IPR2016–01833
`ON Semi v. In-Depth Test LLC
`Page 1
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`In-Depth
` Test
`2018
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`

`
` 511
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`. 1-1
`
`55543
`Shewhart
`Statistical method
`from the viewpoint
`of quality control
`A.'*-
`,
`,-
`.
`r/
`
`HOCH ESTER PUBLIC LIBRARY
`FDHM EA-NOV. B5-EON
`
`

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`

`
`

`
`STATISTICAL METHOD
`
`FROM THE VIEVVPOINT OF
`
`QUALITY CONTROL
`
`.
`
`by
`
`WALTER A. SI-IEWHART, Pl1.TJ.
`Member of the ’1"e::fm.3'caE Sfafi"
`Bell '."‘¢>E-ephorze Lubor'az‘or'f€:-
`New York
`
`-t.-:f:'.h the ed-:'.:‘ar:':1l ass-Estance of
`
`W. EDWARDS DEMING, PILD.
`Sam}:-r Mafliemat-iciarz
`The De',rJar£mem'. of xigricultu-re
`I-I"ash'Engion
`
`
`
`THE G‘R,~\D1'-ATE SCHOOL
`
`THE D1-3FAl{'l‘]'HEI\"l' 01-‘
`
`:\r;[m.'t-'I.TI-'HF.
`
`W',xsHrxc:':'oN
`
`193$}
`
`

`
`C0py1'igI.1t 1939
`THE GR..\DU.»\"I‘F2 SCHOUL
`'13-15: Dncp.-\w1'.uEx'1‘ OF AGaIcU1.'rL'rtE
`WAsu1z~:GT01~:
`
`Reprifitted, 1945
`
`PRINTED IN THE IINITED 5'l‘A'l‘E.-3 OF AMERICA
`BY THE LANCASTER PRESS. INC" I...-LN'C'A.E'1'lJIi, PA.
`
`
`
`

`
`-
`
`'r,'_. A‘,
`
`FOREWORD FROM THE EDITOR
`
`1-1
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`'
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`'
`
`I -In March of 1938 Dr. Shewhart, through the courtesy of the Bell Tele-
`'__'_n'e Laboratories, delivered a series of four lectures under the title of this
`' k at -the Graduate School of the Department of Agriculture. Of late
`'
`there has been a tremendous interest among agricultural research
`ers in distribution theory and in ‘statistical testing of hypotheses, as a
`uence of which there has -grown up a corresponding thirst for knowl-
`and new methods in inference. The Graduate School has persistently
`..-:VOIJ_ll‘ed to supply the requisite academic courses, .and to supplement
`a wherever possible by lecturers from other fields and other lands.
`' is a brief description of the circumstances under which Dr. Shewhart
`_ _e' to Washington.
`We--found that though his experience had been in manufacturing, we in
`' _"'culture are faced with the same problems, but not with the same penalties
`misuses and abuses of the theories that we apply. When machines are
`"'g out‘ pieceparts by the thousands or even millions monthly,
`the
`"Km rial statistician does not have to wait long to see his predictions
`.4 out.
`In agriculture, years are often required—a crop must be sowed
`harvested again and again until the evidence is definitely for or against
`- prediction that one treatment is actually better than another, and by
`time the question is settled, not only the statistician who made the
`._ "ction, but the prediction itself may be forgotten. With time in our
`"'1' it is easy to become careless about fundamentals.
`An inference, if it is to have scientific value, must constitute a prediction
`:« cerning future data.
`If the inference is to be made purely with the help
`the distribution theories of statistics, the experiments that constitute
`',
`H‘ - evidence for the inference must arise from a state of statistical control;
`that state is reached there is no universe, normal or otherwise, and
`tati.$tician’s calculations by themselves are an illusion if not a delusion.
`fact"-is that when distribution theory is not applicable‘ for lack of control,
`inference, statistical or otherwise, is little better than conjecture. The
`--of statistical control is therefore the goal of all experimentation.
`Dr. Shewhart is in a position to speak with authority on some aspects of
`‘ -.c- questions.
`In his experience he has found that it is exceedingly more
`us It than is commonly supposed to weed out the causes of larger varia-
`but that it can usually be done through careful attention to the control
`_
`_ audio the physical mechanism of the experiment or production process.
`_
`it
`- _ n ortunately not one but many experiments seem to be required.
`iii
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`

