Also available from ASQ Quality Press: The Certified Quality Technician Handbook, Second Edition H. Fred Walker, Donald W. Benbow, and Ahmad K. Elshennawy The Certified Quality Engineer Handbook, Third Edition Connie M. Borror, editor The Metrology Handbook, Second Edition Jay L. Bucher, editor The Uncertainty of Measurements: Physical and Chemical Metrology Impact and Analysis S. K. Kimothi Quality Audits for Improved Performance, Third Edition Dennis R. Arter Reliability Data Analysis with Excel and Minitab Kenneth S. Stephens HALT, HASS, and HASA Explained: Accelerated Reliability Techniques, Revised Edition Harry W. McLean The Quality Toolbox, Second Edition Nancy R. Tague Root Cause Analysis: Simplified Tools and Techniques, Second Edition Bjørn Andersen and Tom Fagerhaug The Certified Manager of Quality/Organizational Excellence Handbook: Third Edition Russell T. Westcott, editor To request a complimentary catalog of ASQ Quality Press publications, call 800-248-1946, or visit our website at http://www.asq.org/quality-press.
The Certified Quality Inspector Handbook Second Edition
H. Fred Walker, Ahmad Elshennawy, Bhisham C. Gupta, and Mary McShane Vaughn
ASQ Quality Press Milwaukee, Wisconsin
American Society for Quality, Quality Press, Milwaukee 53203 © 2013 by ASQ All rights reserved. Published 2012 Printed in the United States of America 17 16 15 14 13 12 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data to come The certified quality inspector handbook / H. Fred Walker . . . [et al.].—2nd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-87389-845-4 (alk. paper) 1. Quality control—Handbooks, manuals, etc. 2. Quality control inspectors— Certification—United States. I. Walker, H. Fred, 1963– TS156.C42345 2012 658.5′62—dc23 2012027602 No part of this book may be reproduced in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Publisher: William A. Tony Acquisitions Editor: Matt Meinholz Project Editor: Paul Daniel O’Mara Production Administrator: Randall Benson ASQ Mission: The American Society for Quality advances individual, organizational, and community excellence worldwide through learning, quality improvement, and knowledge exchange. Attention Bookstores, Wholesalers, Schools, and Corporations: ASQ Quality Press books, video, audio, and software are available at quantity discounts with bulk purchases for business, educational, or instructional use. For information, please contact ASQ Quality Press at 800‑248‑1946, or write to ASQ Quality Press, P.O. Box 3005, Milwaukee, WI 53201-3005. To place orders or to request a free copy of the ASQ Quality Press Publications Catalog, visit our website at http://www.asq.org/quality-press. Printed on acid-free paper
In loving memory of my father, Carl Ellsworth Walker. —Fred In loving memory of my mother, Ikram. —Ahmad In loving memory of my parents, Roshan Lal and Sodhan Devi. —Bhisham In loving memory of my father, Charles H. McShane. —Mary
Table of Contents
List of Figures and Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Use This Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii xxi xxii xxiii
Section I Technical Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 1 A. Basic Shop Math. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of Real Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Positive and Negative Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decimals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Squares and Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Factorials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Truncating, Rounding, and Significant Digits. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 2 2 3 7 9 10 10 10
Chapter 2 B. Basic Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Solving Algebraic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Chapter 3 C. Basic Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Areas of Basic Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Perimeter and Circumference of Basic Geometric Shapes. . . . . . . . . . . . . . . . . . Volume of Basic Geometric Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Area of Basic Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Complementary and Supplementary Angles. . . . . . . . . . . . . . . . . . . . . . . . . . . .
18 18 20 22 23 25
Chapter 4 D. Basic Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Right Triangle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonometric Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solving for Unknown Sides and Angles of a Right Triangle. . . . . . . . . . . . . . . . Inverse Trigonometric Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oblique Triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solving Oblique Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26 26 27 29 31 31 31
Chapter 5 E. Measurement Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 English System Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 vii
viii Table of Contents SI/Metric System Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 English-to-SI/Metric Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Chapter 6 F. Numeric Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scientific Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decimals and Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Section II Metrology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Chapter 7 A. Common Gauges and Measurement Instruments. . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Variable Gauges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Attribute Gauges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Transfer Gauges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Measurement Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56 56 57 63 69 69
Chapter 8 B. Special Gauges and Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Electronic Gauging Tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Automatic Gauging Components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Pneumatic Gauging Components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of Gauge Uses and Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 9 C. Gauge Selection, Handling, and Use. . . . . . . . . . . . . . . . . . . . . . . . 1. Gauge Selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Gauge Handling, Preservation, and Storage. . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Gauge Correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 10 D. Surface Plate Tools and Techniques. . . . . . . . . . . . . . . . . . . . . . . . 88 1. Surface Plate Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2. Angle Measurement Instruments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Chapter 11 E. Specialized Inspection Equipment. . . . . . . . . . . . . . . . . . . . . . . . . 1. Measuring Mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Measuring Finish. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Measuring Shape and Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Optical Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Digital Vision Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Coordinate Measuring Machine (CMM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94 94 98 100 100 105 107
Chapter 12 F. Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Calibration Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Calibration Standards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Equipment Traceability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Gauge Calibration Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Out-of-Calibration Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
112 112 116 117 118 118
Chapter 13 G. Measurement System Analysis (MSA). . . . . . . . . . . . . . . . . . . . . Process Variability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluating Measurement System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . The Range-Based Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The ANOVA Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement Capability Indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
120 121 121 122 127 133
Table of Contents
Section III Inspection and Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Chapter 14 A. Blueprints, Drawings, Geometric Dimensioning & Tolerancing (GD&T) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Blueprints and Engineering Drawings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Terminology and Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Position and Bonus Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Part Alignment & Datum Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
136 136 137 142 145 147
Chapter 15 B. Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Advantages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sampling Concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Types of Attribute Sampling Plans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sampling Standards and Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variables Sampling Plans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sequential Sampling Plans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous Sampling Plans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
149 149 150 151 153 154 156 157 158
Chapter 16 C. Inspection Planning and Processes. . . . . . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inspection Planning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Inspection Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Inspection Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Product Traceability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Identification of Nonconforming Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Level of Severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control of Nonconforming Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Disposition of Nonconforming Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
161 161 162 163 166 169 171 172 173 176
Chapter 17 D. Testing Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Nondestructive Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Destructive Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Functionality Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Hardness Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
179 179 186 189 191
Chapter 18 E. Software for Test Equipment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Software Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Testing vs. Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functional Testing in Software Development. . . . . . . . . . . . . . . . . . . . . . . . . . . . Software Testing Terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
196 196 197 197 198
Section IV Quality Assurance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Chapter 19 A. Basic Statistics and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . Graphical Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
206 206 223 241
Chapter 20 B. Statistical Process Control (SPC). . . . . . . . . . . . . . . . . . . . . . . . . . . 250 Basic Concepts of Quality and Its Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 What Is a Process?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Table of Contents Check Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cause-and-Effect (Fishbone or Ishikawa) Diagram. . . . . . . . . . . . . . . . . . . . . . . Defect Concentration Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Run Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Charts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average Run Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operating Characteristic Curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common Causes vs. Special Causes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Limits vs. Specification Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Charts for Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Charts for Attributes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Capability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
252 253 255 256 257 260 261 262 265 265 275 293
Chapter 21 C. Quality Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 1. Terms and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 2. Products and Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 Chapter 22 D. Quality Audits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terms and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Types of Audits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Roles and Responsibilities in Audits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Audit Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Audit Tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Communication Tools and Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Corrective Action Requests (CARs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Audit Outcomes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
308 309 309 311 311 312 313 313 313
Chapter 23 E. Quality Tools and Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 Seven Basic Quality Control Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 Chapter 24 F. Problem-Solving Tools and Continuous Improvement Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Plan-Do-Check-Act (PDCA) or Plan-Do-Study-Act (PDSA) Cycles. . . . . . . 2. Lean Tools for Eliminating Waste. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Six Sigma Phases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Root Cause Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Failure Mode and Effects Analysis (FMEA) . . . . . . . . . . . . . . . . . . . . . . . . . . .
