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STATISTICS: Textbooks and Monographs D. B. Owen Founding Editor, 1972–1991 Editors N. Balakrishnan Edward G. Schilling McMaster University Rochester Institute of Technology William R. Schucany Southern Methodist University Editorial Board Thomas B. Barker Nicholas Jewell Rochester Institute of Technology University of California, Berkeley Paul R. Garvey Sastry G. Pantula The MITRE Corporation North Carolina State University Subir Ghosh University of California, Riverside Daryl S. Paulson Biosciences Laboratories, Inc. David E. A. Giles University of Victoria Aman Ullah University of California, Arjun K. Gupta Riverside Bowling Green State University Brian E. White The MITRE Corporation ß 2008 by Taylor & Francis Group, LLC.
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STATISTICS: Textbooks and Monographs Recent Titles Visualizing Statistical Models and Concepts, R. W. Farebrother and Michaël Schyns Financial and Actuarial Statistics: An Introduction, Dale S. Borowiak Nonparametric Statistical Inference, Fourth Edition, Revised and Expanded, Jean Dickinson Gibbons and Subhabrata Chakraborti Computer-Aided Econometrics, edited by David E.A. Giles The EM Algorithm and Related Statistical Models, edited by Michiko Watanabe and Kazunori Yamaguchi Multivariate Statistical Analysis, Second Edition, Revised and Expanded, Narayan C. Giri Computational Methods in Statistics and Econometrics, Hisashi Tanizaki Applied Sequential Methodologies: Real-World Examples with Data Analysis, edited by Nitis Mukhopadhyay, Sujay Datta, and Saibal Chattopadhyay Handbook of Beta Distribution and Its Applications, edited by Arjun K. Gupta and Saralees Nadarajah Item Response Theory: Parameter Estimation Techniques, Second Edition, edited by Frank B. Baker and Seock-Ho Kim Statistical Methods in Computer Security, edited by William W. S. Chen Elementary Statistical Quality Control, Second Edition, John T. Burr Data Analysis of Asymmetric Structures, Takayuki Saito and Hiroshi Yadohisa Mathematical Statistics with Applications, Asha Seth Kapadia, Wenyaw Chan, and Lemuel Moyé Advances on Models, Characterizations and Applications, N. Balakrishnan, I. G. Bairamov, and O. L. Gebizlioglu Survey Sampling: Theory and Methods, Second Edition, Arijit Chaudhuri and Horst Stenger Statistical Design of Experiments with Engineering Applications, Kamel Rekab and Muzaffar Shaikh Quality by Experimental Design, Third Edition, Thomas B. Barker Handbook of Parallel Computing and Statistics, Erricos John Kontoghiorghes Statistical Inference Based on Divergence Measures, Leandro Pardo A Kalman Filter Primer, Randy Eubank Introductory Statistical Inference, Nitis Mukhopadhyay Handbook of Statistical Distributions with Applications, K. Krishnamoorthy A Course on Queueing Models, Joti Lal Jain, Sri Gopal Mohanty, and Walter Böhm Univariate and Multivariate General Linear Models: Theory and Applications with SAS, Second Edition, Kevin Kim and Neil Timm Randomization Tests, Fourth Edition, Eugene S. Edgington and Patrick Onghena Design and Analysis of Experiments: Classical and Regression Approaches with SAS, Leonard C. Onyiah Analytical Methods for Risk Management: A Systems Engineering Perspective, Paul R. Garvey Confidence Intervals in Generalized Regression Models, Esa Uusipaikka Introduction to Spatial Econometrics, James LeSage and R. Kelley Pace Acceptance Sampling in Quality Control, Edward G. Schilling and Dean V. Neubauer ß 2008 by Taylor & Francis Group, LLC.
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Acceptance Sampling in Quality Control Second Edition Edward G. Schilling Rochester Institute of Technology Rochester, New York, U.S.A. Dean V. Neubauer Corning Incorporated Horseheads, New York, U.S.A. ß 2008 by Taylor & Francis Group, LLC.
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Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2009 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-58488-952-6 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For orga- nizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Schilling, Edward G., 1931- Acceptance sampling in quality control / Edward G. Schilling, Dean V. Neubauer. -- 2nd ed. p. cm. -- (Statistics : textbooks and monographs) Includes bibliographical references and index. ISBN 978-1-58488-952-6 (hardcover : alk. paper) 1. Acceptance sampling. I. Neubauer, Dean V. II. Title. III. Series. TS156.4.S34 2009 658.5’62--dc22 2008050948 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com ß 2008 by Taylor & Francis Group, LLC.
