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Author: Galit Shmueli Publisher: Axelrod Schnall Publishers ISBN: Category : Mathematics Languages : en Pages : 122
Book Description
Various procedures that are used in the field of industrial statistics, include switching/stopping rules between different levels of inspection. These rules are usually based on a sequence of previous inspections, and involve the concept of runs. A run is a sequence of identical events, such as a sequence of successes in a slot machine. However, waiting for a run to occur is not merely a superstitious act. In quality control, as in many other fields (e.g. reliability of engineering systems, DNA sequencing, psychology, ecology, and radar astronomy), the concept of runs is widely applied as the underlying basis for many rules. Rules that are based on the concept of runs, or "run-rules", are very intuitive and simple to apply (for example: "use reduced inspection following a run of 5 acceptable batches"). In fact, in many cases they are designed according to empirical rather than probabilistic considerations. Therefore, there is a need to investigate their theoretical properties and to assess their performance in light of practical requirements. In order to investigate the properties of such systems their complete probabilistic structure should be revealed. Various authors addressed the occurrence of runs from a theoretical point of view, with no regard to the field of industrial statistics or quality control. The main problem has been to specify the exact probability functions of variables which are related to runs. This problem was tackled by different methods (especially for the family of "order k distributions"), some of them leading to expressions for the probability function. In this work we present a method for computing the exact probability functions of variables which originate in systems with switching or stopping rules that are based on runs (including k-order variables as a special case). We use Feller's (1968) methods for obtaining the probability generating functions of run related variables, as well as for deriving the closed form of the probability function from its generating function by means of partial fraction expansion. We generalize Feller's method for other types of distributions that are based on runs, and that are encountered in the field of industrial statistics. We overcome the computational complexity encountered by Feller for computing the exact probability function, using efficient numerical methods for finding the roots of polynomials, simple recursive formulas, and popular mathematical software packages (e.g. Matlab and Mathematica). We then assess properties of some systems with switching/stopping run rules, and propose modifications to such rules.
Author: Galit Shmueli Publisher: Axelrod Schnall Publishers ISBN: Category : Mathematics Languages : en Pages : 122
Book Description
Various procedures that are used in the field of industrial statistics, include switching/stopping rules between different levels of inspection. These rules are usually based on a sequence of previous inspections, and involve the concept of runs. A run is a sequence of identical events, such as a sequence of successes in a slot machine. However, waiting for a run to occur is not merely a superstitious act. In quality control, as in many other fields (e.g. reliability of engineering systems, DNA sequencing, psychology, ecology, and radar astronomy), the concept of runs is widely applied as the underlying basis for many rules. Rules that are based on the concept of runs, or "run-rules", are very intuitive and simple to apply (for example: "use reduced inspection following a run of 5 acceptable batches"). In fact, in many cases they are designed according to empirical rather than probabilistic considerations. Therefore, there is a need to investigate their theoretical properties and to assess their performance in light of practical requirements. In order to investigate the properties of such systems their complete probabilistic structure should be revealed. Various authors addressed the occurrence of runs from a theoretical point of view, with no regard to the field of industrial statistics or quality control. The main problem has been to specify the exact probability functions of variables which are related to runs. This problem was tackled by different methods (especially for the family of "order k distributions"), some of them leading to expressions for the probability function. In this work we present a method for computing the exact probability functions of variables which originate in systems with switching or stopping rules that are based on runs (including k-order variables as a special case). We use Feller's (1968) methods for obtaining the probability generating functions of run related variables, as well as for deriving the closed form of the probability function from its generating function by means of partial fraction expansion. We generalize Feller's method for other types of distributions that are based on runs, and that are encountered in the field of industrial statistics. We overcome the computational complexity encountered by Feller for computing the exact probability function, using efficient numerical methods for finding the roots of polynomials, simple recursive formulas, and popular mathematical software packages (e.g. Matlab and Mathematica). We then assess properties of some systems with switching/stopping run rules, and propose modifications to such rules.
Author: Andrew N O'Connor Publisher: RIAC ISBN: 1933904062 Category : Mathematics Languages : en Pages : 220
Book Description
The book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering.
