The Effect of Median Based Estimators on CUSUM Chart

Cumulative Sum (CUSUM) chart has been used extensively to monitor mean shifts.It is highly sought after by practitioners and researchers in many areas of quality control due to its sensitivity in detecting small to moderate shifts. Normality assumption governs its ability to monitor the process mean. When the assumption is violated, CUSUM chart typically loses its practical use. As normality is hard to achieve in practice, the usual CUSUM chart is often substituted with robust charts.This is to provide more accurate results under slight deviation from normality. Thus, in this paper, we investigate the impact of using robust location estimators, namely, median and Hodges-Lehmann on CUSUM performance. By pairing the location estimators with a robust scale estimator known as median absolute deviation about the median (MADn), a duo median based CUSUM chart is attained.The performances of both charts are studied under normality and contaminated normal distribution and evaluated using the average run length (ARL). While demonstrating an average power to detect the out-of-control situations, the in-control performances of both charts remain unaffected in the presence of outliers. This could very well be advantageous when the proposed charts are tested on a real data set in the future. A case in point is when the statistical tool is used to monitor changes in clinical variables for the health care outcomes.By minimising the false positives, a sound judgement can be made for any clinical decision

The Effect of Median Based Estimators on CUSUM Chart

Cumulative Sum (CUSUM) chart has been used extensively to monitor mean shifts. It is highly sought after by practitioners and researchers in many areas of quality control due to its sensitivity in detecting small to moderate shifts. Normality assumption governs its ability to monitor the process mean. When the assumption is violated, CUSUM chart typically loses its practical use. As normality is hard to achieve in practice, the usual CUSUM chart is often substituted with robust charts. This is to provide more accurate results under slight deviation from normality. Thus, in this paper, we investigate the impact of using robust location estimators, namely, median and Hodges-Lehmann on CUSUM performance. By pairing the location estimators with a robust scale estimator known as median absolute deviation about the median (MADn), a duo median based CUSUM chart is attained. The performances of both charts are studied under normality and contaminated normal distribution and evaluated using the average run length (ARL). While demonstrating an average power to detect the outof-control situations, the in-control performances of both charts remain unaffected in the presence of outliers. This could very well be advantageous when the proposed charts are tested on a real data set in the future. A case in point is when the statistical tool is used to monitor changes in clinical variables for the health care outcomes. By minimising the false positives, a sound judgement can be made for any clinical decision

Data Analytics and Managing Health and Medical Care

The purpose is to introduce the demand for the quality movement practice in problems associated with public health diagnostic testing and other health related problems We examine problems involving 1 Multivariate control charts which simultaneously monitor correlated variables 2 we explain why the scale on multivariate control charts is unrelated to the scale of the individual Variables control charts and 3 discover that out of control signals in multivariate charts do not reveal which variable or combination of variables causes the signal and application of quality monitoring New methods provide methods for MPC charts focus on the average run length as the decision factor We indicate that other decision criteria in multivariate control charts are availableand these methods can be useful in evaluating the design and implementation of multivariate charts in special circumstance

Contributions to predicting contaminant leaching from secondary materials used in roads

Slags, coal ashes, and other secondary materials can be used in road construction. Both traditional and secondary materials used in roads may contain contaminants that may leach and pollute the groundwater. The goal of this research was to further the understanding of leaching and transport of contaminants from pavement materials. Towards this goal, a new probabilistic framework was introduced which provided a structured guidance for selecting the appropriate model, incorporating uncertainty, variability, and expert opinion, and interpreting results for decision making. In addition to the framework, specific contributions were made in pavement and embankment hydrology and reactive transport, Bayesian statistics, and aqueous geochemistry of leaching. Contributions on water movement and reactive transport in highways included probabilistic prediction of leaching in an embankment, and scenario analyses of leaching and transport in pavements using HYDRUS2D, a contaminant fate and transport model. Water flow in a Minnesota highway embankment was replicated by Bayesian calibration of hydrological parameters against water content data. Extent of leaching of Cd from a coal fly ash was estimated. Two dimensional simulations of various scenarios showed that salts in the base layer of pavements are depleted within the first year whereas the metals may never reach the groundwater if the pavement is built on adsorbing soils. Aqueous concentrations immediately above the groundwater estimated for intact and damaged pavements can be used for regulators to determine the acceptability of various recycled materials. Contributions in the aqueous geochemistry of leaching included a new modeling approach for leaching of anions and cations from complex matrices such as weathered steel slag. The novelty of the method was its simultaneous inclusion of sorption and solubility controls for multiple analytes. The developed model showed that leaching of SO4, Cr, As, Si, Ca, Mg, and V were controlled by corresponding soluble solids. Leaching of Pb was controlled by Pb(VO4)3 solubility at low pHs and by surface precipitation reactions at high pHs. Leaching of Cd and Zn were controlled by surface complexation and surface precipitation, respectively