`
`iv
`
`FOREWORD
`
`_
`
`The scientific viewpoint is that every statement must be capable of
`being tested.
`If a statement can not be put to a test, it has no value in
`practice. Dr. Shewhart kept this viewpoint throughout his lectures. Here
`for the first time we see operationally verifiable meanings for well-known
`statistical terms such as random variable, accuracy, precision, true value,
`probability, degree of rational belief, and the like, all of which are necessary
`if statistics is to take its rightful place as a tool of science. Here also we
`see a criterion of meaning that has been found useful in guiding the applica-
`tion of statistical technique in industry.
`Most of us have thought of the statistician’s work as that of measuring
`and predicting and planning, but few of us have thought it the statistician’s
`duty to try to bring about changes in the things that he measures.
`It is
`evident, however, from the first chapter that this viewpoint is absolutely
`essential if the statistician and the manufacturer or research worker are to
`make the most of each other’s accomplishments. What they are capable
`of turning out jointly is the sum of their independent eiforts augmented by
`a strong positive interaction term. Likewise the value of a book is not
`just the sum of the values of the chapters separately; each chapter, even
`each paragraph, has a meaning that is conditioned by all the others. The
`subject of quality control is not fully expressed by any single idea, and the
`first chapter must be interpreted in the light of the last.
`It has been the duty of the editor to promote clarity by altering the
`manuscript where it has seemed desirable to do so in order that the ideas
`expressed _in the book will be understood, operationally,
`in the sense in
`which Dr. Shewhart understands them himself. Most of
`the cross-
`referencing, and many of the footnotes, signed and unsigned, are from the
`editor.
`It has been of particular satisfaction to work so closely with Dr.
`Shewhart on the production of this book, because it was he who introduced
`me to some of the modern statistical literature back in 1928.
`It is a pleasure to record the generous assistance of Lee Garby (Mrs.
`C. D. G.) for checking the references and for making a number of suggestions
`in proof. The expert help of the accommodating printer, the Lancaster Press,
`I11c., has been a delight to the author and editor.
`In conclusion, it is fitting
`that attention should be drawn to the fact that this book is one more
`contribution to science from the staff of the Bell Telephone Laboratories.
`If the worid were deprived of the contributions to science that have origi-
`nated from that great organization, it would be a. different one indeed.
`W. E. D.
`
`W.asHINs.'roN
`February 1939
`
`
`
`

`
`r _Sta_tistic_a1_ n1'e_th_ods of’. research. have been highly developed“ in‘ the sad
`cI_1_lt1f1_re._
`-Sirnilai-1y‘, statistical. methods. of central have been de1._rel_op_e,o:l_
`ustry for the purpose" of ...attaining economic control oi_"'quality of
`” ct" in -massproduction.
`It is reasonable "to expect that much is-:to_' be".
`:-ed by correlatingso far as possible the development of these two kinds.
`statis'ti_cal technique.
`In the hope of helping ‘to efi"ect this corre1a_ti'_on;
`with pleasure that I accepted the invitation to give a "series of ‘four
`-.4 on statistical method from the viewpoint of quality centrolbe-'.
`the Graduate 'S'c'ho_'ol ‘of the Depaitment of Agriculture-. The subject
`e'_r_.'of these le_cture's'is limited to.-an exposition of some of the elementary
`undamentai principles and techniques basic to the eflicient use of -the
`Istical method in the attainment of a state of statistical control, the
`lishment of tolerance limits, the pr_esenta_tion_ of da13.«'i;-_a.nd the specifics-'
`of "accuracy and precision.
`I -am indebted to many, and."-in particular
`W. Edwards Deming, for the helpful c'rit'ioisms and. stimulating.
`cations brought-out in the discussion periods following the Itmtures and
`‘irate-conferenc'es.
`. II-11 'p'r'ep'_ariJ_1__'g these lectures for publication, it- has been a pleasure and
`vfil_e'_ge'to havethe wholehearted cooperation of the editor, Dr. Deming,
`_ has contributed many helpful suggestions and hasdone much to help
`" ‘the text. My colleague, Mr. H. F. Dodge, has given continuing‘
`and advice over -the past several ‘years in the: developrn'ent cf‘ the"
`teri__al'here. presented. Miss Miriam Harold has co‘ntrilo'ute'd many help-
`suggestions at al.l.stage's_of the work and has for the most part borne the
`of-' accumulating and analyzing the‘. data, drawing the figures, .and'_
`_g--'tl1e_'n1a'nuscript in final form. To ‘each of these, I am "deeply in?
`. For many courtesies.extended to me at the time tllelectures were,
`__ , I am indebted to Dr. A. F. Woods, Director of the Graduate School.
`
`August 1939-
`
`-*".'I'3au_. Tnnnpnons Luconzvronrns. Inc.
`New Year:
`
`W. A. ISHEWHART
`
`PREFACE
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`"
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`