318 318 320 325 326 327
Chapter 25 G. Resources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Environmental and Safety Support. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Reference Documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Technical Reports. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Employees as Resources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
348 349 350 352 353
Section V Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 Appendix A ASQ Quality Inspector Certification Body of Knowledge 2012. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Appendix B Computer Resources to Support the CQI Handbook. . . . . . . . . . 368 Appendix C General Tables of Units of Measurement . . . . . . . . . . . . . . . . . . . . 398
Table of Contents
Appendix D Standard Normal Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 Appendix E Factors Helpful in Constructing Control Charts for Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 Appendix F Values of K1 for Computing Repeatability Using the Range Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 Appendix G Values of K2 for Computing Reproducibility Using the Range Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 Appendix H Sample Tables of ANSI/ASQ Z1.4-2008 and ANSI/ASQ Z1.9-2008 Standards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Glossary of Inspection Terms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
List of Figures and Tables
Section I Table 1.1
Properties of real numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Example prime factorization tree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Place values for ABCDEFG.HIJKLM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Decimal and fraction equivalents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Additional properties of real numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Inverse operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Calculation of area for basic geometric shapes . . . . . . . . . . . . . . . . . . . . . . . . . 19
Calculation of perimeter and circumference of basic geometric shapes . . . . 21
Calculation of volume of basic geometric shapes. . . . . . . . . . . . . . . . . . . . . . . 23
Calculation of surface area for basic geometric shapes. . . . . . . . . . . . . . . . . . . 24
The right triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Calculation of trigonometric functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Values of trigonometric functions for common angles. . . . . . . . . . . . . . . . . . . 29
Finding angles in a right triangle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Oblique triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Oblique triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Three sides known. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Two sides and angle between known . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Two sides and opposite angle known. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
One side and two angles known . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Converting measures of length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Converting measures of area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Converting measures of volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Converting measures of weight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Converting measures of liquid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Converting measures of pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Converting measures of length—metric units. . . . . . . . . . . . . . . . . . . . . . . . . . 42
Converting measures of area—metric units. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Converting measures of volume—metric units. . . . . . . . . . . . . . . . . . . . . . . . . 43
Converting measures of mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
xiv List of Figures and Tables Table 5.11
Converting liquid measures—metric units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Converting measures of length—English and metric units. . . . . . . . . . . . . . . 44
Converting measures of area—English and metric units. . . . . . . . . . . . . . . . . 45
Converting measures of volume—English and metric units. . . . . . . . . . . . . . 46
Converting measures of weight and mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Converting measures of liquid—English and metric units . . . . . . . . . . . . . . . 47
Converting temperatures—Celsius to Fahrenheit. . . . . . . . . . . . . . . . . . . . . . . 47
Converting temperatures—Fahrenheit to Celsius. . . . . . . . . . . . . . . . . . . . . . . 47
Converting temperatures—English and metric units. . . . . . . . . . . . . . . . . . . . 48
Powers of 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Common fractions and their decimal equivalents. . . . . . . . . . . . . . . . . . . . . . . 52
Section II Figure 7.1
Fine-adjustment style vernier caliper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
LCD digital-reading caliper with 0–152 mm (0–6 in.) range . . . . . . . . . . . . . . 58
Digital-reading, single-axis height gauge for two-dimensional measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
A 0–25 mm micrometer caliper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Micrometer reading of 10.66 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Scales of a vernier micrometer showing a reading of 10.666 mm. . . . . . . . . . 61
A digital micrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
An indicating micrometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
A schematic showing the process of wringing gauge blocks. . . . . . . . . . . . . . 63
Examples of typical gauges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Elements of electronic gauges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
(a) Light-wave interference with an optical flat, (b) application of an optical flat, (c) diagram of an interferometer. . . . . . . . . . . . . . . . . . . . . . 75
Diagram of air gauge principles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Summary of commonly used gauges and their applications. . . . . . . . . . . . . . 79
Granite surface plate for checking the flatness of a part, with dial indicator and leveling screws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Simple dial indicator mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
An application of dial indicators for inspecting flatness by placing the workpiece on gauge blocks and checking full indicator movement (FIM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Application of a sine bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Addition and subtraction of angle blocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
(a) Typical surface highly magnified, (b) profile of surface roughness, (c) surface quality specifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
(a) Skid-type or average surface finish measuring gauge, (b) skidless or profiling gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Optical tooling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Optical comparator system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
List of Figures and Tables
Horizontal optical comparator with a 356 mm (14 in.) viewing screen, digital readout, and edge-sensing device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
CMM classifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
The calibration system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Calibration standards hierarchy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Components of total variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
(a) Accurate and precise, (b) accurate but not precise, (c) not accurate but precise, (d) neither accurate nor precise. . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Diagram showing the linear relationship between the actual and the observed values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Data on an experiment involving three operators, 10 bolts, and three measurements (in mm) on each bolt by each operator. . . . . . . . . . . . . . . . . . . 125
Two-way ANOVA table with interaction (Minitab printout). . . . . . . . . . . . . . 128
Two-way ANOVA table without interaction (Minitab printout). . . . . . . . . . . 129
Gauge R&R (Minitab printout). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
An example: percent Torrence contribution by the various components of the measurement system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Percent contribution of variance components for the data in Example 13.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 – X and R chart for the data in Example 13.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Figure 13.10 Interaction between operators and parts for the data in Example 13.1 . . . . . 132 Figure 13.11 Scatter plot for measurements versus operators. . . . . . . . . . . . . . . . . . . . . . . . 132 Figure 13.12 Scatter plot for measurements versus parts (bolts). . . . . . . . . . . . . . . . . . . . . . 133
Section III Figure 14.1
Blueprint for a house floor plan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Placement of the title block and notes on engineering drawings. . . . . . . . . . 138
Example of title and notes blocks on an engineering drawing. . . . . . . . . . . . 139
Example of a revision block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Example of a technical engineering drawing with an indication of geometric tolerances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Visual representation of the control frame of a hole. . . . . . . . . . . . . . . . . . . . . 141
Features that can be specified by geometric tolerancing . . . . . . . . . . . . . . . . . 141
Simple 2-D example of position tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Top, front, and right side views of an item. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Figure 14.10 Engineering drawing line types and styles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Table 14.1
Other feature control symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Figure 14.11 Example of symbols on an engineering drawing . . . . . . . . . . . . . . . . . . . . . . . 145 Figure 14.12 Form tolerance example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Figure 15.1
