Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control

445 Pages·2018·8.962 MB·English

by  Dharmaraja Selvamuthu, Dipayan Das

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
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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