Cusum charts for preliminary analysis of individual observations

A preliminary Cusum chart based on individual observations is developed from the uniformly most powerful test for the detection of linear trends. This Cusum chart is compared with several of its competitors which are based on the likelihood ratio test and on transformations of standardized recursive residuals on which for instance the Q-chart methodology is based. It turns out that the new proposed Cusum chart is not only superior in the detection of linear trend out-of-control conditions, but also in the detection of other out-of-control situations. Approximate control limits, determined from simulation, and an example of its use in practice are given for the proposed Cusum chart.Cusum chart;detection of linear trends

Cusum charts for preliminary analysis of individual observations

A preliminary Cusum chart based on individual observations is developed from the uniformly most powerful test for the detection of linear trends. This Cusum chart is compared with several of its competitors which are based on the likelihood ratio test and on transformations of standardized recursive residuals on which for instance the Q-chart methodology is based. It turns out that the new proposed Cusum chart is not only superior in the detection of linear trend out-of-control conditions, but also in the detection of other out-of-control situations. Approximate control limits, determined from simulation, and an example of its use in practice are given for the proposed Cusum chart

A Risk‐Adjusted O–E CUSUM with Monitoring Bands for Monitoring Medical Outcomes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97491/1/biom1822.pd

Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

A weighted cumulative sum (WCUSUM) to monitor medical outcomes with dependent censoring

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108011/1/sim6139.pd

Distribution-free cumulative sum control charts using bootstrap-based control limits

This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS197 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Guaranteed Conditional Performance of Control Charts via Bootstrap Methods

To use control charts in practice, the in-control state usually has to be estimated. This estimation has a detrimental effect on the performance of control charts, which is often measured for example by the false alarm probability or the average run length. We suggest an adjustment of the monitoring schemes to overcome these problems. It guarantees, with a certain probability, a conditional performance given the estimated in-control state. The suggested method is based on bootstrapping the data used to estimate the in-control state. The method applies to different types of control charts, and also works with charts based on regression models, survival models, etc. If a nonparametric bootstrap is used, the method is robust to model errors. We show large sample properties of the adjustment. The usefulness of our approach is demonstrated through simulation studies.Comment: 21 pages, 5 figure

Evaluating Failure Outcomes with Applications to Transplant Facility Performance.

We develop several methods to evaluate mortality experience of medical facilities with applications to transplant facilities' post-transplant mortality and pre-transplant waitlist mortality. We aim to compare the center-specific outcomes with the standard practice while providing timely feedback to the centers. In Chapter II, we introduce a risk-adjusted O-E (Observed-Expected) Cumulative Sum (CUSUM) chart along with monitoring bands as decision criterion, to monitor the post-transplant mortality in transplant programs. This can be used in place of a traditional but complicated V-mask and yields a more simply interpreted chart. The resulting plot provides bounds that allow for simultaneous monitoring of failure time outcomes with signals for `worse than expected' or `better than expected'. The plots are easily interpreted in that their slopes provide graphical estimates of relative risks and direct information on additional failures needed to trigger a signal. In Chapter II, we discuss the construction of a weighted CUSUM to evaluate pre-transplant waitlist mortality of facilities where transplantation can be considered as dependent censoring. Patients are evaluated based on their current medical condition as reflected in a time dependent variable the Model for End-Stage Liver Disease score, which is used to prioritize to receive liver transplants. We assume a ‘standard’ transplant practice through a transplant model, utilizing Inverse Probability Censoring Weights (IPCW) to construct a weighted CUSUM. We evaluate the properties of a weighted zero-mean process as the basis of the proposed weighted CUSUM. A rule of setting control limits is discussed. Case study on regional transplant waitlist mortality is carried out to demonstrate the usage of the proposed weighted CUSUM. In Chapter III, we provide an explicit road map for using a Cox dependent censoring model in the IPCW approach, complete with details of implementation. In addition, we evaluate an alternative parametric IPCW approach to gain efficiency. Simulation studies and case study on the national liver transplant waitlist mortality are conducted to demonstrate the similarity in estimates between Cox IPCW and PWE IPCW, and the computational savings by the PWE IPCW as compared to the Cox IPCW. In the last chapter, we discuss the future directions of our work.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/96101/1/renajsun_1.pd

Model based control charts in stage 1 quality control

In this paper a general method of constructing control charts for preliminary analysis of individual observations is presented, which is based on recursive score residuals. A simulation study shows that certain implementations of these charts are highly effective in detecting assignable causes