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`The application of statistical methods in mass pro-
`duction makes possible the most efficient use of raw
`materials and manufacturing processes, effects econ-
`omies in production, and makes possible the highest
`economic standards of quality for the manufactured
`goods used by all of us. The story of the application,
`however, is of much broader interest. The economic
`control of quality of manufactured goods is perhaps
`the simplest type of soien£1Ific_cont1'ol. Recent studies
`in this field throw light on such broad questions as:
`What is the fundamental role of statistical method in
`such control‘? How far can man go in controlling his
`physical environment? How does this depend upon
`the human factor of inteiligence and how upon the
`element of chance‘?
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`

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`CONTENTS
`
`CHAPTER I—STATISTICAL CONTROL
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`1
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`.CHAPTER II—HOW ESTABLISH LIMITS OF VARIABILITY?
`;.
`. 1s INVOLVED IN THE rnonnnn? §Note on the meaning of
`tolerance limits". Probabilities involved. §'I'hree typical toler-
`zance -ranges.
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`-."1>nonLEM mom THE VIEWPOINT or STATISTICAL THEORY. §A
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`_ practical example
`Esrasmsn TOLERANCE Lmurs IN THE sIM1>LEs-r oasn?
`§ A toler-
`ance range for the bowl universe.
`§ Student's theory inadequate
`{or tolerance limits.
`§A study of three types of ranges .
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`. .56-~63"
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`_ DUCTION. Three steps in quality control. Three senses of sta-
`-'t'istica.l control .
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`nrroun-ranr nrsronrcar. s'mc.Es IN THE corrrnon or QUALITY.
`§_Developments since 1870. §A requirement regarding control.
`'§A probable inference regarding control .
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`-T e :s -STATE or srarrsrrcan conrrnon.
`§ The physical -state of statistical
`control. The ideal bowl experiment.
`§Tl1e mathematical state
`of statistical control.
`§ An attempt at defining random order for
`infinite sequences. §An attempt at defining random order for
`"finite sequences. §There is no unique description of a state of
`control.
`§ How to build a model of a state of statistical control.
`Postulate I .
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`. .8—23
`rrcar. CONTROL as AN ornnxrrosr.
`§ The operation of statistical
`‘control. §Some comments on the first step in the operation of
`icontrol. The importance of order.
`§Son1e comments on the
`second step in the operation of control.
`§ Some comments on the
`third and fourth steps in the operation of control. Practical re-
`quirements imposed on the criterion of control. Criterion I.
`§Some comments on_the fifth step in the operation of control-.
`§The operation of statistical control as a whole.
`§Exarnp1e of
`what can be done in practice.
`§ Two kinds of errors in the opera-
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`=‘- .:o1_a'oMEN-r or sra-rrsrrcan CONTROL.
`§ Postulate II .
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`-sromrrcancn on srarrsrrcan con-rnor. .
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`‘Em-URE or s-rarrsrros IN MASS rnonocrron .
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`viii
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`CONTENTS
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`PMUES
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`How EsTABLIsH TOLERANCE Lnurrs IN ‘THE PRACTICAL CASE‘? §The
`necessity for control.
`§Engineering and “research” data are
`not to be regarded differently with respect to the assumption of
`statistical control.
`§ Where does the statist-ician’s Work begin? . 63—71
`FURTHER CoNsIDEnA'rIoNs REGARDING TOLERANCE LIMITS.
`§ Standard
`methods of measuring.
`§Setting tolerance limits vi-"hen control
`is lacking .
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`CHAPTER III—'THE PRESENTATION OF THE RESULTS OF
`MEASUREMENTS OF PHYSICAL PROPERTIES
`AND CONSTANTS
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`§InCreased knowledge of quality
`THE NATURE on THE PROBLEM.
`necessary. §Some considerations of summaries of the density of
`iron. §The importance of
`the problem of presenting data.
`§ The presentation of data from the viewpoint of language. There
`is scientific language and emotive language .
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`THREE COMPONENTS or KNoWLEDGE—EvIDENCE, PREDICTION, DEGREE
`or BELIEF‘ .
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`§ Pre-