An OC curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
AOQ curve for N = ∞, n = 50, c = 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Switching rules for normal, tightened, and reduced inspection. . . . . . . . . . . 155
Structure and organization of ANSI/ASQ Z1.9-2008. . . . . . . . . . . . . . . . . . . . 158
xvi List of Figures and Tables Figure 15.5
Decision areas for a sequential sampling plan. . . . . . . . . . . . . . . . . . . . . . . . . . 159
Inspection decisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
An example of a flowchart of a repair job. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Factors affecting the measuring process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Standards pertaining to MRB operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Visual inspection ensures consistency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Inspection using X-ray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Example of an inspection using X-ray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Eddy current method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
The general inspection principle for ultrasonic testing. . . . . . . . . . . . . . . . . . . 183
Magnetic particle inspection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Liquid penetrant testing steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Tensile test for a furnace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Free-bend test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Figure 17.10 Crash testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Figure 17.11 Tension test machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Figure 17.12 Torque can be calculated by multiplying the force applied to a lever by its distance from the lever’s fulcrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Figure 17.13 Compression test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Figure 17.14 Brinell hardness test method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Figure 17.15 Rockwell hardness test method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Figure 17.16 The Vickers hardness test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Section IV Table 19.1
Classification of annual revenues of 110 small to midsize companies located in the Midwestern region of the United States. . . . . . . . . . . . . . . . . . . 207
Complete frequency distribution table for the 110 small to midsize companies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Complete frequency distribution table for the data in Example 19.2. . . . . . . 208
Frequency table for the data on rod lengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Dot plot for the data on defective motors received in 20 different shipments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Understanding defect rates as a function of various process steps. . . . . . . . . 212
Pie chart for defects associated with manufacturing process steps. . . . . . . . 213
Bar chart for annual revenues of a company over a five-year period . . . . . . 214
Frequency distribution table for the data in Example 19.7. . . . . . . . . . . . . . . . 215
Bar graph for the data in Example 19.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Pareto chart for the data in Example 20.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Frequencies and weighted frequencies when different types of defects are not equally important. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Pareto chart when weighted frequencies are used. . . . . . . . . . . . . . . . . . . . . . 217
Cholesterol levels and systolic blood pressures of 30 randomly selected US males. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
List of Figures and Tables xvii
Scatter plot for the data in Table 19.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Frequency distribution table for the survival time of parts. . . . . . . . . . . . . . . 220
Frequency histogram for survival time of parts under extreme operating conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Relative frequency histogram for survival time of parts under extreme operating conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Figure 19.10 Frequency polygon for the data in Example 19.9. . . . . . . . . . . . . . . . . . . . . . . . 222 Figure 19.11 Relative frequency polygon for the data in Example 19.9 . . . . . . . . . . . . . . . . 222 Figure 19.12 A typical frequency distribution curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Figure 19.13 Three types of frequency distribution curves. . . . . . . . . . . . . . . . . . . . . . . . . . 223 Figure 19.14 Frequency distributions showing the shape and location of measures of centrality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Figure 19.15 Two frequency distribution curves with equal mean, median, and mode values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Figure 19.16 Application of the empirical rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Figure 19.17 Amount of soft drink contained in a bottle. . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Figure 19.18 Dollar value of units of bad production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 Figure 19.19 Salary data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Figure 19.20 Quartiles and percentiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Figure 19.21 Box-whisker plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Figure 19.22 Box plot for the data in Example 19.24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Figure 19.23 Box plot for the data shown in Example 19.25. . . . . . . . . . . . . . . . . . . . . . . . . . 241 Figure 19.24 The normal density function curve with mean μ and standard deviation σ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 Figure 19.25 Curves representing the normal density function with different means, but with the same standard deviation . . . . . . . . . . . . . . . . . 243 Figure 19.26 Curves representing the normal density function with different standard d eviations, but with the same mean. . . . . . . . . . . . . . . . . . . . . . . . . . 243 Figure 19.27 The standard normal density function curve. . . . . . . . . . . . . . . . . . . . . . . . . . 244 Figure 19.28 Probability (a ≤ Z ≤ b) under the standard normal curve. . . . . . . . . . . . . . . . . 244 Table 19.10
A portion of the standard normal distribution table from Appendix D. . . . . 244
Figure 19.29 Shaded area equal to P(1.0 ≤ Z ≤ 2.0). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Figure 19.30 Two shaded areas showing P(–1.5 ≤ Z ≤ 0) = P(0 ≤ Z ≤ 1.5) . . . . . . . . . . . . . . . 245 Figure 19.31 Two shaded areas showing P(–2.2 ≤ Z ≤ –1.0) = P(1.0 ≤ Z ≤ 2.2). . . . . . . . . . . . 245 Figure 19.32 Shaded area showing P(–1.5 ≤ Z ≤ 0.8) = P(–1.5 ≤ Z ≤ 0) + P(0 ≤ Z ≤ 0.8). . . . 246 Figure 19.33 Shaded area showing P(Z ≤ 0.7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Figure 19.34 Shaded area showing P(Z ≥ 1.0). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Figure 19.35 Shaded area showing P(Z ≥ 2.15). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Figure 19.36 Shaded area showing P(Z ≤ –2.15). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Figure 19.37 Converting normal N(6,4) to standard normal N(0,1). . . . . . . . . . . . . . . . . . . . 248 Figure 19.38 Shaded area showing P(0.5 ≤ Z ≤ 2.0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 Figure 19.39 Shaded area showing P(–1.0 ≤ Z ≤ 1.0). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Figure 19.40 Shaded area showing P(–1.5 ≤ Z ≤ –0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
xviii List of Figures and Tables Figure 20.1
Flowchart of a process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Check sheet summarizing the data of a study over a period of four weeks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Initial form of a cause-and-effect diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
A completed cause-and-effect diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
A damaged item shaped as a rectangular prism. . . . . . . . . . . . . . . . . . . . . . . 255
Percentage of nonconforming units in 30 different shifts. . . . . . . . . . . . . . . . . 256
Run chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
A pictorial representation of the components of a control chart . . . . . . . . . . 257 – OC curves for the X chart with 3-sigma limits, for different sample sizes n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Figure 20.7 Table 20.3
Diameter measurements (mm) of ball bearings used in the wheels of heavy construction equipment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 – X and R control chart for the ball-bearing data in Table 20.3. . . . . . . . . . . . . 270 – X and S control chart for the ball-bearing data in Table 20.3 . . . . . . . . . . . . . 275
Control charts for attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Number of nonconforming computer chips out of 1000 inspected each day during the study period of 30 days. . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Figure 20.10 p chart for nonconforming computer chips, using trial control limits for the data in Table 20.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Table 20.6
Number of nonconforming computer chips with different size samples inspected each day during the study period of 30 days. . . . . . . . . . 283
Figure 20.11 p chart for nonconforming chips with variable sample sizes, using trial control limits for the data in Table 20.6. . . . . . . . . . . . . . . . . . . . . . 284 Figure 20.12 np chart for nonconforming computer chips, using trial control limits for the data in Table 20.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Table 20.7
Total number of nonconformities in samples of five rolls of paper . . . . . . . . 287
Figure 20.13 c control chart of nonconformities for the data in Table 20.7. . . . . . . . . . . . . . 288 Table 20.8
Number of nonconformities on printed boards for laptops per sample; each sample consists of five inspection units. . . . . . . . . . . . . . . . . . . . 290
Figure 20.14 u chart of nonconformities for the data in Table 20.8, constructed using Minitab. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Table 20.9