Author: Anant P. Godbole Publisher: Springer Science & Business Media ISBN: 9780792328346 Category : Mathematics Languages : en Pages : 364
Book Description
The Probability Theory of Patterns and Runs has had a long and distinguished history, starting with the work of de Moivre in the 18th century and that of von Mises in the early 1920's, and continuing with the renewal-theoretic results in Feller's classic text An Introduction to Probability Theory and its Applications, Volume 1. It is worthwhile to note, in particular, that de Moivre, in the third edition of The Doctrine of Chances (1756, reprinted by Chelsea in 1967, pp. 254-259), provides the generating function for the waiting time for the appearance of k consecutive successes. During the 1940's, statisticians such as Mood, Wolfowitz, David and Mosteller studied the distribution theory, both exact and asymptotic, of run-related statistics, thereby laying the foundation for several exact run tests. In the last two decades or so, the theory has seen an impressive re-emergence, primarily due to important developments in Molecular Biology, but also due to related research thrusts in Reliability Theory, Distribution Theory, Combinatorics, and Statistics.
Author: Ron S. Kenett Publisher: John Wiley & Sons ISBN: 1119714966 Category : Mathematics Languages : en Pages : 884
Book Description
Modern Industrial Statistics The new edition of the prime reference on the tools of statistics used in industry and services, integrating theoretical, practical, and computer-based approaches Modern Industrial Statistics is a leading reference and guide to the statistics tools widely used in industry and services. Designed to help professionals and students easily access relevant theoretical and practical information in a single volume, this standard resource employs a computer-intensive approach to industrial statistics and provides numerous examples and procedures in the popular R language and for MINITAB and JMP statistical analysis software. Divided into two parts, the text covers the principles of statistical thinking and analysis, bootstrapping, predictive analytics, Bayesian inference, time series analysis, acceptance sampling, statistical process control, design and analysis of experiments, simulation and computer experiments, and reliability and survival analysis. Part A, on computer age statistical analysis, can be used in general courses on analytics and statistics. Part B is focused on industrial statistics applications. The fully revised third edition covers the latest techniques in R, MINITAB and JMP, and features brand-new coverage of time series analysis, predictive analytics and Bayesian inference. New and expanded simulation activities, examples, and case studies—drawn from the electronics, metal work, pharmaceutical, and financial industries—are complemented by additional computer and modeling methods. Helping readers develop skills for modeling data and designing experiments, this comprehensive volume: Explains the use of computer-based methods such as bootstrapping and data visualization Covers nonstandard techniques and applications of industrial statistical process control (SPC) charts Contains numerous problems, exercises, and data sets representing real-life case studies of statistical work in various business and industry settings Includes access to a companion website that contains an introduction to R, sample R code, csv files of all data sets, JMP add-ins, and downloadable appendices Provides an author-created R package, mistat, that includes all data sets and statistical analysis applications used in the book Part of the acclaimed Statistics in Practice series, Modern Industrial Statistics with Applications in R, MINITAB, and JMP, Third Edition, is the perfect textbook for advanced undergraduate and postgraduate courses in the areas of industrial statistics, quality and reliability engineering, and an important reference for industrial statisticians, researchers, and practitioners in related fields. The mistat R-package is available from the R CRAN repository.
