JWCL232_fm_i-xvi.qxd 1/23/10 1:18 PM Page xvi JWCL232_fm_i-xvi.qxd 1/21/10 7:40 PM Page i This online teaching and learning environment integrates the entire digital textbook with the most effective instructor and student resources WR ÀW HYHU\ OHDUQLQJ VW\OH :LWK WileyPLUS 6WXGHQWV DFKLHYH FRQFHSW ,QVWUXFWRUV SHUVRQDOL]H DQG PDQDJH PDVWHU\ LQ D ULFK WKHLU FRXUVH PRUH HIIHFWLYHO\ ZLWK VWUXFWXUHG HQYLURQPHQW DVVHVVPHQW DVVLJQPHQWV JUDGH WKDW·V DYDLODEOH WUDFNLQJ DQG PRUH PDQDJH WLPH EHWWHU VWXG\ VPDUWHU VDYH PRQH\ From multiple study paths, to self-assessment, to a wealth of interactive visual and audio resources, WileyPLUS gives you everything you need to personalize the teaching and learning experience. ( , 7 <2 8 5 6 » ZZZZLOH\plusFRP JWCL232_fm_i-xvi.qxd 1/21/10 7:40 PM Page ii ALL THE HELP, RESOURCES, AND PERSONAL SUPPORT YOU AND YOUR STUDENTS NEED! 0LQXWH 7XWRULDOV DQG DOO 6WXGHQW VXSSRUW IURP DQ &ROODERUDWH ZLWK \RXU FROOHDJXHV RI WKH UHVRXUFHV \RX \RXU H[SHULHQFHG VWXGHQW XVHU ILQG D PHQWRU DWWHQG YLUWXDO DQG OLYH VWXGHQWV QHHG WR JHW VWDUWHG $VN \RXU ORFDO UHSUHVHQWDWLYH HYHQWV DQG YLHZ UHVRXUFHV www.com/firstday IRU GHWDLOV www.com 3UHORDGHG UHDG\WRXVH 7HFKQLFDO 6XSSRUW <RXU WileyPLUS DVVLJQPHQWV DQG SUHVHQWDWLRQV )$4V RQOLQH FKDW $FFRXQW 0DQDJHU www.com/college/quickstart DQG SKRQH VXSSRUW 7UDLQLQJ DQG LPSOHPHQWDWLRQ VXSSRUW www.com/support www.( ,7 <2856 JWCL232_fm_i-xvi.qxd 1/21/10 7:40 PM Page iii Applied Statistics and Probability for Engineers Fifth Edition Douglas C. Montgomery Arizona State University George C. Runger Arizona State University John Wiley & Sons, Inc.
JWCL232_fm_i-xvi.qxd 1/23/10 1:17 PM Page iv To: Meredith, Neil, Colin, and Cheryl Rebecca, Elisa, George, and Taylor EXECUTIVE PUBLISHER Don Fowley ASSOCIATE PUBLISHER Daniel Sayre ACQUISITIONS EDITOR Jennifer Welter PRODUCTION EDITOR Trish McFadden MARKETING MANAGER Christopher Ruel SENIOR DESIGNER Kevin Murphy MEDIA EDITOR Lauren Sapira PHOTO ASSOCIATE Sheena Goldstein EDITORIAL ASSISTANT Alexandra Spicehandler PRODUCTION SERVICES MANAGEMENT Aptara COVER IMAGE Norm Christiansen This book was set in 10/12 pt. TimesNewRomanPS by Aptara and printed and bound by R. Donnelley/Willard Division. The cover was printed by Phoenix Color.
This book is printed on acid-free paper. ⬁ Copyright © 2011 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc.
222 Rosewood Drive, Danvers, MA 01923, website www. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, website http://www.com/go/permissions. To order books or for customer service, please call 1-800-CALL WILEY (225-5945). ISBN–13: 978-0-470-05304-1 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 JWCL232_fm_i-xvi.qxd 1/21/10 10:21 PM Page v Wiley Books by These Authors Website: www.com/college/montgomery Engineering Statistics, Fourth Edition by Montgomery, Runger, and Hubele Introduction to engineering statistics, with topical coverage appropriate for a one-semester course.
A modest mathematical level, and an applied approach. Applied Statistics and Probability for Engineers, Fifth Edition by Montgomery and Runger Introduction to engineering statistics, with topical coverage appropriate for either a one- or two-semester course. An applied approach to solving real-world engineering problems. Introduction to Statistical Quality Control, Sixth Edition by Douglas C.
Montgomery For a first course in statistical quality control. A comprehensive treatment of statistical methodology for quality control and improvement. Some aspects of quality management are also included, such as the six-sigma approach. Design and Analysis of Experiments, Seventh Edition by Douglas C.
Montgomery An introduction to design and analysis of experiments, with the modest prerequisite of a first course in statistical methods. For senior and graduate students and for practitioners, to design and analyze experiments for improving the quality and efficiency of working systems. Introduction to Linear Regression Analysis, Fourth Edition by Montgomery, Peck, and Vining A comprehensive and thoroughly up-to-date look at regression analysis, still the most widely used technique in statistics today. Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Third Edition by Myers, Montgomery, and Anderson-Cook Website: www.com/college/myers The exploration and optimization of response surfaces, for graduate courses in experimental design, and for applied statisticians, engineers, and chemical and physical scientists.
Generalized Linear Models: With Applications in Engineering and the Sciences by Myers, Montgomery, and Vining Website: www.com/college/myers An introductory text or reference on generalized linear models (GLMs). The range of theoretical topics and applications appeals both to students and practicing professionals. Introduction to Time Series Analysis and Forecasting by Montgomery, Jennings, and Kulahci Methods for modeling and analyzing time series data, to draw inferences about the data and generate forecasts useful to the decision maker. Minitab and SAS are used to illustrate how the methods are implemented in practice.