Number of nonconformities on printed boards for laptops per sample, with varying sample size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
Figure 20.15 u chart of nonconformities for the data in Table 20.9, constructed using Minitab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 Table 20.10
Data showing the lengths of tie rods for cars. . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Different processes with same value of Cpk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
Parts per million of nonconforming units for different values of Cpk. . . . . . . 301
The Plan-Do-Check-Act cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
Blank design FMEA form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
Blank process FMEA form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
Design FMEA severity criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
Process FMEA severity criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
List of Figures and Tables xix
Design FMEA occurrence criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
Process FMEA occurrence criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
Design FMEA detection criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Process FMEA detection criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Design FMEA example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
Process FMEA example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Part V Figure B.1
The screen that appears first in the Minitab environment. . . . . . . . . . . . . . . . 369
Minitab window showing the menu command options . . . . . . . . . . . . . . . . . 370
Minitab window showing input and output for Column Statistics . . . . . . . 372
Minitab window showing various options available under the Stat menu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
Minitab display of the histogram for the data given in Example B.3. . . . . . . 375
Minitab window showing Edit Bars dialog box . . . . . . . . . . . . . . . . . . . . . . . . 376
Minitab display of a histogram with five classes for the data in Example B.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
Minitab dot plot output for the data in Example B.4 . . . . . . . . . . . . . . . . . . . . 377
Minitab scatter plot output for the data given in Example B.5. . . . . . . . . . . . 379
Minitab display of box plot for the data in Example B.6 . . . . . . . . . . . . . . . . . 380
Minitab display of graphical summary for the data in Example B.7 . . . . . . . 381
Minitab display of the bar graph for the data in Example B.8. . . . . . . . . . . . . 383
Minitab display of the pie chart for the data in Example B.9. . . . . . . . . . . . . . 384
Minitab window showing the Xbar-R Chart dialog box . . . . . . . . . . . . . . . . . 387
Minitab window showing the Xbar-R Chart—Options dialog box. . . . . . . . 388
Minitab window showing the Xbar-S Chart dialog box . . . . . . . . . . . . . . . . . 389
Data for 25 samples each of size five from a given process. . . . . . . . . . . . . . . 390
Minitab window showing the Capability Analysis (Normal Distribution) dialog box. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
Minitab window showing the Minitab process capability analysis. . . . . . . . 392
Minitab window showing the P Chart dialog box . . . . . . . . . . . . . . . . . . . . . . 393
Minitab window showing the C Chart dialog box. . . . . . . . . . . . . . . . . . . . . . 395
Minitab window showing the U Chart dialog box. . . . . . . . . . . . . . . . . . . . . . 397
ANSI/ASQ Z1.4-2008 Table VIII: Limit numbers for reduced inspection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
ANSI/ASQ Z1.4-2008 Table I: Sample size code letters. . . . . . . . . . . . . . . . . . 425
ANSI/ASQ Z1.4-2008 Table I I-A: Single sampling plans for normal inspection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
ANSI/ASQ Z1.4-2008 Table III-A: Double sampling plans for normal inspection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
ANSI/ASQ Z1.4-2008 Table IV-A: Multiple sampling plans for normal inspection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
4.20 ANSI/ASQ Z1.9-2008 Table A-2: Sample size code letters.. . . . . . . . . . . 430
List of Figures and Tables
ANSI/ASQ Z1.9-2008 Table C-1: Master table for normal and tightened inspection for plans based on variability unknown (single specification limit—Form 1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
ANSI/ASQ Z1.9-2008 Table B-5: Table for estimating the lot percent nonconforming using standard deviation method. Values tabulated are read as percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
ANSI/ASQ Z1.9-2008 Table B-3: Master table for normal and tightened inspection for plans based on variability unknown (double specification limit and Form 2—single specification limit). . . . . . . . 441
he quality inspector is the person perhaps most closely involved with dayto-day activities intended to ensure that products and services meet customer expectations. The quality inspector is required to understand and apply a variety of tools and techniques as codified in the American Society for Quality (ASQ) Certified Quality Inspector (CQI) Body of Knowledge (BoK). The tools and techniques identified in the ASQ CQI BoK include technical math, metrology, inspection and test techniques, and quality assurance. Quality inspectors frequently work with the quality function of organizations in the various measurement and inspection laboratories, as well as on the shop floor supporting and interacting with quality engineers and production/service delivery personnel. This book, The Certified Quality Inspector Handbook (CQIH), was commissioned by ASQ Quality Press to support individuals preparing to perform, or those already performing, this type of work. The CQIH is intended to serve as a ready reference for quality inspectors and quality inspectors in training, as well as a comprehensive reference for those individuals preparing to take the ASQ CQI examination. Examples and problems used throughout the handbook are thoroughly explained, are algebra-based, and are drawn from real-world situations encountered in the quality profession.
he authors would like to thank their families. Fred would like to acknowledge the patience and support of his wife Julie and sons Carl and George as he worked on this book. Ahmad would like to acknowledge the patience and support provided by his wife Hanan, sons Mohammed and Omar, and daughter Leemar. Without their love, devotion, and encouragement, work on this book would not have been possible or meaningful. Bhisham is indebted to his wife Swarn, daughters Anita and Anjali, son Shiva, sons-in-law Prajay and Mark, daughter-in-law Aditi, and granddaughters Priya and Kaviya for their deep love and devotion. Without the encouragement of both our families, this project would not have been possible or meaningful. Mary thanks her husband Jim and their six children for their support and understanding while she was working on this project. We are grateful to the several anonymous reviewers whose constructive suggestions greatly improved this book. We also want to thank Matt Meinholz and Paul O’Mara of ASQ Quality Press for their patience and cooperation throughout this project. H. Fred Walker Ahmad K. Elshennawy Bhisham C. Gupta Mary McShane Vaughn
How to Use This Book
o assist readers in using this book as a ready reference or as a study aid, the book has been organized so as to conform explicitly to the ASQ CQI BoK. Each chapter title, all major topical divisions within the chapters, and every main point has been titled and then numbered exactly as they appear in the CQI BoK. To gain the most benefit from reading this book, it is intended that readers initially read the material in the order in which it is presented. Having read the material sequentially from beginning to end, readers are encouraged to then reread material unfamiliar or unclear to them to gain additional insights and mastery. It should be noted that many references were used to support development of the ASQ CQI BoK and by the authors to write this book. Individuals learning about quality inspection should expect to begin building a library of their own support materials—materials that have been identified in this book as well as identified and recommended on ASQ’s website.
Section I Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6
A. Basic Shop Math B. Basic Algebra C. Basic Geometry D. Basic Trigonometry E. Measurement System F. Numeric Conversions
Chapter 1 Section I.A
A. Basic Shop Math
Basic Shop Math Solve basic shop math problems using addition, subtraction, multiplication, division of fractions and decimals, squares and square roots. Use methods such as truncating and rounding to obtain significant digits for positive and negative numbers. (Apply) Body of Knowledge I.A
Properties of Real Numbers When performing arithmetic operations on numbers, keep in mind the fundamental properties as shown in Table 1.1. Let a, b, and c represent real numbers.
Positive and Negative Numbers A positive number is one that is greater than zero; a negative number is less than zero. For example, the number 6 is a positive number, while –2 is a negative number.
Table 1.1 Properties of real numbers. Property
Commutative property for addition
Commutative property for multiplication
Associative property for addition
(a + b) + c = a + (b + c)
Associative property for multiplication
(a × b) × c = a × (b × c)
Chapter 1 A. Basic Shop Math
Adding and Subtracting with Positive and Negative Numbers We can add and subtract positive and negative numbers, as the examples show: 4 +-3 = 1 -4 + 3 =-1 -4 +-3 =-7
Multiplying and Dividing with Positive and Negative Numbers We can also multiply and divide positive and negative numbers, as the examples show: 4 # 3 = 12 4 # - 3 = - 12 - 4 # 3 = - 12 - 4 # - 3 = 12 8'2 = 4
8 ' ^- 2h = - 4 -8 ' 2 =-4
Fractions A fraction relates a number of parts to the whole, and is usually written in the form a b The number a is the numerator and the number b is the denominator. For example, the fraction 3 8 refers to 3 parts from a total of 8 parts. Here, 3 is the numerator and 8 is the denominator.
Section I Technical Mathematics
Equivalent Fractions Equivalent fractions are those that express the same proportion of parts to the whole. For example, the fractions 1 , 2 , 40 2 4 80 are equivalent.