`THE RESULTS or MEASUREMENT PRESENTED As ORIGINAL DATA.
`senting data as facts; can it be done‘? §Original data must be
`considered as evidence for inferences of various kinds. Rule 1.
`
`§Two difierent problems of presentation—data may or may not
`arise from statistical control. §Four important characteristics
`of original data.
`§ Summarizing original data; by symmetric fun c-
`tions; by Tchebychefi”s theorem. Rule 2 .
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`. .86—92
`THE RESULTS on MEASUREMENT PRESEN'l‘ED As MEANINGFUL PREDIC-
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`TIONS. §Every interpretation involves a prediction. Criterion
`of meaning.
`§ Prediction involved in
`estimatio11—type P3.
`“Best" estirnates.
`§ Prediction involved in the use of the Student
`range-—type P1.
`§P1'actical need for clarification of predictive
`meaning.
`§ Prediction involved in the use of the tolerance rangc—
`type P2.
`§ Common Characteristics of the preclictions .
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`THE RESULTS or MEASUREMENT 1=nEsENTED As KNOWLEDGE-"IDEAL
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`CONDITIONS. §To every prediction there corresponds a certain
`degree of rational belief.
`§Nonstat'Ic character of knowledge.
`§Limits to knowing. Predictions based on the bowl universe
`have maximum validity.
`§ The object of a scientific investigation
`and the presentation of its results.
`§'I‘he presentation of results
`from the normal bowl.
`§ The preseinzation of results from a bowl
`when its distribution is known but is not normal.
`§ The presenta-
`tion of results from a bowl when its distribution is unknown. .101—110
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`1 I
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`CONTENTS
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`ix
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`PAGES
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`R_E-SUI.-TS OF MEASUREMENT PRESENTEDAS 1(NOWLEDGE'—CUSTOMAR'1’
`CO1_\l'D_ITIONS.
`§ Complications in real measurements not in a state
`of s'ta_tistical_ control. §Consistency between diflerent methods
`more"iInportant than consistency in repetition.
`.§ A word on the
`detection of constant errors by "tests of significance.”
`§N'eed
`for the attainment of statistical control.
`§Distinction between
`‘summarizing data for evidence of statistical control, and for setting
`tolerance limits after it has been attained.
`§ Tolerance limits when
`L statistical control has not been attempted.
`§ Need for evidence of
`.eonsistency—constant errors.
`§Kinds of information needed for
`-setting limitsin uncontrolled conditions .
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`. .110—118-
`_CLUDING COMMENTS .
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`CHAPTER IV—THE SPECIFICATION OF ACCURACY
`AND PRECISION
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`§AppliecI science more exacting
`gmons ssrncrs or THE rnosnnm.
`than pure science regarding accuracy and precision.
`§Fiveiold
`-objective.
`§ Broad interest: in the problem .
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`} ::; MEANING or ACCURACY AND PRECISION-—-PRELIMINARY COMMENTS.
`'§ Why statements about accuracy ‘and precision are often indefinite.
`'§-Accuracy and precision in the theory of _errors. Customary
`assumptions.
`§ Some difficulties with the usual theory .
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`: TIONAL MEANING.
`§ Operation or method of measurernent; two
`aspects.
`§Consistency and reproducibility.
`§A requirement
`concerning a verifiable statement about precision.
`§Practica1
`and theoretical verifiabiiity. §The operational meaning of" a
`quality characteristic.
`§ Physical and logical aspects of theoret_ical
`_ verifi'ability. Examples . .
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`. ..130—137
`. OPERATIONAL MEANING or ACCURACY AND rnncrsron.
`§Sorne
`fundamental difliculties. §Practically verifiable meaning" of ac—
`curacy and precision. §The meaning of these concepts in use.
`§ Practically verifiable procedures for realizing 1;’, X’, X”, pa, and
`randomness. Distinction between the meanings of concepts and
`operationally verifiable procedures.
`§Nced for specifying the
`minimum quantity of evidence "for forming "a judgment regarding
`accuracy and precision. §The meaning of abstract concepts is
`.1:":ot'unique .
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`. ..138-144
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`"cLUsIoNs .
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`t COMMENTS ON srMsoLs AND NOMENCLATURE .
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`. .152—155
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`- 4'
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`

