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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 Badiru, Adedeji Bodunde, 1952- Handbook of industrial engineering equations, formulas, and calculations / authors, Adedeji B. Badiru, Olufemi A. Omitaomu. p. cm. -- (Industrial innovation series) “A CRC title.” Includes bibliographical references and index. ISBN 978-1-4200-7627-1 (hardcover : alk. paper) 1. Industrial engineering--Mathematics--Handbooks, manuals, etc. 2. Engineering mathematics--Handbooks, manuals, etc. I. Omitaomu, Olufemi Abayomi. II. Title. III. Series. T57.B33 2011 620.001’51--dc22 2010028413 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To our families for their unflinching support of our intellectual pursuits. Contents Preface .................................................................xxix Authors ................................................................xxxi 1 Computational Foundations of Industrial Engineering Efficacy of Mathematical Modeling ...............................................................................1-1 Industrial Engineering and Computations....................................................................1-1 Definition and Applications ...........................................................................................1-5 Orientation to STEM.......................................................................................................1-6 IE Catchphrases ...............................................................................................................1-6 Span and Utility of IE......................................................................................................1-6 Heritage from Industrial Revolution..............................................................................1-7 Historical Accounts.........................................................................................................1-8 Chronology of Applications..........................................................................................1-10 Importance of IE Calculations ..............................................................................1-14 Importance of Calculations Guide ...............................................................................1-16 Basic Queuing Equations ..............................................................................................1-17 Queuing Birth–Death Processes...................................................................................1-21 Laws of Motion of Queuing Birth and Death..............................................................1-21 Queuing Birth–Death Law 1 .................................................................................1-21 Queuing Birth–Death Law 2 .................................................................................1-21 Queuing Birth–Death Law 3 .................................................................................1-21 Data Types for Computational Analysis......................................................................1-22 Nominal Scale ........................................................................................................1-22 Ordinal Scale ..........................................................................................................1-22 Interval Scale ..........................................................................................................1-22 Ration Scale ............................................................................................................1-23 Cardinal Scale.........................................................................................................1-23 References ......................................................................................................................1-23 ix x Contents 2 Basic Mathematical Calculations Quadratic Equation .........................................................................................................2-1 Overall Mean....................................................................................................................2-2 Chebyshev’s Theorem .....................................................................................................2-2 Permutations....................................................................................................................2-2 Combinations ..................................................................................................................2-2 Failure.......................................................................................................................2-3 Probability Distribution..................................................................................................2-3 Probability........................................................................................................................2-3 Distribution Function .....................................................................................................2-3 Expected Value ................................................................................................................2-4 Variance ...........................................................................................................................2-5 Binomial Distribution .....................................................................................................2-5 Poisson Distribution........................................................................................................2-5 Mean of a Binomial Distribution....................................................................................2-6 Normal Distribution........................................................................................................2-6 Cumulative Distribution Function.................................................................................2-6 Population Mean .............................................................................................................2-6 Standard Error of the Mean............................................................................................2-6 t-Distribution...................................................................................................................2-7 Chi-Squared Distribution ...............................................................................................2-7 Definition of Set and Notation .......................................................................................2-7 Set Terms and Symbols ...................................................................................................2-8 Venn Diagrams................................................................................................................2-8 Operations on Sets...........................................................................................................2-9 De Morgan’s Laws ...........................................................................................................2-9 Counting the Elements in a Set.....................................................................................2-10 Permutations..................................................................................................................2-10 Combinations ................................................................................................................2-11 Probability Terminology...............................................................................................2-11