Profile control charts based on nonparametric LL-1 regression methods

Classical statistical process control often relies on univariate characteristics. In many contemporary applications, however, the quality of products must be characterized by some functional relation between a response variable and its explanatory variables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. This paper develops a novel nonparametric $L$-1 location-scale model to screen the shapes of profiles. The model is built on three basic elements: location shifts, local shape distortions, and overall shape deviations, which are quantified by three individual metrics. The proposed approach is applied to the previously analyzed vertical density profile data, leading to some interesting insights.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS501 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Effectiveness of Profile Monitoring to Enhance Functional Performance of Particleboards

This paper explores connection between profile monitoring and functional performance of manufactured products. In particular, the empirical relationship between the vertical density profile of the particleboards and their functional performances (the internal bond and the surface soundness) is studied. Results based on a real case study showed that the profile shape clearly affects the final performance of the panel, and thus profile monitoring is really worth to keep the final quality of the product at its target level. This result motivates the second objective of the paper, which consists of comparing performance of two (parametric and nonparametric) approaches for vertical density profile monitoring

Using semiparametric‐mixed model and functional linear model to detect vulnerable prenatal window to carcinogenic polycyclic aromatic hydrocarbons on fetal growth

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106079/1/bimj1458.pd

Regression Trees for Longitudinal Data

While studying response trajectory, often the population of interest may be diverse enough to exist distinct subgroups within it and the longitudinal change in response may not be uniform in these subgroups. That is, the timeslope and/or influence of covariates in longitudinal profile may vary among these different subgroups. For example, Raudenbush (2001) used depression as an example to argue that it is incorrect to assume that all the people in a given population would be experiencing either increasing or decreasing levels of depression. In such cases, traditional linear mixed effects model (assuming common parametric form for covariates and time) is not directly applicable for the entire population as a group-averaged trajectory can mask important subgroup differences. Our aim is to identify and characterize longitudinally homogeneous subgroups based on the combination of baseline covariates in the most parsimonious way. This goal can be achieved via constructing regression tree for longitudinal data using baseline covariates as partitioning variables. We have proposed LongCART algorithm to construct regression tree for the longitudinal data. In each node, the proposed LongCART algorithm determines the need for further splitting (i.e. whether parameter(s) of longitudinal profile is influenced by any baseline attributes) via parameter instability tests and thus the decision of further splitting is type-I error controlled. We have obtained the asymptotic results for the proposed instability test and examined finite sample behavior of the whole algorithm through simulation studies. Finally, we have applied the LongCART algorithm to study the longitudinal changes in choline level among HIV patients

From Profile to Surface Monitoring: SPC for Cylindrical Surfaces Via Gaussian Processes

Quality of machined products is often related to the shapes of surfaces that are constrained by geometric tolerances. In this case, statistical quality monitoring should be used to quickly detect unwanted deviations from the nominal pattern. The majority of the literature has focused on statistical profile monitoring, while there is little research on surface monitoring. This paper faces the challenging task of moving from profile to surface monitoring. To this aim, different parametric approaches and control-charting procedures are presented and compared with reference to a real case study dealing with cylindrical surfaces obtained by lathe turning. In particular, a novel method presented in this paper consists of modeling the manufactured surface via Gaussian processes models and monitoring the deviations of the actual surface from the target pattern estimated in phase I. Regardless of the specific case study in this paper, the proposed approach is general and can be extended to deal with different kinds of surfaces or profiles

Intraurban Spatiotemporal Variability of Ambient Air Pollutants across Metropolitan St. Louis

