Handbook Of Industrial Engineering Equations, Formulas .

CRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742 2011 by Taylor and Francis Group, LLCCRC Press is an imprint of Taylor & Francis Group, an Informa businessNo claim to original U.S. Government worksPrinted in the United States of America on acid-free paper10 9 8 7 6 5 4 3 2 1International Standard Book Number: 978-1-4200-7627-1 (Hardback)This book contains information obtained from authentic and highly regarded sources. Reasonable effortshave been made to publish reliable data and information, but the author and publisher cannot assumeresponsibility for the validity of all materials or the consequences of their use. The authors and publishershave attempted to trace the copyright holders of all material reproduced in this publication and apologize tocopyright holders if permission to publish in this form has not been obtained. If any copyright material hasnot 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 utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,including photocopying, 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 RosewoodDrive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses andregistration for a variety of users. For organizations 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 usedonly for identification and explanation without intent to infringe.Library of Congress Cataloging-in-Publication DataBadiru, Adedeji Bodunde, 1952Handbook 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. Engineeringmathematics--Handbooks, manuals, etc. I. Omitaomu, Olufemi Abayomi. II. Title. III.Series.T57.B33 2011620.001’51--dc22Visit the Taylor & Francis Web site athttp://www.taylorandfrancis.comand the CRC Press Web site athttp://www.crcpress.com2010028413

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ContentsPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxixAuthors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxi1Computational Foundations of Industrial EngineeringEfficacy of Mathematical Modeling .1-1Industrial Engineering and Computations .1-1Definition and Applications .1-5Orientation to STEM.1-6IE Catchphrases .1-6Span and Utility of IE .1-6Heritage from Industrial Revolution.1-7Historical Accounts .1-8Chronology of Applications.1-10Importance of IE Calculations .1-14Importance of Calculations Guide .1-16Basic Queuing Equations .1-17Queuing Birth–Death Processes.1-21Laws of Motion of Queuing Birth and Death .1-21Queuing Birth–Death Law 1 .1-21Queuing Birth–Death Law 2 .1-21Queuing Birth–Death Law 3 .1-21Data Types for Computational Analysis .1-22Nominal Scale .1-22Ordinal Scale .1-22Interval Scale .1-22Ration Scale .1-23Cardinal Scale.1-23References .1-23ix

x2ContentsBasic Mathematical CalculationsQuadratic Equation .2-1Overall Mean.2-2Chebyshev’s Theorem .2-2Permutations.2-2Combinations .2-2Failure .2-3Probability Distribution .2-3Probability.2-3Distribution Function .2-3Expected Value .2-4Variance .2-5Binomial Distribution .2-5Poisson Distribution.2-5Mean of a Binomial Distribution.2-6Normal Distribution.2-6Cumulative Distribution Function.2-6Population Mean .2-6Standard Error of the Mean .2-6t-Distribution.2-7Chi-Squared Distribution .2-7Definition of Set and Notation .2-7Set Terms and Symbols .2-8Venn Diagrams.2-8Operations on Sets.2-9De Morgan’s Laws .2-9Counting the Elements in a Set.2-10Permutations.2-10Combinations .2-11Probability Terminology .2-11Basic Probability Principles .2-11Random Variable.2-12Mean Value x̂ or Expected Value μ .2-12Series Expansions .2-12Mathematical Signs and Symbols .2-15Greek Alphabets .2-16Algebra .2-17Laws of Algebraic Operations .2-17Special Products and Factors .2-17Powers and Roots.2-19Proportion .2-19Sum of Arithmetic Progression to n Terms .2-20Sum of Geometric Progression to n Terms.2-20

ContentsxiArithmetic Mean of n Quantities, A .2-20Geometric Mean of n Quantities, G .2-20Harmonic Mean of n Quantities, H .2-20Generalized Mean .2-20Solution of Quadratic Equations .2-21Solution of Cubic Equations .2-21Trigonometric Solution of the Cubic Equation .2-22Solution of Quadratic Equations .2-23Partial Fractions.2-23Nonrepeated Linear Factors.2-23Repeated Linear Factors .2-24General terms.2-24Repeated Linear Factors .2-25Factors of Higher Degree .2-25Geometry.2-25Triangles .2-25Right Triangle .2-26Equilateral Triangle .2-26General Triangle .2-26Menelaus’ Theorem.2-27Ceva’s Theorem .2-27Quadrilaterals .2-27Rectangle .2-27Parallelogram .2-27Rhombus .2-28Trapezoid.2-28General Quadrilateral .2-28Theorem .2-28Regular Polygon of n Sides Each of Length b.2-28Circle of radius r .2-28Regular Polygon of n sides Inscribed in a Circle of Radius r .2-29Regular Polygon of n Sides Circumscribing a Circle of Radius r .2-29Cyclic Quadrilateral.2-29Prolemy’s Theorem .2-29Cyclic-Inscriptable Quadrilateral .2-30Sector of Circle of Radius r .2-30Radius of a Circle Inscribed in a Triangle of Sides a, b, and c .2-30Radius of a Circle Circumscribing a Triangle of Sides a, b, and c .2-30Segment of a Circle of Radius r.2-30Ellipse of Semimajor Axis a and Semiminor Axis b .2-31Segment of a Parabola .2-31Planar Areas by Approximation .2-31Solids Bounded By Planes .2-31Cube.2-32

xiiContentsRectangular Parallelepiped (or Box).2-32Prism.2-32Truncated Triangular Prism .2-32Pyramid .2-32Frustum of a Pyramid.2-33Prismatoid .2-33Regular Polyhedra.2-33Sphere of Radius r .2-34Right Circular Cylinder of Radius r and Height h.2-34Circular Cylinder of Radius r and Slant Height .2-35Cylinder of Cross-Sectional Area A and Slant Height .2-35Right Circular Cone of Radius r and Height h .2-35Spherical Cap of Radius r and Height h .2-35Frustum of a Right Circular Cone of Radii a and b and Height h .2-35Zone and Segment of Two Bases .2-35Lune .2-36Spherical Sector.2-36Spherical Triangle and Polygon .2-36Spheroids.2-36Ellipsoid.2-36Oblate Spheroid .2-36Prolate Spheroid.2-37Circular Torus.2-37Formulas from Plane Analytic Geometry .2-37Distance d between Two Points.2-37Slope m of Line Joining Two Points .2-37Equation of a Line Joining Two Points .2-37Equation of a Line in Terms of x-intercept a 0 and y-intercept b 0 .2-38Normal Form for Equation of a Line.2-38General Equation of a Line.2-38Distance From a Point (x1 , y1 ) to the Line Ax By C 0.2-38Angle ψ between Two Lines Having Slopes m1 and m2 .2-38Area of a Tri

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 .