Author: Andrew Metcalfe Publisher: CRC Press ISBN: 1439895481 Category : Mathematics Languages : en Pages : 792
Book Description
Engineers are expected to design structures and machines that can operate in challenging and volatile environments, while allowing for variation in materials and noise in measurements and signals. Statistics in Engineering, Second Edition: With Examples in MATLAB and R covers the fundamentals of probability and statistics and explains how to use these basic techniques to estimate and model random variation in the context of engineering analysis and design in all types of environments. The first eight chapters cover probability and probability distributions, graphical displays of data and descriptive statistics, combinations of random variables and propagation of error, statistical inference, bivariate distributions and correlation, linear regression on a single predictor variable, and the measurement error model. This leads to chapters including multiple regression; comparisons of several means and split-plot designs together with analysis of variance; probability models; and sampling strategies. Distinctive features include: All examples based on work in industry, consulting to industry, and research for industry Examples and case studies include all engineering disciplines Emphasis on probabilistic modeling including decision trees, Markov chains and processes, and structure functions Intuitive explanations are followed by succinct mathematical justifications Emphasis on random number generation that is used for stochastic simulations of engineering systems, demonstration of key concepts, and implementation of bootstrap methods for inference Use of MATLAB and the open source software R, both of which have an extensive range of statistical functions for standard analyses and also enable programing of specific applications Use of multiple regression for times series models and analysis of factorial and central composite designs Inclusion of topics such as Weibull analysis of failure times and split-plot designs that are commonly used in industry but are not usually included in introductory textbooks Experiments designed to show fundamental concepts that have been tested with large classes working in small groups Website with additional materials that is regularly updated Andrew Metcalfe, David Green, Andrew Smith, and Jonathan Tuke have taught probability and statistics to students of engineering at the University of Adelaide for many years and have substantial industry experience. Their current research includes applications to water resources engineering, mining, and telecommunications. Mahayaudin Mansor worked in banking and insurance before teaching statistics and business mathematics at the Universiti Tun Abdul Razak Malaysia and is currently a researcher specializing in data analytics and quantitative research in the Health Economics and Social Policy Research Group at the Australian Centre for Precision Health, University of South Australia. Tony Greenfield, formerly Head of Process Computing and Statistics at the British Iron and Steel Research Association, is a statistical consultant. He has been awarded the Chambers Medal for outstanding services to the Royal Statistical Society; the George Box Medal by the European Network for Business and Industrial Statistics for Outstanding Contributions to Industrial Statistics; and the William G. Hunter Award by the American Society for Quality.
Author: Bhisham C. Gupta Publisher: John Wiley & Sons ISBN: 1119516633 Category : Mathematics Languages : en Pages : 1040
Book Description
Introduces basic concepts in probability and statistics to data science students, as well as engineers and scientists Aimed at undergraduate/graduate-level engineering and natural science students, this timely, fully updated edition of a popular book on statistics and probability shows how real-world problems can be solved using statistical concepts. It removes Excel exhibits and replaces them with R software throughout, and updates both MINITAB and JMP software instructions and content. A new chapter discussing data mining—including big data, classification, machine learning, and visualization—is featured. Another new chapter covers cluster analysis methodologies in hierarchical, nonhierarchical, and model based clustering. The book also offers a chapter on Response Surfaces that previously appeared on the book’s companion website. Statistics and Probability with Applications for Engineers and Scientists using MINITAB, R and JMP, Second Edition is broken into two parts. Part I covers topics such as: describing data graphically and numerically, elements of probability, discrete and continuous random variables and their probability distributions, distribution functions of random variables, sampling distributions, estimation of population parameters and hypothesis testing. Part II covers: elements of reliability theory, data mining, cluster analysis, analysis of categorical data, nonparametric tests, simple and multiple linear regression analysis, analysis of variance, factorial designs, response surfaces, and statistical quality control (SQC) including phase I and phase II control charts. The appendices contain statistical tables and charts and answers to selected problems. Features two new chapters—one on Data Mining and another on Cluster Analysis Now contains R exhibits including code, graphical display, and some results MINITAB and JMP have been updated to their latest versions Emphasizes the p-value approach and includes related practical interpretations Offers a more applied statistical focus, and features modified examples to better exhibit statistical concepts Supplemented with an Instructor's-only solutions manual on a book’s companion website Statistics and Probability with Applications for Engineers and Scientists using MINITAB, R and JMP is an excellent text for graduate level data science students, and engineers and scientists. It is also an ideal introduction to applied statistics and probability for undergraduate students in engineering and the natural sciences.
Author: N. Balakrishnan Publisher: Springer Science & Business Media ISBN: 1461241405 Category : Mathematics Languages : en Pages : 576
Book Description
Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.
