Past Projects

Application of Multivariate Statistical Process Control Methods to Infection Control Hand Washing Data

Univariate and multivariate statistical process control charts were applied to readily available hand washing data and evaluated as a means to monitor compliance and reduce spread of hospital-acquired infections. Noncompliance to hand washing guidelines is well known as one of the most common causes of nosocomial infections, yet monitoring staff compliance directly after every patient interaction is infeasible and expensive. As a surrogate, towel and soap consumption data can be easily monitored to detect changes in hand washing rates. In an observational study of two intensive care units spanning several months, the number of hand washing episodes per shift was found to be strongly correlated with three measures of the consumption of soap and towels located at the hand washing sinks (weight of soap consumed, weight of towels consumed, and height of towels consumed per day, which also are strongly cross-correlated with each other).

Shewhart and exponentially weighted moving average control charts were applied to actual hand washing data collected during the observational study and to soap and towel consumption data. Soap and towel consumption were monitored both individually using univariate control charts and in combination using multivariate control charts that incorporate the cross-correlation between the surrogate measures. The performance of these surrogate charts tended to closely follow that of charts based on actual hand washing. In particular, multivariate control charts for average and standard deviation based on Hotelling's T2 statistic were found to be very effective and easy tools for monitoring hand washing compliance. Further information on this study can be found in the project report (forthcoming).

Computer Simulation and Capacity Analysis of a Hospital Consolidation

This project studied various space and staffing alternatives as part of a multi-million dollar food services consolidation at a major Boston-area hospital. A computer simulation program was developed in the SIMAN modeling language to help determine the number of seats, food servers, and cashiers needed over the course of the day and the resultant impact on capacity and utilization. A sensitivity analysis also was conducted on projected growth in customer volumes and used by architects and others involved in space planning decisions. A second version of the program also was implemented in the MedModel simulation software, which includes a graphical animation of the process. Results also were compared to those obtained from a queueing (approximation) spreadsheet. A more complete summary of this study and the model code can be found in the project report (forthcoming).

The Bias and Skewness of Process Capability Indices

Process capability indices have become one of the most common approaches for demonstrating the ability of a process to produce conforming product. A variety of indices have been proposed over the past two decades, along with a significant body of criticism of statistical and management shortcomings with the use of these measures. This project investigated the bias, skewness, and kurtosis of common process capability indices (Cp, Cpk, Cpm, Cjkp) for normally distributed random variables with its parameters estimated from the overall data or using standard control chart estimates (Rbar/d2 and Sbar/c4).

Nonconforming Parts Per Million (NCPPM) as an Estimator of Process Capability

As an alternative to process capability indices, we investigate the use of nonconforming parts per million (NCPPM-hat) as an estimator of process capability; that is, directly estimating the fraction of all items expected to fall outside of specifications. This project developed a C++ simulation tool to determine various statistical properties (mean, variance, bias, skewness, kurtosis) of these estimates for any of several possible underlying distributions, for different approaches to estimating that distributions parameters, and for different sample sizes and number of samples. Investigated distributions include the exponential, normal, lognormal, gamma, Raleigh, and Weibull and parameters estimated via maximum likelihood from the entire data set and 3 control chart estimates using subgroup statistics (S/c4, Rbar/d2, and Sbar/c4).

Application of Start-Up Q Charts to Coronary Artery Bypass Graft Data

The project investigated the application of Q-type start-up statistical control charts to heart surgery complication and infection data. We developed research code to recursively compute and construct special-purpose Shewhart, EWMA, and Cusum control charts based on updating uniform minimum variance unbiased estimating functions of geometric distributions (particularly for limited data or start-up conditions). Examples based on heart surgery complication were able to detect statistical changes in the data in real-time better than traditional methods that require a decent amount of past historical data to estimate the underlying parameters used to construct the control limits.

Special Purpose SPC Programs

Several projects has focused on developing computer and web-based programs to construct special-purpose statistical process control methods. These programs include (1) a Java web-based program for constructing number-between g control charts, (2) a Visual Basic simulation program for analysis of aggregated and risk-adjusted statistical quality control charts (for aggregate non-homogeneous events), (3) a FORTRAN recursive program for constructing geometric Q charts under start-up conditions, and (4) commercial-grade SPC software that constructs all standard Shewhart, EWMA, Cusum charts as well as standardized, number-between, and risk-adjusted special-purpose methods. We also have developed several analysis programs for determining the average run lengths, optimal subgroup sizes to minimize average number items inspected, and economic optimal design of various standard and special-purpose control charts. Some of these programs can be found in our tools page.

Use of Experimental Design in Printed Circuit Board Manufacture

This project focused on the use of experimental design methods to optimize the peel (pull) strength produced by a bond film oxidation process used in the manufacture of printed wire boards. This boding process allows a costly production step to be eliminated if it can be controlled effectively. Design of experiments (DOE) and regression analysis were used develop predictive equations of pull strength mean and standard deviation. These results were used in two non-linear optimization models to identify the process settings that would produce the minimum amount of nonconforming product or the minimum total cost.

Applying Statistical Process Control in Semiconductor Wafer Fabrication

This project investigated the application of statistical process control to semiconductor fabrication contamination data. Monitoring and control of particle contaminants in wafer fabrication processes is important for maximizing yield. Contrary to standard Poisson assumptions particles tend to appear on wafers in clusters and have a coefficient of variation greater than 1, suggesting that compound probability distributions may be appropriate for modeling such processes. Several empirical data sets from a wafer fabrication process were analyzed to identify the most appropriate count distribution, including Neyman, Thomas, Poisson, negative binomial, and a shifted Poisson model that allows the mean to not equal the variance. Numeric code was developed to conduct goodness-of-fit tests, estimate PDF parameters, and construct appropriate control charts. The Neyman, Thomas, negative binomial, and shifted Poisson distributions were found to produce fits than the Poisson, with the negative binomial being the most robust across data sets. The implications on control chart performance in each case illustrate the significant potential increase in false alarm rates if using standard c and u control charts based on the Poisson.

Application of SPC Methods in Neonatal Intensive Care

A preliminary study was conducted to investigate the application of statistical process control methods to patient physiologic data in neonatal intensive care units (NICU) at the Brigham and Women's hospital. Important applications include re-ventilation rates, ventilation durations, NICU lengths-of-stay, successful weaning rates, and others.

Simulation of Alternate Flow Policies of a City Emergency Room Redesign

This project developed a computer simulation program to help study the benefits of consolidating and redesigning emergency departments as part of a merger between Boston City Hospital and Boston University Hospital.

Internet-Based Distributed SPC Surveillance

This project developed and integrated standard and special purpose statistical process control methods into a web-based surveillance information systems for the U.S. Air Force Surgeon General's Office (USAF Bolling Air Force Base) to. The developed system incorporates statistical and related methods in order to identify unusual events and patterns of concern in large, highly distributed data streams and has been used to monitor in real-time disease and symptom occurrence rates across the U.S. Air Force's worldwide healthcare network. Further details can be found in the following paper.