Simplified Fractions A simplified fraction refers to a fraction in which the numerator and the denominator do not share any factors in common. A simplified fraction is found by dividing both numerator and denominator by the greatest common factor (GCF). We can find the GCF by factoring both numerator and denominator, and choosing the largest factor in common. For example, given the fraction 27 45 we can factor the numerator and the denominator 3#9 5#9 and determine that the GCF is 9. Dividing the numerator and the denominator each by 9 yields the simplified fraction 3 5
Proper and Improper Fractions A proper fraction is one in which the numerator is less than the denominator. The fractions 2 , 14 , 75 3 17 100 are all examples of proper fractions. An improper fraction is one in which the numerator is larger than the denominator. Improper fractions can be converted into a mixed number, or a whole number and a proper fraction, by dividing the denominator into the numerator. For example: 10 = 7 10 = 1 3 g 7 7
Adding and Subtracting Fractions with Like Denominators To add or subtract fractions with equal denominators: 1. Add or subtract the numerators and leave the denominator the same 2. Simplify the resulting fraction if necessary 3+4-1 = 6 = 3 8 8 8 8 4
Chapter 1 A. Basic Shop Math
Adding and Subtracting Fractions with Unequal Denominators
1. Find the least common denominator (LCD) using prime factorization 2. Find the equivalent fractions using the LCD 3. Perform the addition or subtraction
Many times, the denominators of the fractions we wish to add or subtract are not equal. In this case:
4. Simplify the resulting fraction if necessary Prime Factorization A prime number is an integer greater than one that is a multiple of only itself and the number 1. For example, the number 7 is a prime number since it can only be divided evenly by the numbers 1 and 7, which are called the factors of 7. Conversely, 8 is not a prime number, since its factors are 1, 2, 4, and 8. A list of the first few prime numbers follows: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. A prime factorization expresses a number in terms of prime number factors. For example, the prime factorization of the number 12 is (2 × 2 × 3). To find the prime factorization of a given number, we can draw a number tree in which we successively break down the factors until we find the prime components. For example, the prime factorization of the number 100 is (2 × 2 × 5 × 5) and can be found using the tree in Figure 1.1. Least Common Denominator To find the LCD, express each denominator in terms of its prime factors. For example, if asked to solve 1 + 12 - 1 = ? 6 18 4
Figure 1.1 Example prime factorization tree.
Section I Technical Mathematics we begin with expressing the denominators in terms of their prime factors:
18 = ^2 # 3 # 3h 4 = ^2 # 2h
Record the maximum number of times each factor is used in any one expression. This will indicate how many times each factor must be multiplied to find the LCD. The factor 2 appears at most two times in the expressions, and the factor 3 appears at most two times. Therefore the LCD is calculated as: LCD = ^2 # 2h # ^3 # 3h = 36 Next, find the equivalent fractions using the LCD. The numerators can be found by cross multiplying: Old numerator = New numerator Old denominator LCD Old numerator # LCD = New numerator Old denominator 1 # 36 = 6 6 12 # 36 = 24 18 1 # 36 = 9 4 Now add the equivalent fractions, and simplify the result if needed: 1 12 1 6 + 24 - 9 = 21 = 7 ` 6 + 18 - 4 j = 36 36 12
Adding or Subtracting Mixed Numbers To add or subtract mixed numbers, we can convert the mixed numbers back into improper fractions and then proceed, or we can first add and subtract the whole number parts and then add and subtract the fractions. For example: 1 3 3 11 6 + 11 17 1 `1 2 + 2 4 j = ` 2 + 4 j = ` 4 j = 4 = 4 4 1 3 1 3 2+3 5 1 `1 2 + 2 4 j = 3 + ` 2 + 4 j = 3 + ` 4 j = `3 + 4 j = 4 4
Multiplying and Dividing Fractions To multiply fractions: 1. Multiply the numerators to obtain the numerator of the result 2. Multiply the denominators to obtain the resulting denominator 3. Simplify the resulting fraction if necessary
Chapter 1 A. Basic Shop Math
To divide fractions, we convert the problem into a multiplication problem: 1. Switch the numerator and the denominator of the second fraction 2. Multiply the numerators to obtain the numerator of the result
3 # 4 # 1 = 12 = 3 8 5 2 80 20
3. Multiply the denominators to obtain the resulting denominator 4. Simplify the resulting fraction if necessary For example: 2 ' 4 = 2 # 6 = 12 = 1 9 6 9 4 36 3
Decimals Given a number of the form: ABCDEFG.HIJKLM we can define the place values for each letter-position as shown in Table 1.2.
Table 1.2 Place values for ABCDEFG.HIJKLM.
Section I Technical Mathematics
Decimal and Fraction Equivalents
Decimal and fraction equivalents are shown in Table 1.3.
Converting Fractions to Decimals Fractions can be converted to decimals by dividing the denominator into the numerator. For example: 3 = 8 3 = 0 . 375 g 8
We read this decimal as 375 thousandths.
Rational and Irrational Numbers A rational number can be represented in fractional form. It has either a finite number of decimal places or an infinite (never-ending) number of repeating decimal places. For example, the numbers 0 . 37, 0 . 6894, 1 . 33562, 4 . 3r , 8 . 519 are all examples of rational numbers. An irrational number is a number that has an infinite number of decimal places that do not repeat. An example of an irrational number is π = 3.14159 . . ., since its digits are nonrepeating and infinite.
Converting Decimals to Percentages To convert a decimal into a percentage, multiply by 100, as shown: 0.375 × 100 = 37.5%
Table 1.3 Decimal and fraction equivalents.
Chapter 1 A. Basic Shop Math
Adding and Subtracting Decimals
To add or subtract decimals, line up the numbers at their decimal places. For example, the numbers 3.475, 11.55, and 2.2 can be added as shown:
Multiplying and Dividing Decimals To multiply or divide decimals, count the total number of decimal places in the problem. The final answer will have that number of decimal places. 3.75
2 decimal places
1 decimal place
8.625 3 decimal places
Squares and Square Roots The square of a number is simply that number multiplied by itself. The square of a number can also be written as that number to the second power. For example, the square of 7 is calculated as 7 # 7 = 7 2 = 49 A square root is denoted as follows: 25 = 25 1/2 = 5, since 25 = ^5 # 5h = 5 2 Every positive number has a square root. For example, using a calculator, we can determine that 54 . 3 = 7 . 369
Imaginary Numbers The square root of a negative number does not exist on the real number line. Rather, the imaginary number i is defined as the square root of negative one. The result is written in terms of i. For example, - 25 = - 1 * 25 = - 1 ) 25 = 5i
Section I Technical Mathematics
Exponents A whole number exponent indicates how many times a number is multiplied by itself. For example: 7 # 7 = 72 7 # 7 # 7 = 73
Order of Operations The order of operations can be remembered by using the mnemonic device of PEMDAS, or Please Excuse My Dear Aunt Sally, which stands for parentheses, exponents, multiplication, division, addition, and subtraction. As an illustration, the expression 6 # 4 + ^9 - 1h ' 2 - 5 2 is correctly evaluated as follows: 6 # 4 + ^9 - 1h ' 2 - 5 2 = 6 # 4 + 8 ' 2 - 5 2 P
= 6 # 4 + 8 ' 2 - 25 E = 24 + 8 ' 2 - 25
Factorials A factorial is a mathematical operation denoted by an exclamation point (!), and is evaluated in the following manner: 5! = 5 × 4 × 3 × 2 × 1 By definition, 0! = 1. Factorials are used when calculating probabilities from the binomial, hypergeometric, and Poisson distributions, among others.