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Dedication This text is dedicated to the memory of Dr. Edward G. Schilling 1931–2008 and To Jean and Kimberly ß 2008 by Taylor & Francis Group, LLC.
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Tribute to Dr. Edward G. Schilling Before this text went into publication, Dr. Edward G. Schilling (Ed), the book’s principal author, passed away. He left behind many dear friends and loved ones, but also a legacy in the field of acceptance sampling. Dr. Harold F. Dodge, one of Ed’s professors at Rutgers, is known as the father of acceptance sampling due to his pioneering work in the field. Dr. Dodge mentored his young protégé and wrote papers with him on acceptance sampling while Ed was at Rutgers. Little did Dr. Dodge know that Ed would become a pioneer and mentor himself in shaping what the world now knows today as modern acceptance sampling. This book is a testimony to not only the work of Dodge, Romig, and others, but also to a larger extent the work done by Dr. Schilling and others to shape the field and extend it in ways that the early pioneers had perhaps envisioned but did not pursue. Ed’s work does not lie entirely in the statistical literature, but rather he also played an integral role in the development of acceptance sampling standards with the Department of Defense, ISO TC 69, ANSI=ASQ, and ASTM. For this body of work, Dr. Edward G. Schilling should be known as the father of modern acceptance sampling. As a former student, a colleague at RIT and on the ISO TC 69 and ASTM E11 Committees, and co-author with Ed on two books, I feel that I have lost a very dear friend. Of course, I can’t feel the loss that his family does losing a wonderful husband and father, but I feel honored to have known such a great man. Dean V. Neubauer ß 2008 by Taylor & Francis Group, LLC.
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O Fortune, variable as the moon, always dost thou wax and wane. Detestable life, first dost thou mistreat us and then, whimsically, thou heedest our desires. As the sun melts the ice, so dost thou dissolve both poverty and power. — Carl Orff, Carmina Burana ß 2008 by Taylor & Francis Group, LLC.
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Contents List of Tables Preface to This Edition Note from the Series Editor for the First Edition Foreword to the First Edition Preface to the First Edition Acknowledgments from the First Edition Authors 1 Introduction Acceptance Quality Control Acceptance Control and Process Control Process Quality Control Background of Acceptance Quality Control Top 10 Reasons for Acceptance Sampling References Problems 2 Probability and the Operating Characteristic Curve Probability Classical Definition Empirical Definition Subjective Definition Random Samples and Random Numbers Counting Possibilities Probability Calculus Operating Characteristic Curve References Problems 3 Probability Functions Probability Distributions Measures of Distribution Functions Hypergeometric Distribution Binomial Distribution Poisson Distribution f-Binomial Distribution Negative Binomial Distribution Exponential and Continuous Distributions Weibull Distribution Normal Distribution Summary of Distributions ß 2008 by Taylor & Francis Group, LLC.
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Tables of Distributions Hypergeometric Tables Binomial Tables Poisson Tables Negative Binomial Tables Exponential and Weibull Tables Normal Distribution Tables Summary Useful Approximations Tests of Fit References Problems 4 Concepts and Terminology Average Run Length of Type B Plans Sample Size and Lot Size Effect of Inspection Error Rectification Curtailment Tolerance and Confidence Intervals Levels and Risks Choosing Quality Levels Classification of Defects Measures of Sampling Plans: Terminology Graphs of Measures Specifying a Plan References Problems 5 Single Sampling by Attributes Operation Selection Tables of Poisson Unity Values Binomial Nomograph f-Binomial Nomograph Thorndyke Chart Hypergeometric Tables Measures References Problems 6 Double and Multiple Sampling by Attributes Operation Double Sampling Multiple Sampling Selection Measures Double Sampling Multiple Sampling Further Considerations References Problems ß 2008 by Taylor & Francis Group, LLC.
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7 Sequential Sampling by Attributes Operation Selection Measures Sequential Sampling for Defects per Unit References Problems 8 Variables Sampling for Process Parameter Single Sampling for Process Parameter Acceptance Control Charts Sequential Plans for Process Parameter (s Known) Sequential Plans for Process Parameter (s Unknown) Cumulative Sum Charts References Problems 9 Bulk Sampling Construction of the Sample Estimation Sampling Plans Simple Random Sampling of a Unique Lot (Components of Variance Unknown) Sampling from Stream of Lots Estimation of Testing and Reduction Variances Estimation of Segment and Increment Variances Application of Plan to Stream of Lots References Problems 10 Sampling by Variables for Proportion Nonconforming Specification Limits Assumptions and Theory Operation X Method k Method Double Specification Limits Selection Tables Formulas Jacobson Nomograph for Plan Selection Measures Jacobson Nomograph for Operating Characteristics Calculation: s Known Calculation: s Unknown Double Specification Limits Measures of Performance M Method Plans Based on Sample Range Double Sampling by Variables Tolerance Intervals and Variables Plans for Percent Nonconforming Sequential Plans for Proportion Nonconforming ß 2008 by Taylor & Francis Group, LLC.
