSUM) charts with the addition of secondary control limits are proposed. Using an approach based on a Markov chain model, the run length properties of such a monitoring scheme can be determined for sudden, or gradual, changes in the failure rates. The proposed control charts are easy to implement, and are shown to be very effective at detecting small changes in the rate of undesirable outcomes, especially when the changes are gradual. This procedure is illustrated using bivariate outcome data arising from a series of paediatric surgeries. The methodology is sufficiently general that it may be adapted for multivariate normal, binomial or Poisson responses.

On the circle closest to a set of points

The objective of this paper is to find a circle whose circumference is as close as possible to a given set of points. Three objectives are considered: minimizing the sum of squares of distances, minimizing the maximum distance, and minimizing the sum of distances. We prove that these problems are equivalent to minimizing the variance, minimizing the range, and minimizing the mean absolute deviation, respectively. These problems are formulated and heuristically solved as mathematical programs. Special efficient heuristic algorithms are designed for two cases: the sum of squares, and the minimax. Computational experience is reported.

A Multivariate Robust Control Chart for Individual Observations

To monitor a multivariate process, a classical Hotellings T2 control chart is often used. However, it is well known that such control charts are very sensitive to the presence of outlying observations in the historical Phase I data used to set the control limit. In this paper, we propose a robust Hotellings T2-type control chart for individual observations based on highly robust and efficient estimators of the mean vector and covariance matrix known as reweighted minimum covariance determinant (RMCD) estimators. We illustrate how to set the control limit for the proposed control chart, study its performance using simulations, and illustrate implementation in a real-world example.

An Overview of the Shainin System™ for Quality Improvement

ABSTRACT The Shainin System™ (SS) is the name given to a problem solving system, with its associated strategies and tools, developed by Dorian Shainin, and widely used and promoted in the manufacturing sector. Dorian Shainin also called this system Statistical Engineering, reflecting his engineering education and background. The consulting firm, Shainin LLC, offers the system under the trademarked name Red X® Strategy. Much of SS is neither well documented, nor adequately discussed in peer-reviewed journals. The goal of this article is to provide an overview of SS, a critical assessment, and a brief comparison with other industrial problem solving systems. The emphasis is on a discussion of the guiding philosophy and principles. Some specific SS tools are examined and compared with alternative methods. In our assessment, the Shainin System is valuable for many types of problems and many of its elements have been, or should be, incorporated into other process improvement methodologies. However, many of the statistical tools and methods promoted in conjunction with SS are neither novel nor necessarily the best.

Making Mixtures Robust to Noise and Mixing Measurement Errors

Mixture experiments involve the mixing or blending of two or more ingredients to form an end product. Typically, the quality of the end product is a function of the relative proportions of the ingredients and other extraneous process factors such as hea..