Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control PDF
Preview Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control
Dharmaraja Selvamuthu · Dipayan Das Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control Dharmaraja Selvamuthu Dipayan Das (cid:129) Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control 123 Dharmaraja Selvamuthu Dipayan Das Department ofMathematics Department ofTextile Technology Indian Institute of Technology Delhi Indian Institute of Technology Delhi NewDelhi, India NewDelhi, India ISBN978-981-13-1735-4 ISBN978-981-13-1736-1 (eBook) https://doi.org/10.1007/978-981-13-1736-1 LibraryofCongressControlNumber:2018949329 ©SpringerNatureSingaporePteLtd.2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. Theregisteredcompanyaddressis:152BeachRoad,#21-01/04GatewayEast,Singapore189721, Singapore Foreword Present-dayresearcheitheracademicorappliedisfacingentirelyadifferentkindof problem with respect to data; in particular, the volume, velocity, variety, and veracity of data available have changed dramatically. Alongside the validity, variability, veracity, of data have brought in new dimensions to associated risk in using such data. While the value of data-driven decision making is becoming the norm these days, the volatility and vulnerability of data pose a newer cautious approach to using data gathered from social networks and sources. However, the age-old problem of visualizing data and value adding from data analysis remains unchanged. In spite of the availability of newer approaches to learning from data, like machine learning, deep learning, and other such modern data analytical tools, a student of engineering or management or social and natural sciences still needs a goodbasicgraspofthestatisticalmethodsandconcepts(1)todescribeasystemin aquantitativeway,(2)toimprovesystemthroughexperiments,(3)tomaintainthe system unaffected by external sources of variation, and (4) to analyze and predict thedynamicsofthesysteminthefuture.Towardthisgoal,studentsneedaresource (1) that does not require too many prerequisites, (2) that is easy to access, (3) that explains concepts with examples, (4) that explains the validity of the methods without getting lost in rigor, and last but not least, (5) that enhances the learning experience. Professors Dharmaraja Selvamuthu and Dipayan Das have translated their years of teaching and writing experience in the fields of descriptive and inferential statistical methods, the design of experiments, and statistical quality control to come out with a valuable resource that has all the desired features outlined above. The efforts of the authors can be seen in the depth and breadth of the topics covered with the intention to be useful in different courses that are taught in engineering colleges and technology institutions. Ontheotherhand,theinstructorswillenjoyusingthisresourceasitmakestheir teaching experience enhanced by the learning outcomes that are bound to accrue fromthecontent,structure,andexpositionofthisbook.Theexercises inthisbook v vi Foreword add value as assessment tools for instructors and also offer additional practice for students. The levels of difficulty in exercises are designed with such end in mind. The authors will be appreciated by both students and instructors for this valuable addition. Goodtextbooksarelikecaringcompanionsforstudents.Thisbookhasachieved that merit. Auckland, New Zealand Prof. Tiru Arthanari University of Auckland Preface Statistics has great relevance to several disciplines like economics, commerce, engineering, medicine, health care, agriculture, biochemistry, and textiles. A large numberofstudentswithvarieddisciplinarybackgroundsneedacourseinbasicsof statistics,thedesignofexperiments,andstatisticalqualitycontrolatanintroductory level to pursue their discipline of interest. The idea of writing this book emerged several years ago since there is no textbook available which covers all the three areas inonebook.Inviewofthediverseaudience,this bookaddresses thesethree areas. No previous knowledge of probability or statistics is assumed, but an understanding of calculus is a prerequisite. The main objective of this book is to give an accessible presentation of concepts from probability theory, statistical methods, the design of experiments, and statistical quality control. Practical examples and end-of-chapter exercises are the highlights of the text as they are purposely selected from different fields. Organized into ten chapters, the book comprises major topics on statistical methods,thedesignofexperiments,andstatistical qualitycontrol.Chapter1isthe introductory chapter which describes the importance of statistical methods, design ofexperiments,andstatisticalqualitycontrol.Chapters2–6alonecouldbeusedas a text for a one-semester, beginner’s level course in statistical methods. Similarly, Chaps. 