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Further Considerations Derivation of n, k Formulas Need for Normality References Problems 11 Attributes Sampling Schemes Sampling Schemes Quick Switching Systems TNT Plans MIL-STD-105E and Derivative Standards Operation Selection Measures Scheme Properties Implementation of MIL-STD-105E Matching Individual Sampling Plans to MIL-STD-105E System Performance MIL-STD-105 Derivatives Further Considerations References Problems 12 Variables Sampling Schemes MIL-STD-414 Operation Selection Measures Implementation of Form 2 Implementation of Form 1 Implementation of Plans for Range and Variability Known Match between MIL-STD-414 and MIL-STD-105E Conversion of MIL-STD-414 to ANSI=ASQ Z1.9 MIL-STD-414 Derivatives ANSI=ASQ Z1.9 ISO 3951-1 Further Considerations References Problems 13 Special Plans and Procedures No-Calc Plans Lot Plot Plans Narrow-Limit Gauging Mixed Variables—Attributes Plan Advantages and Disadvantages of Mixed Plans Generalized Mixed Dependent Procedure Measures: Independent Mixed Plan Measures: Dependent Mixed Plan MIL-STD-414 Dependent Mixed Plans Comparison of Independent and Dependent Mixed Plans Comparison of Mixed with Other Type Plans ß 2008 by Taylor & Francis Group, LLC.
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References Problems 14 Series of Lots: Rectification Schemes Single-Sampling AOQL Plan Dodge–Romig Sampling Scheme Operation Selection Measures Further Considerations Constructing LTPD Plan with Minimum ATI Constructing AOQL Plan with Minimum ATI Anscombe Rectifying Inspection Procedure Operation Selection Measures Credit-Based Shemes References Problems 15 Continuous Sampling Plans Dodge Continuous Plans Dodge CSP-1 Dodge–Torrey CSP-2 and CSP-3 Measures of CSP-1, 2, and 3 Stopping Rules and Selection of CSP-1 Plans Multilevel Plans Tightened Multilevel Plans Block Continuous Plans Wald–Wolfowitz Plan Girshick Plan MIL-STD-1235B References Problems 16 Cumulative Results Plans Skip-Lot Sampling Plans SkSP-1 SkSP-2 Chain Sampling Plans ChSP-1 Two-Stage Plans Deferred Sentencing Schemes Demerit Rating Plan CRC Plan References Problems 17 Compliance Sampling LSP Procedure Protection ß 2008 by Taylor & Francis Group, LLC.
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Producer’s Risk Examples of LSP Applications Further Considerations TNT Scheme Procedure Protection Selection Quick Switching System (QSS) MIL-STD-1916 Structure Operation Implementation Measures Further Considerations Simplified Grand Lot Procedure Simon’s Approach Simplified Procedure: Attributes Example: Attributes Simplified Procedure: Variables Continuing Series of Lots Further Considerations Nomograph for Samples Having Zero Defectives Accept on Zero (AOZ) Plans U.S. Department of Defense Approach Squeglia Plans AOZ and AQL Plans Chain Sampling Alternative Summary References Problems 18 Reliability Sampling Censored Sampling Variables Plans for Life Testing and Reliability Handbook H-108 Operation Failure Terminated Time Terminated Sequential Proportion Failing by Specified Time Selection Example of H-108 Application Failure Terminated Time Terminated Sequential Proportion of Lot Failing by Specified Time Measures Further Considerations Technical Report TR7 Mean Life Criterion Hazard Rate Criterion ß 2008 by Taylor & Francis Group, LLC.
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Reliable Life Criterion TR7 Tables Operation TR7 with the MIL-STD-105E System Further Considerations References Problems 19 Administration of Acceptance Sampling Selection and Implementation of a Sampling Procedure Determining Quality Levels. Setting AQL Setting AOQL Setting IQ Setting LTPD (or LQ) Relation of Levels Setting PQL and CQL Economic Considerations Mandatory Standards Computer Programs Basic Principle of Administration References Problems Appendix Answers to Problems ß 2008 by Taylor & Francis Group, LLC.
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