6,126 research outputs found

    A Modified \u3cem\u3eX̄\u3c/em\u3e Control Chart for Samples Drawn from Finite Populations

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    The X̄ chart works well under the assumption of random sampling from infinite populations. However, many process monitoring scenarios may consist of random sampling from finite populations. A modified X̄ chart is proposed in this article to solve the problems encountered by the standard X̄ chart when samples are drawn from finite populations

    Nonparametric monitoring of sunspot number observations: a case study

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    Solar activity is an important driver of long-term climate trends and must be accounted for in climate models. Unfortunately, direct measurements of this quantity over long periods do not exist. The only observation related to solar activity whose records reach back to the seventeenth century are sunspots. Surprisingly, determining the number of sunspots consistently over time has remained until today a challenging statistical problem. It arises from the need of consolidating data from multiple observing stations around the world in a context of low signal-to-noise ratios, non-stationarity, missing data, non-standard distributions and many kinds of errors. The data from some stations experience therefore severe and various deviations over time. In this paper, we propose the first systematic and thorough statistical approach for monitoring these complex and important series. It consists of three steps essential for successful treatment of the data: smoothing on multiple timescales, monitoring using block bootstrap calibrated CUSUM charts and classifying of out-of-control situations by support vector techniques. This approach allows us to detect a wide range of anomalies (such as sudden jumps or more progressive drifts), unseen in previous analyses. It helps us to identify the causes of major deviations, which are often observer or equipment related. Their detection and identification will contribute to improve future observations. Their elimination or correction in past data will lead to a more precise reconstruction of the world reference index for solar activity: the International Sunspot Number.Comment: 27 pages (without appendices), 6 figure

    Double Sampling Auxiliary Information Chart And Exponentially Weighted Moving Average Auxiliary Information Chart, Both Based On Variable Sampling Interval, And Measurement Errors Based Triple Sampling Chart

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    The concept of using auxiliary information (AI) in control charts is growing in popularity among researchers. Control charts using the AI technique have been found to be more effective than control charts without the AI technique. The first objective of this thesis is to develop a variable sampling interval (VSI) double sampling (DS) chart using the AI technique (called VSI DS-AI chart) for monitoring the process mean. The charting statistics, optimal designs and implementation of the VSI DS-AI chart are discussed. The steady-state average time to signal (ssATS) and steady-state expected average time to signal (ssEATS) criteria are used as the performance measures of the proposed VSI DS-AI chart. The ssATS and ssEATS results of the VSI DS-AI chart are compared with those of the double sampling AI, variable sample size and sampling interval AI, exponentially weighted moving average AI (EWMA-AI) and run sum AI (RS-AI) charts. The comparison reveals that the VSI DS-AI chart performs better than the competing charts for all shift sizes, except the EWMA-AI and RS-AI charts for small shifts

    Statistical Methodologies of Functional Data Analysis for Industrial Applications

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    This thesis stands as one of the first attempt to connect the statistical object oriented data analysis (OODA) methodologies with the industry field. Indeed, the aim of this thesis is to develop statistical methods to tackle industrial problems through the paradigm of the OODA. The new framework of Industry 4.0 requires factories that are equipped with sensor and advanced acquisition systems that acquire data with a high degree of complexity. OODA can be particularly suitable to deal with this increasing complexity as it considers each statistical unit as an atom or a data object assumed to be a point in a well-defined mathematical space. This idea allows one to deal with complex data structure by changing the resolution of the analysis. Indeed, from standard methods where the atom is represented by vector of numbers, the focus now is on methodologies where the objects of the analysis are whole complex objects. In particular, this thesis focuses on functional data analysis (FDA), a branch of OODA that considers as the atom of the analysis functions defined on compact domains. The cross-fertilization of FDA methods to industrial applications is developed into three parts in this dissertation. The first part presents methodologies developed to solve specific applicative problems. In particular, a first consistent portion of this part is focused on \textit{profile monitoring} methods applied to ship CO\textsubscript{2} emissions. A second portion deals with the problem of predicting the mechanical properties of an additively manufactured artifact given the particle size distribution of the powder used for its production. And, a third portion copes with the cluster analysis for the quality assessment of metal sheet spot welds in the automotive industry based on observations of dynamic resistance curve. Stimulated by these challenges, the second part of this dissertation turns towards a more methodological line that addresses the notion of \textit{interpretability} for functional data. In particular, two new interpretable estimators of the coefficient function of the function-on-function linear regression model are proposed, which are named S-LASSO and AdaSS, respectively. Moreover, a new method, referred to as SaS-Funclust, is presented for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. In the last part, two ongoing researches on FDA methods for industrial application are presented. In particular, the first one regards the definition of a new robust nonparametric functional ANOVA method (Ro-FANOVA) to test differences among group functional means by being robust against the presence of outliers with an application to additive manufacturing. The second one sketches a new methodological framework for the real-time profile monitoring