7–10 alone could be used as a text for a one-semester course in design of experiments. Chapters 2–6 and 10 could be used as a text for a one-semester introductory course in statistical and quality control. The whole book serves as a master-level introductory course in all the three topics, as required in textile engineering or industrial engineering. At the Indian Institute of Technology (IIT) Delhi, the course Introduction to Statistics and Design of Experiments for whichthistextwasdevelopedhasbeentaughtforoveradecade,chieflytostudents majoringinengineeringdisciplinesormathematics.Chapter2introducesthebasic conceptsofprobabilitytheory,conditionalprobability,thenotionofindependence, and common techniques for calculating probabilities. To introduce probability concepts and to demonstrate probability calculations, simple probabilistic experi- ments such as selecting a card from a deck or rolling a die are considered. In addition, the standard distributions, moments, and central limit theorem with vii viii Preface examplesarealsodiscussedinChap.2.Chapter3presentsthedescriptivestatistics, which starts with concepts such as data, information, and description. Various descriptive measures, such as central tendency measures, variabilitymeasures, and coefficient of variation, are presented in this chapter. Inference in mathematics is based on logic and presumably infallible at least when correctly applied, while statistical inference considers how inference should proceed when the data are subject to random fluctuation. Sampling theory can be employed to obtain infor- mationaboutsamplesdrawnatrandomfromaknownpopulation.However,oftenit is more important to be able to infer information about a population from samples drawn from it. Such problems are dealt with in statistical inference. The statistical inference may be divided into four major areas: theory, estimation, tests of hypothesis, and correlation and regression analysis. This book treats these four areasseparately,dealingwiththetheoryofsamplingdistributionsandestimationin Chap. 4, hypothesis testing in Chap. 5, and correlation and regression analysis in Chap.6.Thestatisticalinferenceisdealtwithindetailwithsamplingdistributionin Chap. 4. The standard sampling distributions such as chi-square, Student’s t, and F distributions are presented. The sample mean and sample variance are studied, andtheirexpectationsandvariancesaregiven.Thecentrallimittheoremisapplied to determine the probability distribution they follow. Then, this chapter deals with point estimation, a method of moments, maximum likelihood estimator, and interval estimation. The classic methods are used to estimate unknown population parameters such as mean, proportion, and variance by computing statistics from random samples and applying the theory of sampling distributions. Chapter5coversastatisticaltestofthehypothesisindetailwithmanyexamples. The topics such as simple and composite hypotheses, types of error, power, operating characteristic curves, p value, Neyman–Pearson method, generalized likelihood ratio test, use of asymptotic results to construct tests, and generalized ratio test statistic are covered. In this chapter, analysis of variance, in particular, one-way ANOVA, is also introduced, whereas its applications are presented inthe later chapters. Chapter 6 discusses the analysis of correlation and regression. This chapterstartsbyintroducingSpearman’scorrelationcoefficientandrankcorrelation and later on presents simple linear regression and multiple linear regression. Further, in this chapter, nonparametric tests such as Wilcoxon, Smirnov, and median tests are presented. The descriptive statistics, sampling distributions, esti- mations, statistical inference, testing of hypothesis, and correlation and regression analysis are presented in Chaps. 2–6 and are applied to the design and analysis of experiments in Chaps. 7–9. Chapter 7 gives an introduction to the design of experiments. Starting with the definition of the design of experiments, this chapter gives a brief history of experimental design along with the need for it. It then discusses the principles and provides us with the guidelines of the design of experiments and ends with the illustration of typical applications of statistically designedexperimentsinprocess-,product-,andmanagement-relatedactivities.This chapter also deals with a very popular design of experiments, known as a com- pletely randomized design, which describes how to conduct an experiment and discussestheanalysisofthedataobtainedfromtheexperiment.Theanalysisofthe Preface ix experimentaldataincludesthedevelopmentofdescriptiveandregressionmodels,a statistical test of hypothesis based on the one-way classification of analysis of variance, and multiple comparisons among treatment means. This chapter presents many numerical examples to illustrate different methods of data analysis. At the end, the reader is asked to solve many numerical problems to have a full under- standing of a completely randomized design. Chapter 8 discusses two important block designs, namely randomized block design and Latin square design. It describes these designs by using practical examples and discusses the analysis of the data obtained from experiments con- ducted in accordance with these designs. The data analysis includes the develop- ment of descriptive models, statistical tests of a hypothesis based on the two-way and three-way