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`

`
`CHAPTER I
`
`STATISTICAL CONTROL
`
`The possibility of improving the economy of steel to the
`consumer is therefore largely a matter of improving its uni-
`formity of quality, of fitting steels better for each of the multi-
`farious uses, rather than of any direct lessening of its cost of
`production.‘
`
`Joan Jonnsron, Director of Research
`United‘ States Steel Corporation
`
`Introduction. Three steps in quality control. Three senses of statis-
`control. Broadly speaking, there are three steps in a quality control
`the specification of what is wanted, the production of things to
`'siy the specification, and the inspection of the things produced to see
`7
`5.3 they satisfy the specification. Corresponding to these three steps there
`[are three senses in which statistical control may play an important part in
`attaining uniformity in the quality of a manufactured product: (a) as a
`iioncept of a statistical state constituting a limit to which one may hope to
`[go in improving the uniformity of quality; (b) as an operation or technique
`‘attaining uniformity; and (c) as a judgment. Here we shall be con-
`{eerned with an exposition of the meaning of statistical control in these
`senses and of the role that each sense plays in the theory and technique
`{If economic control. But first we should consider briefly the history of
`‘.3318 control of quality up to the time when engineers introduced the statistical
`-control chart technique, which is in itself an operation of control.
`
`Sons Inronranrr Hrsronroiin Sraons IN THE Con-rnor. on Qoanrrr
`
`
`
`J Puts fitted
`313,000 years ago
`
`To attain a perspective from" which to View recent developments, let us
`' look at fig. 1. That which to a large extent differentiates man from animais
`is his control of his surroundings and particularly his pro-
`duction and use of tools. Apparently the human race began
`the fashioning and use of stone tools about a million years
`ago, as may be inj'e'rred from the recent discovery just north of London 3
`_
`1 “ The applications of science to the making and finishing of steel,” .l|<l'echa,nicai Engineer-
`iag, vol. 57, pp. 79-86, 1935.
`3 This discovery is reported in Man Rises to Parnassus by H. F. Osborn (Princeton
`Tiniversity Press, 1928). The photograph of the stone irnpiernents (fig. 1) of a million
`- years ago has been reproduced by permission from this most interesting book. Those of
`-'
`implements of 150,000 and 10,000 years ago have been reproduced by permission from
`.
`the fascinating story told in Early Steps in Human Progress by H. J. Peaks (J. B. L'1ppin—
`.
`‘eott, Philadelphia, 1933).
`1
`
`

`
`2
`
`STATISTICAL METHOD FROM THE VIEWPOINT OF QUALITY CONTROL
`
`of the crude stone implements shown at the left in fig. 1. Little progress
`irrcontrol seems to have been made, however, until about 10,000 years ago
`when man began to fit parts together in the fashion evidenced by the holes
`in the instruments of that day.
`
`150,000
`Yams Aeo
`
`10,000
`Yams Ace
`
`150 Yams Aoo
`
`PARTS
`
`INTRODUCTION
`
`or
`
`INTERCHANGEABLE
`
`FIG.
`
`1
`
`Interchangeable parts-
`exact, 1787
`
`Throughout this long period, apparently each man made his own tools,
`such as they were. As far back as 5000 years ago the Egyptians are sup—
`posed to have made and used interchangeable bows
`and arrows to a limited extent, but it was not until
`about 1787, or about a hundred and fifty years ago,
`that we had the first real introduction of the concept of interchangeable
`parts. Only yesterday, as it were, did man first begin to study the tech-
`nique of mass production!
`From the viewpoint of ideology, it is significant that this first step was
`taken under the sway of the concept of an exact science, according to which
`an attempt was made to produce pieceparts to
`exact dimensions. How strange such a proce-
`dure appears to us today, accustomed as we are to
`the use of tolerances. But as shown in fig. 2, it was not until about 1840
`that the concept of a “go” tolerance limit was introduced and not until
`about 1870 that we find the “go, no-go” tolerance limits.“
`Why these three steps: "exact,” “go,” “go, no-go”? The answer is
`quite simple. Manufacturers soon found that they could not make things
`
`"Go” tolerance limits, 1840;
`“go, no-go," 1B'?O
`
`3 It will be noted that the first six dates shown in fig. 2 are given with question marks
`—aut.l1orities are not in unanimous agreement as to the exact dates.
`1 think, however,
`that the dates here shown will he admitted by all to be sufficiently close approximations.
`
`
`
`