    New Variable Sampling Interval Run Sum Standard Deviation And Run Sum Multivariate Coefficient Of Variation Charts

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    In Statistical Process Control (SPC), the control charting technique is an effective method to solve quality issues in manufacturing and service industries. The R and S charts are commonly used to monitor the process variance in industries due to the charts’ simplicity and high sensitivity toward large shifts. However, these charts are not sensitive toward small and moderate shifts in the process variance. On the other hand, the more sophisticated charts, such as the exponentially weighted moving average (EWMA) S chart and the cumulative sum (CUSUM) S chart are very effective in detecting small changes in the process variance. However, most quality practitioners do not adopt these charts in real applications due to their design complexity. In view of this setback, the variable sampling interval (VSI) approach is incorporated into the run sum (RS) S chart, in order to suggest an effective, yet a simple chart, for detecting small, moderate and large shifts in the process variance. Apart from that, the coefficient of variation (CV) is an important quality characteristic to take into account when the process mean and standard deviation are not constant, even though the process is in-control

    General Profile Monitoring Through Nonparametric Techniques

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    This Ph.D. thesis is devoted to Statistical Process Control (SPC) methods for monitoring over time the stability of a relation between two variables (profile). Very often in literature the functional form of the relation is assumed to be known, whereas in this work we concentrated on generic and unknown relations which have to be estimated with the usual nonparametric regression techniques. The original contributes are two, resented in chapters 2 and 3 respectively. In Chapter 1 we make a brief overview on the topic in order to make you become familiar with these specific problems of Statistical Process Control (SPC) applications and we introduce you to the original parts of this work. In Chapter 2 we envelope and compare five new control charts for monitoring on-line unknown general, and not only linear, relations among variables over time under the assumption of the normality of the errors; these charts combine in an original way the following techniques: self-starting methods, useful to drop the distinction between Phase I and Phase II of the analysis; very known multivariate charting schemes as MEWMA and CUSCORE; nonparametric testing techniques as wavelet methods and kernel linear smoothing. In Chapter 3, instead, we construct a test statistic useful to check with a completely nonparametric procedure the stability of a process retrospectively, thus off-line. Both second and third chapters are structured in the following way: brief literature review; framework and model considered in our study; simulation study; a section with some useful complements on the topics and relative research carried out; conclusion and suggestions for future research

    Integrated Projection and Regression Models for Monitoring Multivariate Autocorrelated Cascade Processes

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    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

    A Cumulative Summation Nonparametric Multiple Stream Process Control Chart Based on the Extended Median Test

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    In statistical process control applications, situations may arise in which several presumably identical processes or “streams” are desired to be simultaneously monitored. Such a monitoring scenario is commonly referred to as a “Multiple Stream Process (MSP).” Charts which have been designed to monitor an MSP typically monitor the means of the streams through collecting samples from each stream and calculating some function of the sample means. The resulting statistic is then iteratively compared to control limits to determine if a single stream or subset of streams may have shifted away from a specified target value. Traditional MSP charting techniques rely on the assumption of normality, which may or may not be met in practice. Thus, a cumulative summation nonparametric MSP control charting technique, based on a modification of the classical extended median test was developed and is referred to as the “Nonparametric Extended Median Test – Cumulative Summation (NEMT-CUSUM) chart.” The development of control limits and estimation of statistical power are given. Through simulation, the NEMT-CUSUM is shown to perform consistently in the presence of normal and non-normal data. Moreover, it is shown to perform more optimally than parametric alternatives in certain circumstances. Results suggest the NEMT-CUSUM may be an attractive alternative to existing parametric MSP monitoring techniques in the case when distributional assumptions about the underlying monitored process cannot reasonably be made
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