Ambient air monitoring networks have been established in the United States since the 1970s to comply with the Clean Air Act. The monitoring networks are primarily used to determine compliance but also provide substantive support to air quality management and air quality research including studies on health effects of air pollutants. The Roxana Air Quality Study (RAQS) was conducted at the fenceline of a petroleum refinery in Roxana, Illinois. In addition to providing insights into air pollutant impacts from the refinery, these measurements increased the St. Louis area monitoring network density for gaseous air toxics and fine particulate matter (PM2.5) speciation and thus provided an opportunity to examine intraurban spatiotemporal variability for these air quality parameters. This dissertation focused on exploring and assessing aspects of ambient air pollutant spatiotemporal variability in the St. Louis area from three progressively expanded spatial scales using a suite of methods and metrics. RAQS data were used to characterize air quality conditions in the immediate vicinity of the petroleum refinery. For example, PM2.5 lanthanoids were used to track impacts from refinery fluidized bed catalytic cracker emissions. RAQS air toxics data were interpreted by comparing to network data from the Blair Street station in the City of St. Louis which is a National Air Toxics Trends Station. Species were classified as being spatially homogeneous (similar between sites) or heterogeneous (different between sites) and in the latter case these differences were interpreted using surface winds data. For PM2.5 species, there were five concurrently operating sites in the St. Louis area - including the site in Roxana - which are either formally part of the national Chemical Speciation Network (CSN) or rigorously follow the CSN sampling and analytical protocols. This unusually large number of speciation sites for a region the size of St. Louis motivated a detailed examination of these data. Intraurban spatiotemporal variability for certain species was evaluated in the context of measurement error. For example, for species otherwise considered homogeneous, differential impacts from local point sources at different locations could be identified after comparing the observed day-to-day variations to those contributed by measurement error. In addition, source apportionment modeling was conducted using single- and multi-site datasets to assign measured PM2.5 mass to emission source categories. A suite of approaches were used to aid in the selection of an appropriate number of factors including metrics recently added to the US EPA Positive Matrix Factorization (EPA PMF) modeling software and the sensitivity of modeling results to perturbations on the measurement uncertainties

Quantile regression for mixed models with an application to examine blood pressure trends in China

Cardiometabolic diseases have substantially increased in China in the past 20 years and blood pressure is a primary modifiable risk factor. Using data from the China Health and Nutrition Survey, we examine blood pressure trends in China from 1991 to 2009, with a concentration on age cohorts and urbanicity. Very large values of blood pressure are of interest, so we model the conditional quantile functions of systolic and diastolic blood pressure. This allows the covariate effects in the middle of the distribution to vary from those in the upper tail, the focal point of our analysis. We join the distributions of systolic and diastolic blood pressure using a copula, which permits the relationships between the covariates and the two responses to share information and enables probabilistic statements about systolic and diastolic blood pressure jointly. Our copula maintains the marginal distributions of the group quantile effects while accounting for within-subject dependence, enabling inference at the population and subject levels. Our population-level regression effects change across quantile level, year and blood pressure type, providing a rich environment for inference. To our knowledge, this is the first quantile function model to explicitly model within-subject autocorrelation and is the first quantile function approach that simultaneously models multivariate conditional response. We find that the association between high blood pressure and living in an urban area has evolved from positive to negative, with the strongest changes occurring in the upper tail. The increase in urbanization over the last twenty years coupled with the transition from the positive association between urbanization and blood pressure in earlier years to a more uniform association with urbanization suggests increasing blood pressure over time throughout China, even in less urbanized areas. Our methods are available in the R package BSquare.Comment: Published at http://dx.doi.org/10.1214/15-AOAS841 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Reduced-rank spatio-temporal modeling of air pollution concentrations in the Multi-Ethnic Study of Atherosclerosis and Air Pollution

There is growing evidence in the epidemiologic literature of the relationship between air pollution and adverse health outcomes. Prediction of individual air pollution exposure in the Environmental Protection Agency (EPA) funded Multi-Ethnic Study of Atheroscelerosis and Air Pollution (MESA Air) study relies on a flexible spatio-temporal prediction model that integrates land-use regression with kriging to account for spatial dependence in pollutant concentrations. Temporal variability is captured using temporal trends estimated via modified singular value decomposition and temporally varying spatial residuals. This model utilizes monitoring data from existing regulatory networks and supplementary MESA Air monitoring data to predict concentrations for individual cohort members. In general, spatio-temporal models are limited in their efficacy for large data sets due to computational intractability. We develop reduced-rank versions of the MESA Air spatio-temporal model. To do so, we apply low-rank kriging to account for spatial variation in the mean process and discuss the limitations of this approach. As an alternative, we represent spatial variation using thin plate regression splines. We compare the performance of the outlined models using EPA and MESA Air monitoring data for predicting concentrations of oxides of nitrogen (NO$_x$)-a pollutant of primary interest in MESA Air-in the Los Angeles metropolitan area via cross-validated $R^2$. Our findings suggest that use of reduced-rank models can improve computational efficiency in certain cases. Low-rank kriging and thin plate regression splines were competitive across the formulations considered, although TPRS appeared to be more robust in some settings.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS786 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org