`
`STATISTICAL CONTROL
`
`
`
`in -respect to a given quality; moreover, it was not necessary
`he_'exa'ctly alike, and it was too costly to try to‘ make -them so.
`,_
`=y.ala'out 1840 they had eased away from the requirement-of exact-
`
`L"-r-I-LE "F ‘N1-I CONTROL
`
`HEGINNING
`OF CONTROL
`scopoosc
`1'
`
`m'rsnmmeE-
`msrs
`5311.-ITY
`FIRST FITTED
`TOGETHER I rear
`cocoa: W37
`‘I
`1
`
`co
`
`co no-co
`
`cumrv
`ccnmoa.
`CHART
`
`-
`
`'_";c'oo'ac
`
`_-
`Exec?
`
`' 193r
`mo
`mo
`mac
`'1‘
`.7
`FIG. 2
`
`
`
`‘v
`
`,_
`
`If we take, for
`i" _ the "go" tolerance. Let us see how this worked.
`, a‘ design involving the use of a cylindrical shaft in a hearing, one '
`Insure interchangeability by simply using 3 suitable "‘go." plug gauge
`' bearing and a suitable “go” ring gauge on the shaft.
`In this-case,
`erence between the dimensions of the two "go” gauges-gave the
`ciearance. Such a method of gauging, however, did not fix the
`clearance. The production man soon realized that a slack fit
`apart and its “go” gauge might result in enough play between the
`:1 its bearing to cause rejection, and for this reason he tried to keep
`:between the part and its “go ” gauge as close as possible, thus involv-
`e. of the same kind of difliculties that had been experienced-in trying
`" e the parts exactly alike. The introduction of the “go, no-go”
`in 1870 was therefore a big forward step in that it fixed the upper and
`tolerance limits on each fitting part, thus giving the production man
`dom with a. resultant reduction in cost. All he had to do was
`. the tolerance 1imits—he didn’t have to waste time trying to be
`sorely exact.
`11 this step was of great importance, something else remained to
`The limits arenecessarily set in such a way that every nowand
`then a. piece of product has a quality characteristic fall-
`ing outside its specifiedrange, and is therefore defective.
`To junk or modify such pieces adds to the cost of produc-
`" - But to find the unknown or chance causes of defectives and totry to
`_' them also costs money. Hence after the introduction of the go,
`tolerance limits, there remained the problem of trying to reduce the
`s p‘ of defectives to a pointwhere the rate of increase in the cost of
`.1 equals the rate of increase in the savings brought about through
`‘'73 "acreage" in the number of rejected parts.
`
`tarts:
`
`
`
`

