Monitoring the Process Mean of Autocorrelated Data

When modeling the stochastic behavior of a sequence { } t X of the quality measurement X on the output of a production process, it is usually assumed the measurements taken over time are independent and identically distributed. Multiple authors have pointed out that significant autocorrelation can affect the performance of traditional control charting procedures. One family of models for time series data are the autoregressive integrated moving average (ARIMA) models. These models are well suited to model production processes, in which the observations are autocorrelated. It is our interest to examine these models. Meaning is given to the process being in-control and out-of-control in terms of the parameters of the model. The performance of the Shewhart X chart and CUSUM X chart are compared. This includes determining the number of unobserved values between samples for the charts to perform as they would be expected if the samples were independent. Some recommendations are given

Optimal Estimation and Sampling Allocation in Survey Sampling Under a General Correlated Superpopulation Model

Sampling from a finite population with correlated units is addressed. The proposed methodology applies to any type of correlation function and provides the sample allocation that ensures optimal efficiency of the population parameters estimates. The expressions of the estimate and its MSE are also provided

Integrated Projection and Regression Models for Monitoring Multivariate Autocorrelated Cascade Processes

This dissertation presents a comprehensive methodology of dual monitoring for the multivariate autocorrelated cascade processes using principal component analysis and regression. Principle Components Analysis is used to alleviate the multicollinearity among input process variables and reduce the dimension of the variables. An integrated principal components selection rule is proposed to reduce the number of input variables. An autoregressive time series model is used and imposed on the time correlated output variable which depends on many multicorrelated process input variables. A generalized least squares principal component regression is used to describe the relationship between product and process variables under the autoregressive regression error model. The combined residual based EWMA control chart, applied to the product characteristics, and the MEWMA control charts applied to the multivariate autocorrelated cascade process characteristics, are proposed. The dual EWMA and MEWMA control chart has advantage and capability over the conventional residual type control chart applied to the residuals of the principal component regression by monitoring both product and the process characteristics simultaneously. The EWMA control chart is used to increase the detection performance, especially in the case of small mean shifts. The MEWMA is applied to the selected set of variables from the first principal component with the aim of increasing the sensitivity in detecting process failures. The dual implementation control chart for product and process characteristics enhances both the detection and the prediction performance of the monitoring system of the multivariate autocorrelated cascade processes. The proposed methodology is demonstrated through an example of the sugar-beet pulp drying process. A general guideline for controlling multivariate autocorrelated processes is also developed

Spatial Autocorrelation

The analysis of spatial distributions and the processes that produce and alter them is a central theme in geographic research and this volume is concerned with statistical methods for analyzing spatial distributions by measuring and testing for spatial autocorrelation. Spatial autocorrelation exists whenever a variable exhibits a regular pattern over space in which its values at a set of locations depend on values of the same variable at other locations. Spatial autocorrelation is present, for example, when similar values cluster together on a map. Spatial autocorrelation statistics make it possible to use formal statistical procedures to measure the dependence among nearby values in a spatial distribution, test hypotheses about geographically distributed variables, and develop statistical models of spatial patterns. Scientific Geography Series Editor: Grant Ian Thrall.https://researchrepository.wvu.edu/rri-web-book/1019/thumbnail.jp

A homogenously weighted moving average scheme for observations under the effect of serial dependence and measurement inaccuracy

The combined effect of serial dependency and measurement errors is known to negatively affect the statistical efficiency of any monitoring scheme. However, for the recently proposed homogenously weighted moving average (HWMA) scheme, the research that exists concerns independent and identically distributed observations and measurement errors only. Thus, in this paper, the HWMA scheme for monitoring the process mean under the effect of within-sample serial dependence with measurement errors is proposed for both constant and linearly increasing measurement system variance. Monte Carlo simulation is used to evaluate the run-length distribution of the proposed HWMA scheme. A mixed-s&m sampling strategy is incorporated to the HWMA scheme to reduce the negative effect of serial dependence and measurement errors and its performance is compared to the existing Shewhart scheme. An example is given to illustrate how to implement the proposed HWMA scheme for use in real-life applications

Estimating Discrete Markov Models From Various Incomplete Data Schemes

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a case, the estimation of transition probabilities is straightforwardly made by counting one-step moves from a given state to another. In many real-life problems, however, the inference is much more difficult as state sequences are not fully observed, namely the state of each individual is known only for some given values of the time variable. A review of the problem is given, focusing on Monte Carlo Markov Chain (MCMC) algorithms to perform Bayesian inference and evaluate posterior distributions of the transition probabilities in this missing-data framework. Leaning on the dependence between the rows of the transition matrix, an adaptive MCMC mechanism accelerating the classical Metropolis-Hastings algorithm is then proposed and empirically studied.Comment: 26 pages - preprint accepted in 20th February 2012 for publication in Computational Statistics and Data Analysis (please cite the journal's paper

Practical Concepts of Quality Control

This book aims to provide a concise account of the essential elements of quality control. It is designed to be used as a text for courses on quality control for students of industrial engineering at the advanced undergraduate, or as a reference for researchers in related fields seeking a concise treatment of the key concepts of quality control. It is intended to give a contemporary account of procedures used to design quality models

Managing social-ecological systems under uncertainty : implications for conservation

Natural resource managers and conservationists are often confronted with the challenges of uncertainty. Limits to knowledge and predictability challenge conservation success and socio-economic, institutional and political context affect implementation of conservation interventions. Using a management strategy evaluation (MSE) conceptual framework, I use a multidisciplinary approach to gain a better understanding of the role and implications of different sources and types of uncertainty for the management of social-ecological systems, giving special attention to the issues of observation and implementation uncertainty. The conservation of harvested ungulate species in the Serengeti, Tanzania, is used as a case study. I investigated which factors should be prioritized in order to increase survey accuracy and precision, and explored the potential effects of budgetary scenarios on the robustness of the population estimates obtained for different savannah ungulate species. The relative importance of each process affecting precision and accuracy varied according to the survey technique and biological characteristics of the species. I applied specialized questioning techniques developed for studying non-compliant and sensitive behaviour, using the unmatched-count technique (UCT) to assess prevalence of illegal hunting in the Serengeti. I found that poaching remains widespread in the Serengeti and current alternative sources of income may not be sufficiently attractive to compete with the opportunities provided by hunting. I explored trade-offs between different types of error when monitoring changes in population abundance and how these are affected by budgetary, observational and ecological conditions. Higher observation error and conducting surveys less frequently increased the likelihood of not detecting trends and misclassifying the shape of the trend but the differences between multiple levels of observation error decreased for higher monitoring length and frequency. Using key informant interviews with the main actors in the monitoring and management system, I provided recommendations for the development and implementation of interventions within long-term integrated and adaptive frameworks. The research presented in this thesis highlights the need to consider the role of people as influential components within social-ecological systems in order to promote effective conservation interventions. Monitoring and implementation must be understood as dynamic features of the system, instead of merely acting upon it, and the multiple sources of uncertainty must be fully considered in conservation planning, requiring the development and application of tools to aid management decision-making under uncertainty.Open Acces