Truncating, Rounding, and Significant Digits To display a result with a certain number of decimal places, we can choose to truncate the number. For example, we can truncate the number 3.527 to two decimal places by writing 3.52. We can round a result to a certain number of digits by looking at the value of the digit to the right of the decimal place of interest. For example, if we want to round the number 3.527 to the hundredths place, we will look at the third decimal place (in this case 7) as our decision point. The rule for rounding is this: If the decision
Chapter 1 A. Basic Shop Math
number is less than 5, do not round up. If it is 5 or greater, round up. Therefore, 3.527 would be rounded up to 3.53. However, if we rounded to the tenths place, 3.527 would be displayed as 3.5, since 2 would be our decision number. When dealing with the precision of a measurement, we must consider significant digits. For example, instrument measurements have a certain inherent precision, which can be expressed in terms of a certain number of significant digits. We must take care to express instrument measurements using the proper number of significant digits.
Adding and Subtracting Measurements When adding or subtracting measurements, the final answer will only be as precise as the least precise reading. Therefore, the number of decimal places of the answer should match that of the least precise reading. In the following example, the reading of 5.2 is the least precise, and the final answer is rounded to the tenths place: 4 . 573 3 . 77 5.2 + 6.1299 19 . 6729 , 19 . 7
Multiplying and Dividing Using Significant Digits When multiplying measurements, display the final result with the same number of significant digits as the least accurate reading. For example, the following result will be rounded to three significant digits since the value 3.21 has three significant digits and 20.45 has four: 20 . 45 # 3 . 21 65.6445 , 65 . 6
Bibliography Achatz, Thomas. 2006. Technical Shop Mathematics. 3rd ed. New York: Industrial Press. Griffith, Gary. 1986. Quality Technician’s Handbook. Englewood Cliffs, NJ: Prentice Hall. Horton, Holbrook L. 1999. Mathematics at Work. 4th ed. New York: Industrial Press.
ASQ/ANSI/ISO 19011:2011 standard, 309, 310–11 assignable causes. See special causes attribute charts, 275–93 attribute gauges, 63–69 attribute sampling plans, 151–54 auditees, 309, 311 auditors, 309, 311 audits, quality, 308–15 autocollimation, 101 automatic gauging, 73–77 Automotive Industry Action Group (AIAG), 120 autoreflection, 101 average outgoing quality (AOQ), 152–53 average outgoing quality limit (AOQL), 153 average run length (ARL), 260–61
acceptance number, 153 acceptance quality limit (AQL), 152 acceptance sampling, 149–52 by attributes, 152 accuracy, 84, 101, 123 actions local, 264–65 on output, 263 on the process, 263 acute angles, 27 air gauges, 56, 57 air match gauging, 79 algebraic equations, solving, 12–16 algebraic inequalities, 16–18 American Automotive Industry Group (AAIG), 301 American National Standards Institute (ANSI), 351 American Society for Testing and Materials (ASTM), 95, 351 angle blocks, 92 angle measurement, 90–92 angles, 26, 28, 30–38 ANOVA method of measurement, 124–33 ANSI/ASME B46.1-1985, 97 ANSI/ASQ Z1.4-2003 standard, sample tables, 424–29 (Appendix H) ANSI/ASQ Z1.4-2008 standard, 152, 154–57 ANSI/ASQ Z1.9-2003 standard, sample tables, 430–41 (Appendix H) area, measurement of, 19–21, 41, 44, 47 AS 9100 standards, 351 ASQ Certified Biomedical Auditors, 308 ASQ Certified HACCP Auditors, 308 ASQ Certified Quality Auditors, 308 ASQ Quality Inspector Certification, 308, 360–66 (Appendix A)
B back-pressure gauges, 77 balances, 95 bar charts, 213–15 bevel protractors, 92 bivariate data, 217–19 Bloom’s Taxonomy, 352, 366–67 (Appendix A) blueprints, 137–45 bonus tolerance, 145 box plots, 237–41 box-whisker plots, 237–41 brainstorming, 254 Brinell hardness test, 191–92
C c charts, 286–89 calibration, 112–18 documentation and history, 114 procedures, 115
446 Index standards, 116–17 systems, 113–16 work orders, 114 calibration environment, 118 specifications, 115 calibration interval, 113–14 caliper digital-reading, 58–59 micrometer, 60–61 vernier, 57–59 cause-and-effect diagrams, 253–55, 316 Celsius temperature, 49, 50 centrality measures, 223–29 Certified Quality Inspector Body of Knowledge (CQI BoK), 352, 360–66 (Appendix A) champion, team, 354 charge coupled device (CCD) cameras, 105 check sheets, 252–53, 317 checklists, audit, 312 circumference, 21–23 combination protractor/depth gauge, 92 common causes, 262–63 complementary angles, 26, 27 compression testing, 190–91 computer resources, 368–97 (Appendix B) confined spaces, 350 conflict resolution, 355–56 conforming products, 275 consensus, 356 consumer’s risk, 152 continuous sampling plans, 158–60 control charts, 257–60, 275–93 for attributes, 275–93 function of, 258, 316 for variables, 265–75, 418–19 (Appendix E) control limits calculation of, 266–70 for np control charts, 284–85 for p charts, 277–79 conversions, measurement, 398–415 (Appendix C) coordinate measuring machines (CMMs), 107–110 corrective action, 18, 174–75 corrective action requests (CARs), 313, 314, 315 Cp process capability index, 295–300 Cpk process capability index, 300–301 critical defect, under ANSI/ASQ Z1.4-2008, 154 criticality assessment, 343
crossed designs, in measurement system analysis, 127, 131, 132, 133 customer satisfaction, 305
D datum structure, 147 decimal-fraction equivalents, 7, 8 defect concentration diagrams, 255–56 defects severity level of, 172–73 standard repair for, 176 degrees, angle, 28, 30, 90 Deming, W. Edwards, 250, 251, 257, 264, 319 Department of the Navy, 327 depth rule, 79 design and process FMEA, 333–45 destructive testing, 186–89 detection, prevention vs., 304–5 dial indicators, 80, 88–90, 98 diascopic projection, 103 differential gauges, 77 digital micrometers, 61, 62, 80 digital reading caliper, 58–59, 79 digital vision systems, 105–6 dispersion, measures of, 229–34 DMAIC methodology, 326 dot plots, 211–12 double sampling plans, 154 double-end gauges, 64, 68 drift, 84 dye penetrant inspection, 185
E eddy current, 182–83 electric limit gauges, 71 electron beam, 57 electronic gauges, 56, 57, 71–73 empirical rule, 232 employee involvement, 353–54 employees as resources, 353–57 empowerment, employee, 353 engineering drawings, 137–45 parts of, 137–41 terminology and symbols in, 142–45 English measurement system, 39–42 conversion to SI/metric system, 46–50 environment, gauge calibration, 118 environmental resources, 349–50 episcopic projection, 103 equations. See algebraic equations equipment, measurement of, 167, 168
Index 447 equipment traceability, 117 ergonomics, 350 error-proofing, 322–23 errors inspection, 166–67 prevention vs. detection of, 304–5 random, 166 systematic, 166 exponents, 10, 51, 52 external measuring snap gauge, 66 external quality audit, 309 extreme values, 227