Author: Ron S. Kenett Publisher: John Wiley & Sons ISBN: 1119714923 Category : Mathematics Languages : en Pages : 880
Book Description
Modern Industrial Statistics The new edition of the prime reference on the tools of statistics used in industry and services, integrating theoretical, practical, and computer-based approaches Modern Industrial Statistics is a leading reference and guide to the statistics tools widely used in industry and services. Designed to help professionals and students easily access relevant theoretical and practical information in a single volume, this standard resource employs a computer-intensive approach to industrial statistics and provides numerous examples and procedures in the popular R language and for MINITAB and JMP statistical analysis software. Divided into two parts, the text covers the principles of statistical thinking and analysis, bootstrapping, predictive analytics, Bayesian inference, time series analysis, acceptance sampling, statistical process control, design and analysis of experiments, simulation and computer experiments, and reliability and survival analysis. Part A, on computer age statistical analysis, can be used in general courses on analytics and statistics. Part B is focused on industrial statistics applications. The fully revised third edition covers the latest techniques in R, MINITAB and JMP, and features brand-new coverage of time series analysis, predictive analytics and Bayesian inference. New and expanded simulation activities, examples, and case studies—drawn from the electronics, metal work, pharmaceutical, and financial industries—are complemented by additional computer and modeling methods. Helping readers develop skills for modeling data and designing experiments, this comprehensive volume: Explains the use of computer-based methods such as bootstrapping and data visualization Covers nonstandard techniques and applications of industrial statistical process control (SPC) charts Contains numerous problems, exercises, and data sets representing real-life case studies of statistical work in various business and industry settings Includes access to a companion website that contains an introduction to R, sample R code, csv files of all data sets, JMP add-ins, and downloadable appendices Provides an author-created R package, mistat, that includes all data sets and statistical analysis applications used in the book Part of the acclaimed Statistics in Practice series, Modern Industrial Statistics with Applications in R, MINITAB, and JMP, Third Edition, is the perfect textbook for advanced undergraduate and postgraduate courses in the areas of industrial statistics, quality and reliability engineering, and an important reference for industrial statisticians, researchers, and practitioners in related fields. The mistat R-package is available from the R CRAN repository.
Author: Cuthbert Daniel Publisher: John Wiley & Sons ISBN: 0470317175 Category : Mathematics Languages : en Pages : 321
Book Description
Other volumes in the Wiley Series in Probability and MathematicalStatistics, Ralph A. Bradley, J. Stuart Hunter, David G. Kendall,& Geoffrey S. Watson, Advisory Editors Statistical Models inApplied Science Karl V. Bury Of direct interest to engineers andapplied scientists, this book presents general principles ofstatistics and specific distribution methods and models. Prominentdistribution properties and methods that are useful over a widerange of applications are covered in detail. The strengths andweaknesses of the distributional models are fully described, givingthe reader a firm, intuitive approach to the selection of the modelmost appropriate to the problem at hand. 1975 656 pp. FittingEquations To Data Computer Analysis of Multifactor Data forScientists and Engineers Cuthbert Daniel & Fred S. Wood Withthe assistance of John W. Gorman The purpose of this book is tohelp the serious data analyst, scientist, or engineer with acomputer to: recognize the strengths and limitations of his data;test the assumptions implicit in the least squares methods used tofit the data; select appropriate forms of the variables; judgewhich combinations of variables are most influential; and state theconditions under which the fitted equations are applicable.Throughout, mathematics is kept at the level of college algebra.1971 342 pp. Methods for Statistical Analysis of Reliability AndLife Data Nancy R. Mann, Ray E. Schafer & Nozer D. SingpurwallaThis book introduces failure models commonly used in reliabilityanalysis, and presents the most useful methods for analyzing thelife data of these models. Highlights include: material onaccelerated life testing; a comprehensive treatment of estimationand hypothesis testing; a critical survey of methods forsystem-reliability confidence bonds; and methods for simulation oflife data and for testing fit. 1974 564 pp.
Author: Galit Shmueli
Author: Galit Shmueli
Author: Galit Shmueli
Author: Andrew N O'Connor
Author: Anant P. Godbole
Author: Ron S. Kenett
Author: Andrew Metcalfe
Author: Bhisham C. Gupta
Author: N. Balakrishnan
Author: Ron S. Kenett
Author: Cuthbert Daniel