`
`4
`
`STATISTICAL METHOD FROM THE VIEWPOINT OF QUALITY CONTROL
`
`For example, in the production of the apparatus going into the telephone
`plant, raw materials are gathered literally from the four corners of the earth.
`More than 110,000 different kinds of pieceparts are produced. At
`the
`various stages of production, inspections are instituted to catch defective
`parts before they reach the place of final assembly to be thrown out there.
`At each stage, one must determine the economic minima for the sizes of the
`piles of defectives thrown out.
`This problem of minimizing the percent defective, however, was not
`the only one that remained to be solved. Tests for many quality character-
`istics—strength, chemical composition, blowing time
`of a fuse, and so on—are destructive. Hence not
`every piece of product can be tested, and engineers
`must appeal to the use of a sample. But how large a
`sample should be taken in a given case in order to gain adequate assurance of
`quality?
`The attempt to solve these two problems gave rise to the introduction
`of the operation of statis_tical control involving the use of the quality control
`chart in 1924, and may therefore be taken as the starting
`point of the application of statistical technique in the
`control of the quality of a manufactured product in
`the sense here considered.
`
`Destructive tests;
`necessity for sampling.
`How large a sample?
`
`The quality control
`chart. 1924
`
`Why after 1900?
`
`Why, you may ask, do we find, some one hundred and fifty years after
`the start of mass production, this sudden quickening of interest in the
`application of statistical methods in this field? There are
`at least two important reasons. First, there was the rapid
`growth in standardization. Fig. 3 shows the rate of growth in the number
`of industrial standardisation organisations both here and abroad. The
`first one was organised in Great Britain in 1901. Then beginning in 1917
`the realization of the importance of national and even international stand-
`ards spread rapidly. The fundamental job of these standardizing organiza-
`tions is to turn out specifications of the aimed-at quality characteristics.
`But when one comes to write such a specification, he runs into two kinds of
`problems: (1) minimizing the number‘ of rejections, and (2) minimizing the
`cost of inspection required to give adequate assurance of quality in the sense dis-
`cussed above. Hence the growth in standardization spread the realization
`of the importance of such problems in industry.
`Second, there was a more or less radical change in ideology about 1900.
`We passed from the concept of the exactness of science in 1787, when in-
`terchangeability was introduced, to probability and statistical concepts
`which came into their own in almost every field of science after 1900.
`Whereas the concept of mass production of 1787 was born of an exact
`science, the concept underlying the quality control chart technique of 1924
`was born of a probable science.
`
`

`
`s"r.-rrrsrrcnn coarrnon
`
`5
`
`" "We may forsimplicity think of the manufacturer trying to produce a
`.- of product with a quality characteristic falling within a given tolerance
`-_- as being analogous to shooting at a mark.
`If one of us were shooting
`'_.a. mark and failed to hit the bull’s-eye, and some one asked us why, we‘
`
`'
`
`_-
`"
`
`InUI
`
`
`SPAIN
`NEW ZEAL-IND
`
`
`
`
`
`NORWAY
`
`SWEDEN
`AUSTR hI.,IA
`CZECHO-SLOVA KIA
`ITALY
`.JA?AN
`HUNGARY
`
`AU STFIIA
`BELCJUM
`CANA DA
`UNITED STATES
`
`SWJTZERLAND
`‘FRANCE
`GERMANY
`
`N ETH E ELAND 5
`
`0 I900
`IQIO
`I920
`H30
`IB40
`Y E A R
`
`
`
`
`
`
`
`
`
`NuuealiorIncuarnim.sraubahclziueoncaiuzm-nous G
`
`FIG. 3
`
`- d likely give as our excuse, CHANCE. Had some one asked the same
`; °_on of" one of our earliest known ancestors, he might have'at_tributed
`_
`_ lack of success to the dictates of fate or to the will of the gods.
`I am
`,‘ 1 ed to think that in many ways one of these excuses is just about as
`a as another. Perhaps we are not muc_h wiser in blaming our failures
`'_'- chance than our ancestors were in blaming theirs on fate or the gods.
`'_ since -1900, the engineer has proved his unwillingness to attribute all
`‘ " failures to chance. This represents a remarkable change in the
`‘logy that characterizes the developments in the application of stat_istics'
`__-the control of quality.
`Developments since 1870. With the introduction of the go, no—go
`ce limits of 1870, it became the more or less generally accepted
`ice to specify that each important quality characteristic X of a given
`- of" product should lie within statedlimits L1 and Lg, represented
`atically in fig. 4. Such a specification is of the nature of an end
`_ " ment on the specified quality characteristic X of a finished piece of
`. u - ct.
`It provides a basis on which the quality of a given product may
`- gauged to determine whether or not it meets the specification. From
`viewpoint, the process of specification is very simple indeed. Knowing
`limits L1 and L3 within which it is desirable that a given quality charac-
`
`