F facilitator, team, 354 factorials, 10–11 Fahrenheit temperature, 49, 50 failure mode and effects analysis (FMEA) assessing criticality in, 343 basic steps in, 330–31 design and process, 333–45 explanation of, 327–28 inputs/outputs, 329–30 risk and, 331–32 standard selection for, 327 team members for, 328–29 failure mode effects and criticality analysis (FMECA), 434 final inspection, 165–66 finish. See surface finish FireWire, 106 first-piece inspection, 165 fishbone diagrams, 253–55, 316 5S concept, 321–22 fixed gauges, 64 flaws, 96 flinching, 167 flow gauges, 77 flowcharts inspection, 163, 164 of process, 251, 252 quality control, 316 with value stream mapping, 323 force testing, 186–88 fractions, 3–7 converted to decimals, 7–8, 52–53 equivalent, 4, 6 frame grabbers, 106 free-bend test, 186–87 frequency distribution curves, 223 frequency distribution tables, 206–11 frequency histograms, 219
frequency polygon, 222 functional testing, in software development, 197 functionality testing, 189–91
G gauge blocks, 62–63, 80 gauge calibration environment, 118 gauge correlation, 86 gauge maker’s rule, 83–84 gauge repeatability and reproducibility (gauge R&R), 120–21. See also measurement system analysis (MSA) gauge repeatability and reproducibility study (GR&R study) ANOVA method, 127–30 graphical representation of, 130–33 gauges applications of, 79–81 attribute, 63–69 electronic, 56, 57, 72–73 handling, preservation, and storage of, 84–86 performance criteria for, 84 pneumatic, 77–79 selection of, 83–84 sensing technologies and, 56–57 skid or skidless, 99 transfer, 69 variable, 57–63 geometric dimensioning and tolerancing (GD&T), 136 geometry review area, 19–21 complementary and supplementary angles, 26 perimeter and circumference, 21–23 surface area, 25–26 volume, 23–25 glossaries, 442–43 Godfrey, B., 306 go/no-go gauges, 63–64, 275 graphical displays, 206–23 Gryna, Frank M., 169, 296, 306 guided bend test, 187
H hardness testing explanation of, 188–89 methods of, 191–94 hearing, conservation, 350
448 Index helium, 74 hierarchical designs, in measurement system analysis, 127 histograms, 219–23, 317
I identification mechanics of, 171–72 principles of, 171 product, 169 imaginary numbers, 10 impact test, 188 improper fractions, 4 incoming material inspection, 163–64 indicating micrometer, 62 inductance-bridge transducers, 71 inequalities, solving, 16–18 in-process inspection, 165 inspection explanation of, 161 final, 165–66 incoming material, 163–64 in-process, 165 planning for, 162–63 tasks involved in, 161–62 testing vs., 197 inspection equipment coordinate measuring machine, 107–10 digital vision systems, 105–6 to measure finish, 98–100 to measure mass, 94–98 to measure shape and profile, 98–100 optical, 100–105 inspection errors, 166–67 inspection gauges, 63, 80 inspection levels, under ANSI/ASQ Z1.4-2008, 155 inspection microscopes, 101 inspection stations, 162–63 inspector qualifications, 168 inspector training, 168–69, 173 interested party, 309 interferometers, 74–76 interferometry, 73–76, 98 internal quality audit, 309 international calibration standards, 116 International Organization of Legal Metrology (OIML), 95–96 International Organization for Standardization (ISO), 96, 351 interquartile range (IQR), 236–37
inverse operations, 12–14 inverse trigonometric functions, 32–33 irrational numbers, 9 Ishikawa diagrams, 253–55, 316 ISO 80000-4 (2006), 95 ISO/IEC 17025, 86 ISO/IEC 80000, 95 ISO 9000 standard, 169, 173, 351 section 7.6, 84–85 section 8.2.4, 85–86 ISO/TS 16949 standard, 169
J Juran, J. M., 296, 306
K K1 values for computing repeatability, 420–21 (Appendix F) K2 values for computing reproducibility, 422 (Appendix G) kaizen, 324 kg m/sec2, 95 kilogram, 94–95
L laser inspection instruments, 101 law of cosines, 34 law of sines, 33–34 lay, 96 lean production, 320–24 least common denominator, 5, 6 least material condition (LMC), 145 Lennox Industries, 172 leveling, 102 levels of cognition (Bloom’s Taxonomy), 366–67 (Appendix A) levels of inspection, under ANSI/ ASQ Z1.4-2008, 155 light waves, 56, 74, 75 limit gauges, 63–64, 80 linear variable displacement transformer (LVDT) transducer, 71 linearity, 84, 123 liquid penetrant testing, 185 lock-out/tag-out, 350 log sheets, 312–13 lot size, 153 lot tolerance percent defective (LTPD), 152
M machine vision, 76–77, 81 machine vision systems, 105–6 magnetic particle inspection, 184–85 magnification, 84 major defect, under ANSI/ASQ Z1.4-2008, 154 mass, measurement of, 45, 48, 94–98 master gauges, 63, 80 material, identification of nonconforming, 171–72 material control, 118 material review board (MRB), 176–77 material safety data sheets (MSDSs), 349 material segregation, 176 mathematics review algebra, 12–18 basic shop math, 2–11 geometry, 19–26 trigonometry, 27–38 mean, 224–25, 227, 229, 231 measurement capability index (MCI) explanation of, 122, 124 as percentage of process specification, 134 as percentage of process variation, 133–34 measurement conversions, 51–54 tables of units of measurement, 398–415 (Appendix C) measurement scales, 69–70 measurement system analysis (MSA), 120–21, 127–33 measurement systems English, 39–42 metric, 42–46 SI, 42–46 Measurement Systems Analysis Reference Manual (AIAG), 120, 122 measures of centrality, 223–29 measures of percentages, 223, 234–37 mechanical gauges, 56, 57 median, 225–27, 229 meeting management, 356–57 metallography, 189 metric measurement system, 42–46 conversion to English system, 46–50 metrology, surface, 96 microhardness testing, 194 microinches, 97 micrometer calipers digital, 61, 62 vernier, 61
micrometers, screw-thread, 68–69 microscopes, inspection, 101 Military Handbooks (MIL-HDBKs), 351 MIL-STD military standards, 351 1235B, 159–60 629A, 327, 343, 346 MINITAB, 129–30, 368–96 minor defect, under ANSI/ASQ Z1.4-2008, 155 mode, 228–29 multidimension gauges, 79 multimeters, 73, 81 multiple sampling plans, 154
N nanometers, 97 National Institute for Standards and Technology (NIST), 95, 116, 117 National Materials Advisory Board (NMAB), 180 negative exponents, 52 negative numbers, 2, 3, 17–18 nested designs, in measurement system analysis, 127 nick-break test, 188 nonconforming materials, 173–77, 275 nonconforming units control chart for fraction of, 276–77 nonconformities vs., 286–89 nonconformities explanation of, 172 vs. nonconforming unit, 286–89 u chart and, 290–93 noncontact instruments, 57 nondestructive testing (NDT), 179–85 nonlimit gauges, 63 normal density function, 242–44 normal distribution, 241–49 normal probability distribution, 241 np charts, 284–85 numbers imaginary, 10 positive and negative, 2–3, 17–18 real, 2, 12, 13
O oblique triangles, 33–38 obtuse angles, 27 Occupational Safety and Health Administration (OSHA), 349–50
450 Index Ohno, Taiichi, 321 100% inspection, 150 operating characteristic (OC) curve, 151, 261–62 operator fallibility, 167, 168 optical comparators, 80, 100–101, 103–5 optical edge finders, 101 optical flats, 74, 75, 76, 81 optical inspection instruments, 100–105 optical projecting comparators, 103 optical tooling, 101–3 order of operations, 10 orthographic views, 142 oscilloscopes, 73, 80 OSHA Code of Federal Regulations (CFR) Title #29, 349–50 out-of-calibration equipment, 118
P p charts control limits for, 277–79 for fraction nonconforming with variable samples, 281–84 for fraction of nonconforming units, 276–77 parentheses, solving equations with, 15–16 Pareto, Vilfredo, 215 Pareto charts, 215–17, 316 part alignment, 147 Pearson correlation coefficient, 218 percentages, 9, 223, 234–37 percentiles, 235–36 perimeter, 21–23 personal computers, in machine vision systems, 106 personal protective equipment (PPE), 349 pie charts, 212, 213 Plan-Do-Check-Act (PDCA) cycle, 318–20 Plan-Do-Study-Act (PDSA) cycle, 318, 319 planizing, 102 plug gauges, 64, 80 plumbing, in optical tooling, 102 pneumatic gauges, 56, 77, 78, 79, 81 population mean, 224, 225, 231 position control, tolerance of, 145 positive numbers, 2, 3 powers of 10, 52 Pp process capability index, 301–2 Ppk process capability index, 301–2 precision, 122–23 prevention, detection vs., 304–5 preventive action, 175