For advanced undergrad/first-year graduate, with a prerequisite of basic statistical methods. Portions of the book require calculus and matrix algebra. JWCL232_fm_i-xvi.qxd 1/21/10 7:40 PM Page vi Preface INTENDED AUDIENCE This is an introductory textbook for a first course in applied statistics and probability for undergraduate students in engineering and the physical or chemical sciences. These individuals play a significant role in designing and developing new products and manufacturing systems and processes, and they also improve existing systems.
Statistical methods are an important tool in these activities because they provide the en- gineer with both descriptive and analytical methods for dealing with the variability in observed data. Although many of the methods we present are fundamental to statistical analysis in other disciplines, such as business and management, the life sciences, and the social sciences, we have elected to focus on an engineering-oriented audience. We believe that this approach will best serve students in engineering and the chemical/physical sciences and will allow them to concentrate on the many applications of statistics in these disciplines. We have worked hard to ensure that our examples and exercises are engineering- and science-based, and in almost all cases we have used examples of real data—either taken from a published source or based on our consulting experiences.
We believe that engineers in all disciplines should take at least one course in statistics. Unfortunately, because of other requirements, most engineers will only take one statistics course. This book can be used for a single course, although we have provided enough material for two courses in the hope that more students will see the important applications of statistics in their everyday work and elect a second course. We believe that this book will also serve as a useful reference.
We have retained the relatively modest mathematical level of the first four editions. We have found that engineering students who have completed one or two semesters of calculus should have no difficulty reading almost all of the text. It is our intent to give the reader an understanding of the methodology and how to apply it, not the mathematical theory. We have made many enhancements in this edition, including reorganizing and rewriting major portions of the book and adding a number of new exercises.
ORGANIZATION OF THE BOOK Perhaps the most common criticism of engineering statistics texts is that they are too long. Both instructors and students complain that it is impossible to cover all of the topics in the book in one or even two terms. For authors, this is a serious issue because there is great variety in both the content and level of these courses, and the decisions about what material to delete without limiting the value of the text are not easy. Decisions about which topics to include in this edition were made based on a survey of instructors.
Chapter 1 is an introduction to the field of statistics and how engineers use statistical methodology as part of the engineering problem-solving process. This chapter also introduces the reader to some engineer- ing applications of statistics, including building empirical models, designing engineering experiments, and monitoring manufacturing processes. These topics are discussed in more depth in subsequent chapters. Chapters 2, 3, 4, and 5 cover the basic concepts of probability, discrete and continuous random vari- ables, probability distributions, expected values, joint probability distributions, and independence.
We have given a reasonably complete treatment of these topics but have avoided many of the mathematical or more theoretical details. Chapter 6 begins the treatment of statistical methods with random sampling; data summary and de- scription techniques, including stem-and-leaf plots, histograms, box plots, and probability plotting; and several types of time series plots. Chapter 7 discusses sampling distributions, the central limit theorem, and point estimation of parameters. This chapter also introduces some of the important properties of esti- mators, the method of maximum likelihood, the method of moments, and Bayesian estimation.
Chapter 8 discusses interval estimation for a single sample. Topics included are confidence intervals for means, variances or standard deviations, proportions, prediction intervals, and tolerance intervals. Chapter 9 discusses hypothesis tests for a single sample. Chapter 10 presents tests and confidence intervals for two samples.
This material has been extensively rewritten and reorganized. There is detailed information and examples of methods for determining appropriate sample sizes. We want the student to become familiar with how these techniques are used to solve real-world engineering problems and to get some understanding of vi JWCL232_fm_i-xvi.qxd 1/22/10 5:42 AM Page vii PREFACE vii the concepts behind them. We give a logical, heuristic development of the procedures rather than a formal, mathematical one.
We have also included some material on nonparametric methods in these chapters. Chapters 11 and 12 present simple and multiple linear regression including model adequacy checking and regression model diagnostics and an introduction to logistic regression. We use matrix algebra throughout the multiple regression material (Chapter 12) because it is the only easy way to understand the concepts presented. Scalar arithmetic presentations of multiple regression are awkward at best, and we have found that undergrad- uate engineers are exposed to enough matrix algebra to understand the presentation of this material.
Chapters 13 and 14 deal with single- and multifactor experiments, respectively. The notions of ran- domization, blocking, factorial designs, interactions, graphical data analysis, and fractional factorials are emphasized. Chapter 15 introduces statistical quality control, emphasizing the control chart and the fun- damentals of statistical process control. WHAT’S NEW IN THIS EDITION? We received much feedback from users of the fourth edition of the book, and in response we have made substantial changes in this new edition.
• The most obvious change is that the chapter on nonparametric methods is gone. We have inte- grated most of this material into Chapter 9 and 10 on statistical hypothesis testing, where we think it is a much better fit if instructors elect to cover these techniques. • Another substantial change is the increased emphasis on the use of P-value in hypothesis test- ing. Many sections of several chapters were rewritten to reflect this.
• We have also rewritten and modified many portions of the book to improve the explanations and try to make the concepts easier to understand. • We have added brief comments at the end of examples to emphasize the practical interpretations of the results. • We have also added approximately 200 new homework exercises. FEATURED IN THIS BOOK Definitions, Key Concepts, and Equations 4-4 MEAN AND VARIANCE OF A CONTINUOUS Throughout the text, definitions and key con- RANDOM VARIABLE cepts and equations are highlighted by a box The mean and variance can also be defined for a continuous random variable.
Integration replaces summation in the discrete definitions. If a probability density function is viewed as a to emphasize their importance. loading on a beam as in Fig. 4-1, the mean is the balance point.
Mean and Suppose X is a continuous random variable with probability density function f(x).