`
`teriaiic-3' should: lie, all:-we .-need to dois to put these_.1in'1'its in writing as a
`on-‘.‘tiie-._q1g1ality or a‘ finished product"-. With such-anpeeifiéation-'
`at--"hand," the-:=ne'nt_-i'.step isto make. the measurements necessary" to classify a;
`"off" p=r_o_df-1-ct-"as conforming" or -'nonooriforming.:te. ap.ecificatio'n-.1
`
`'
`‘
`
`QUALITY X
`
`I
`L1
`FIG. 4
`
`'
`
`1
`Lg
`
`'
`
`§i1_1!1?!!=._=1=°I=Bi¢-stion 9f :0.
`'nj9-gvotolonn-:e limits
`unsatisfactory
`
`At-this‘ point, however, two problems a.rise.. Suppose" that the q_uaIi'ty
`.i1.1ider'conside'ra"tion,"the blowing time of a fusefor.-..exam_'ple, ‘is one that can".
`be determined only by d'estruo'_tive=_tests. How can"
`one give "assurance that the quality of a fuse will‘
`meet its specification without destroying the fuse in;
`_
`_
`the process? Or again, even where the quality
`eharac,teri.stic. can be measured -wit.ho_'ut destruction,
`there is ‘always a__
`certain fraction iofalling 0ut_eide.the tolerance’ limits. How can we re'_dn_oe
`this-nonconformingiii-action to an-fiI.ec.onOInic minimum? A little refiection
`shows’ thnt.the'-simple specification of the go, no-_g"o. tolerance limits (p.- 3)
`_ _i_§.7not "in: such instolnces 2'-from the’-viewpoint of economy and
`' assurance of ‘l‘!¢¥1il5}'-
`‘
`of thisj.chapt_er,'n.-‘e shall consider con-
`As was mentioned at the
`trolffrom ‘the v'ieWpoint_s of specification, produet'io_’n,. and inspection of '
`quality-, as is ne<':es_sary if we are to understand clearly the role played by
`statistical theory" in"the economic-control of thequality of a rnanufactui-'e.d
`"product. To illustrate, suppose we fix our attention on some kind of
`nia}terial,'pieoepa.rt,_ 'or'ph_}_'sical object that we wish to produce in large
`quantifies, and let ustsymboliae the pieces of this product by the letters
`
`-
`
`011 ‘O2:
`
`' ' '4 of} '
`
`'
`
`'3 oil: 0II+l:
`
`'
`
`'
`
`'3 'O'I+J'I
`
`' ' "
`
`presum-ing theta-'-.gi.ven proo_oss_ of:'-'p.rjgclu._ction may be-employed to turn -out
`indefinitely large number of‘ pieces‘-;. We_'_sl1s.l_1_soo_n see that corre_sp'em_1,
`ingfto the3.three_steps in control there are at least thrvee senses in which the
`"statistical control” may be-used in respect to such an 'mfim't'e__ -
`sequence of product.
`.
`In the first pla.ce,.prior to the production of any-ofthe 0's, the engineer
`may, propose" to attain-a sequence. of .0’s that have the property of
`_b_ee_n- produced -under a_ state jof"=statistical control,
`In the s‘e._c9nd_ place.. the engineer, "before he." starts
`the. production. of any -specific sequence of"objects,- is
`sure to focus his attention on the acts or‘ operations that hewishes.
`to be denied out in the‘produetion- of thepieces of -product. Often-, when
`
`I ¢onc_ept- of the state:
`-i:é::e.:'t4itiaide1..controI
`
`"
`
`

`
`BTATI STI CAL CONTROL
`
`
`
`_" is to produce a sequence ‘of _objects having -a specified quality
`_risti_c within s_ome specified limits, the engineer will refer to the
`of production as an operation of control. The available scientific
`
`-i-"3"" °f °°m“'1'
`‘H
`
`{control -.of quality" by means of gauges, measuring instruments, and
`'
`different forms of mechanical technique: much of this
`literature makes no reference to the use of -statistics,
`though in recent years the actual _opera_tions of con-
`trol have often involved the use of statistical tech-
`_
`such as, for example, the control chart.
`In order to distinguish the
`not‘ control in the more general sensefrorn thatin which statistical
`‘es are used for the purp