primary calibration standards, 117 prime factorization, 5 prime numbers, 5, 6 problem-solving tools failure mode and effects analysis, 327–46 lean production, 320–24 Plan-Do-Check-Act cycle, 318–20 root cause analysis, 326–28 Six Sigma, 325–26 process action on, 263 explanation of, 251, 306 flowchart of, 252 interrelatedness of product and, 307 process audits, 310 process capability analysis, 293–94 process capability index (PCI), 293, 295–302 process equipment, 114 process evaluation, 263 process FMEA. See design and process FMEA process variability, 121 producer’s risk, 152 product identification, 169 product traceability, 169–71 product/service audits, 310 profile, 96, 100 progressive gauges, 64 progressive plug gauges, 64 protractors, 92 pyrometers, 73, 81 Pythagorean theorem, 28, 30
Q QS 9000 standards, 351 qualitative data, frequency distribution table for, 207–9 quality. See also statistical process control (SPC) components of, 305 concept of, 250–51 cost of poor, 306 definition of, 250, 325 statistical process control and, 250–51, 275 quality assurance, 176 quality audits, 308–15 quality control tools, 316–17 quality improvement, 304–7 Quality Systems (QS), 351 quantitative data, frequency distribution table for, 209–11 quartiles, 236
R radiation method of nondestructive testing, 180–82 random causes. See common causes random errors, 166 range, 230 range-based method, of measurement system analysis, 122–27, 420–21 (Appendix F), 422 (Appendix G) rational numbers, 9 rational subgroups, for control charts, 259–60 real numbers, 2, 12, 13 rectifying sampling, 150 reference calibration standards, 117 reference documents, 350–51 reference gauges, 63, 80 relative frequency histograms, 219 relative frequency polygon, 222 repeatability, 84, 122–23 k1 values for computing, 420–21 (Appendix F) reproducibility, 123, 124, 125 k2 values for computing, 422 (Appendix G) resolution, 84 resources computer, 368–97 (Appendix B) employees as, 353–57 environmental and safety, 349–50 reference documents, 350–51 technical reports, 352 right triangles, 27, 28, 30–32 ring gauges, 64–66, 80 Rockwell hardness test, 192–93 root cause analysis (RCA), 326–27 roughness, 96–100 rounding numbers, 11 roundness measurement, 100 rule of ten, 83–84 run, 260 run charts, 256–57
S safety resources, 349–50 sample mean, 224, 225 sample size, 153, 224 sample standard deviation, 231 sample statistics, 266 sample variance, 231 sampling advantages of, 150–51 ANSI/ASQ Z1.4-2008 standard for, 152, 154–56
concepts related to, 151–53 function of, 149–50 sampling plans, 151, 156–60, 313 Sauer Danfoss Company, 171 scatter plots, 217–19, 317 scientific method, 325 scientific notation, 52–54 screening, 150 screw pitch gauges, 69, 80 screw thread micrometers, 68–69, 80 secondary calibration standards, 117 sensitivity, 84 sequential sampling plans, 157–58 serious defect, 172–73 shape measurements, 100 Shewhart, Walter A., 250, 318 Shewhart control charts, 260 – Shewhart X and R control charts explanation of, 265–66 interpretation of, 270–71 when process mean and process standard deviation are known, 271–72 – Shewhart X and S control charts control limits in, 273–74 explanation of, 272–73 shop math, 3–11 SI measurement system, 42–46, 94–95 conversions to English system, 46–50 significant digits, 11 simple protractors, 92 simplified fractions, 4 sine bar, 91 sine tables, 91 single sampling plans, 153–54 single-valued frequency distribution table, 208 Six Sigma, 325–26 skew, of data set, 229 snap gauges, 64, 66–68, 80 Society of Automotive Engineers, 327 software in machine vision systems, 106 verification of, 196–97 software testing, 196–203 special causes, 262–65 spline gauges, 68, 80 square, of number, 2 square root, 9 stability, 84, 123 standard deviation, 231, 232, 242 standard normal distribution, 243 standard normal distribution table, 244–47, 416–18 (Appendix D) standard normal random variable, 242
452 Index standard repair, 176 standardize, 322 statistical process control (SPC). See also quality average run length and, 260–61 cause-and-effect diagrams, 253–55 check sheets, 252–53 control charts, 257–60, 275–93 defect concentration diagrams, 255–56 explanation of, 98, 250 operating characteristic curve and, 261–62 process and, 251–52 process capability analysis for, 293–302 quality and, 250–51, 275 run charts for, 256–57 tools of, 251–52 variation and, 262–65 Statistical Quality Control Handbook (Western Electric), 270 steel rules, 57, 79 Sturgis’s formula, 209 supplementary angles, 26 surface area, of geometric shapes, 25–26 surface finish measurement of, 98–100 standards to define, 96 surface measurement, 96 surface metrology, 96–98 surface plate equipment, 88–90 explanation of, 88, 89 surface quality specifications, 96–98 sustain, 322 switching procedures, in sampling, 155 symbols, on drawings, 142–45 system audits, 310 systematic errors, 166
T teams, 354–55 technical reports, 352 temperature conversions, 49–50 templates, 69, 80 10:1 rule, 83–84 tensile testing, 186, 187 tension testing, 186, 187, 189 testing destructive, 186–89 functional, 197 functionality, 189–91 hardness, 191–94 inspection vs., 197
nondestructive, 179–85 software, 196–203 third-party audit, 309 thread plug gauges, 68–69 thread snap gauges, 67–68 tolerance of position control, 145 tolerances, 145, 146 torque testing, 189–90 traceability equipment, 117 explanation of, 117, 169, 203 product, 169–71 tracing code, 170 training, inspector, 168–69, 173 transfer calibration standards, 117 transfer gauges, 69 transit, 102 triangles, 27–28, 30–38 trigonometric functions, 29–33 inverse, 32–33 trigonometric identities, 30 trigonometry review, 27–38 truncating numbers, 11 two-way ANOVA table with interaction, 127–28 without interaction, 128–30 Type I errors acceptance sampling plans and, 152 out-of-calibration equipment and, 118 Type II errors acceptance sampling plans and, 152 out-of-calibration equipment and, 118
U u charts, 289–93 ultrasonic testing, 183–84 units of measurement tables, 398–415 (Appendix C) Universal Serial Bus and FireWire (IEEE 1394), 106 U.S. Department of Defense (DoD), 351
V value stream mapping, 323–24 variability, in measurement process, 121, 124 variable gauges, 57–63 variable inductance transducers, 71 variable transformer transducers, 71 variables charts, 418–19 (Appendix E) variables sampling plans, 156–57 variance, 230–31
Index 453 variation, 263 vendor certification/qualification, 150 venturi gauges, 79 vernier calipers, 57–59, 61, 79 vernier height gauges, 59, 80, 90 Vickers hardness test, 193–94 visual method of nondestructive testing, 180, 181 volume, of geometric shapes, 23–25
W waviness, 96, 98–100 weight, and mass, 94–95 weighted mean, 227 working calibration standards, 117 working gauges, 63, 80 working papers, 313–14 wringing, 63
– X control charts, 260, 262. See also Shewhart – – X and R control charts; Shewhart X and S control charts X-rays inspection, 77, 180–82 nondestructive testing, 81
Y Y14.3-2008 Multiview and Sectional View Drawings standard, 142
