Multivariate EWMA Control Chart with Adaptive Sample Sizes

Standard multivariate control charts usually employ fixed sample sizes at equal sampling intervals to monitor a process. In this study, a multivariate exponential weighted moving average (MEWMA) chart with adaptive sample sizes is investigated. Performance measure of the adaptive-sample-size MEWMA chart is obtained through a Markov chain approach. The performance of the adaptive-sample-size MEWMA chart is compared with the fixed-sample-size control chart in terms of steady-state average run length for different magnitude of shifts in the process mean. It is shown that the adaptive-sample-size chart is more efficient than the fixed-sample-size MEWMA control chart in detecting shifts in the process mean.     

Economic Design of Cumulative Sum Control Charts for Monitoring a Process with Correlated Samples

The underlying assumption for the design of control charts is the measurements within a sample are independently distributed. However, there are many situations where the uncorrelation assumption may be unacceptable in practice. In this paper, the economic design of cumulative sum (CUSUM) control chart for correlated data within a sample is developed. The genetic algorithm is applied to find the optimal design parameters of the CUSUM control chart by minimizing the cost function. An illustrative example is given. A sensitivity analysis is then conducted to evaluate the effects of cost parameters, process parameters, and correlation coefficient on the economic design.     

The Design of the Multivariate Synthetic Exponentially Weighted Moving Average Control Chart

A multivariate synthetic exponentially weighted moving average (MSEWMA) control chart is presented in this study. The MSEWMA control chart consists of a multivariate exponentially weighted moving average (MEWMA) control chart and a conforming run length control chart. The average run length of the MSEWMA control chart is obtained using a Markov chain approach. From the numerical comparisons, it is shown that the MSEWMA control chart is more efficient than the multivariate synthetic T ² control chart and the MEWMA control chart for detecting shifts in the process mean vector.     

A Regression Model for the AUC of Clustered Ordinal Test Results and Working Independent Optimal Weights

We study a regression model on the area under the receiver operating characteristic curves (AUC) for clustered (or repeatedly measured) test results. To account for cluster information, we consider a weighted estimating equation for Dodd and Pepe (2003 Dodd , L. , Pepe , M. ( 2003 ). Semiparametric regression for the area under the receiver operating charateristic curve . Journal of the American Statistical Association 98 : 409 – 417 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar])'s regression model with working independence weights. We find the optimal weight in the given class of working independence weights to minimize the variance (or MSE) of regression estimators. We apply the proposed procedure to analyzing our recent experiment on diagnosing a liver disorder. In this experiment, we investigated MRI images of patients having symptoms of potential liver disorder to compare the performance of different MRI picturing methods in testing for liver disorders.     

The Synthetic Mean Square Error Control Chart

A synthetic mean square error (MSE) control chart is presented in this study for monitoring the changes in the mean and standard deviation of a normally distributed process. The synthetic MSE control chart is a combination of the standard MSE control chart and the conforming run length (CRL) control chart. From the numerical comparisons, the synthetic MSE control chart is always more efficient than the standard MSE control chart in detecting shifts in the process mean and standard deviation. The synthetic MSE chart also performs better than the exponentially weighted moving average-semicircle (EWMA-SC) chart, except for some cases where the process mean shifts are small.     

Elicitation of health values from mortality risk reduction

There are concerns regarding uncertainty about the accuracy of applying available empirical willingness-to-pay (WTP) estimates for reducing accidental deaths to value changes in risks of pollution-related deaths. In this study, we develop a theoretical model on defining WTP, and its determinants, and derive WTP estimates for changes in pollution-related mortality risks with varying morbidity and timing attributes. A survey is designed and conducted with 100 subjects. Each subject was to complete five choice sets and provided a range of implicit values of statistical life (VSL). The choices are estimated using the logit procedure. And, using the results of estimated multinomial logit model, the VSL is estimated to about $6.2 million.     

Socioeconomic Differences in the Health of Black Union Army Soldiers

This paper investigates patterns of socioeconomic difference in the wartime morbidity and mortality of black Union Army soldiers. Among the factors that contributed to a lower probability of contracting and dying from diseases were (1) lighter skin color, (2) a non-field occupation, (3) residence on a large plantation, and (4) residence in a rural area prior to enlistment. Patterns of disease-specific mortality and timing of death suggest that the differences in the development of immunity against diseases and in nutritional status prior to enlistment were responsible for the observed socioeconomic differences in wartime health. For example, the advantages of light-skinned soldiers over dark-skinned and of enlisted men formerly engaged in non-field occupations over field hands resulted from differences in nutritional status. The lower wartime mortality of ex-slaves from large plantations can be explained by their better-developed immunity as well as superior nutritional status. The results of this paper suggest that there were substantial disparities in the health of the slave population on the eve of the Civil War.     

Testing for Stochastic Monotonicity

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications in economics. Our test is based on the supremum of a rescaled U‐statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part, and so we have to extend existing results that only apply to either one or the other case. We also propose a refinement to the asymptotic approximation that we show works much better in finite samples. We apply our test to the study of intergenerational income mobility.     

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.