classifications of analysis of variance, and multiple comparisons amongtreatmentmean.Also,inthischapter,manynumericalexamplesaresolved, and several numerical problems are given at the end of the chapter as exercises. Chapter8dealswithanimportantclassofexperimentaldesigns,knownasfactorial designs.Thischapterdiscussesthedesignandanalysisoffactorialexperimentswith twoorthreefactors,whereeachfactormighthavethesamelevelordifferentlevels. Italsodiscussesthedesignandanalysisof22and23fullfactorialexperiments.This chapter explains two important design techniques, namely blocking and con- founding, which are often followed by a factorial experiment. The design and analysisoftwo-levelfractionalfactorialdesignandtheconceptofdesignresolution are explained. In this chapter, many numerical examples are given to illustrate the concepts of different factorial designs and their methods of analysis. Additional end-of-chapterexercisesareprovidedtoassessstudents’understandingoffactorial experiments. Chapter 9 deals with response surface methodology, a collection of mathematical and statistical tools and techniques used in developing, understand- ing, and optimizing processes and products along with a description of response surface models. It discusses the analysis of first-order and second-order response surface models. It describes popular response surface designs that are suitable for fitting the first-order and second-order models. Also, it describes the multi-factor optimization technique based on the desirability function approach. This chapter reportsmanynumericalexamplestoillustratedifferentconceptsofresponsesurface methodology. At the end, readers are asked to solve several numerical problems based on the response surface methodology. Chapter 10 deals with statistical quality control. This chapter discusses acceptance sampling techniques used for inspection of incoming and outgoing materials in an industrial environment. It describes single and double sampling plans for attributes and acceptance sampling of variables. Further, this chapter also describes a very important tool in process control,knownasacontrolchart,whichisusedtomonitoramanufacturingprocess with quality assurance in mind. It provides an introduction to control chart. It describes Shewhart’s three-sigma control charts for variables and attributes. It discusses the process capability analysis. Also, it describes an advanced control chartwhichisveryefficienttodetectasmallshiftinthemeanofaprocess.Finally, this chapter discusses many numerical examples to illustrate different concepts of acceptance sampling techniques and quality control charts. x Preface The exposition of the entire book is processed with easy access to the subject matter without sacrificing rigor, at the same time keeping prerequisites to a mini- mum. A distinctive feature of this text is the “Remarks” following most of the theoremsanddefinitions.InRemarks,aparticularresultorconceptbeingpresented isdiscussedfromanintuitivepointofview.Alistofreferencesisgivenattheend of each chapter. Also, at the end of each chapter, there is a list of exercises to facilitatetheunderstandingofthemainbodyofeachchapter.Mostoftheexamples and exercises are classroom-tested in the course that we taught over many years. Since the book is the outcome of years of teaching experience continuously improved with students’ feedback, it is expected to yield a fruitful learning expe- rience for the students, and the instructors will also enjoy facilitating such creative learning. We hope that this book will serve as a valuable text for students. We would like to express our gratitude to our organization—Indian Institute of Technology Delhi—and numerous individuals who have contributed to this book. Many former students of IIT Delhi, who took courses, namely MAL140 and TTL773, provided excellent suggestions that we have tried to incorporate in this book. We are immensely thankful to Prof. A. Rangan of IIT Madras for his encouragementandcriticism duringthewritingofthis book.Wearealsoindebted to our doctoral research scholars, Dr. Arti Singh, Mr. Puneet Pasricha, Ms. Nitu Sharma,Ms.AnubhaGoel,andMr.AjayK.Maddineni,fortheirtremendous help during the preparation of the manuscript in LaTeX and also for reading the manuscript from a student point of view. We gratefully acknowledge the book grant provided by the office of Quality ImprovementProgrammeoftheIITDelhi.OurthanksarealsoduetoMr.Shamim AhmadfromSpringerforhisoutstandingeditorialworkforthisbook.Wearealso gratefultothoseanonymousrefereeswhoreviewedourbookandprovideduswith excellentsuggestions.Onapersonalnote,wewishtoexpressourdeepappreciation to our families for their patience and support during this work. Intheend,wewishtotellourdear readers thatwehavetriedhardtomake this book free of mathematical and typographical errors and misleading or ambiguous statements.However,itmightbepossiblethatsomearestillbeingleftinthisbook. We will be grateful to receive such corrections and also suggestions for further improvement of this book. New Delhi, India Dharmaraja Selvamuthu April 2018 Dipayan Das
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