SANS 29901-2010 Selected illustrations of full factorial experiments with four factors《选择的含4个参数的阶乘试验的实例》.pdf

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1、 Collection of SANS standards in electronic format (PDF) 1. Copyright This standard is available to staff members of companies that have subscribed to the complete collection of SANS standards in accordance with a formal copyright agreement. This document may reside on a CENTRAL FILE SERVER or INTRA

2、NET SYSTEM only. Unless specific permission has been granted, this document MAY NOT be sent or given to staff members from other companies or organizations. Doing so would constitute a VIOLATION of SABS copyright rules. 2. Indemnity The South African Bureau of Standards accepts no liability for any

3、damage whatsoever than may result from the use of this material or the information contain therein, irrespective of the cause and quantum thereof. ISBN 978-0-626-23815-5 SANS 29901:2010Edition 1ISO/TR 29901:2007Edition 1SOUTH AFRICAN NATIONAL STANDARD Selected illustrations of full factorial experim

4、ents with four factors This national standard is the identical implementation of ISO/TR 29901:2007 and is adopted with the permission of the International Organization for Standardization. Published by SABS Standards Division 1 Dr Lategan Road Groenkloof Private Bag X191 Pretoria 0001Tel: +27 12 428

5、 7911 Fax: +27 12 344 1568 www.sabs.co.za SABS SANS 29901:2010 Edition 1 ISO/TR 29901:2007 Edition 1 Table of changes Change No. Date Scope National foreword This South African standard was approved by National Committee SABS TC 169, Applications of statistical methods, in accordance with procedures

6、 of the SABS Standards Division, in compliance with annex 3 of the WTO/TBT agreement. This SANS document was published in March 2010. Reference numberISO/TR 29901:2007(E)ISO 2007TECHNICAL REPORT ISO/TR29901First edition2007-11-01Selected illustrations of full factorial experiments with four factors

7、Illustrations choisies de plans dexprience factoriels complets quatre facteurs SANS 29901:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO/TR 29901:2007(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with

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10、 care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. COPYRIGHT PROTECTED DOCUMENT ISO 2007 All rights reserved. Unless otherwise specified

11、, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISOs member body in the country of the requester. ISO copyright office Case p

12、ostale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2007 All rights reservedSANS 29901:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO/TR 299

13、01:2007(E) ISO 2007 All rights reserved iiiContents Page Foreword iv Introduction v 1 Scope . 1 2 Normative references . 1 3 Terms and definitions. 2 4 Symbols and abbreviated terms . 4 5 Generic description of full factorial designs . 4 5.1 Overview of the structure of the four factor examples in A

14、nnexes A through E. 4 5.2 Overall objective(s) of the experiment 4 5.3 Response variable(s) 5 5.4 Factors affecting the response(s). 5 5.5 “Full” factorial design 5 5.6 Analyse the results Numerical summaries and graphical displays 6 5.7 Present the results 7 5.8 Perform confirmation runs 7 6 Descri

15、ption of Annexes A through E 7 6.1 Comparing and contrasting the examples. 7 6.2 Experiment summaries 7 Annex A (informative) Solder bar experiment . 8 Annex B (informative) Direct mail marketing campaign. 17 Annex C (informative) Button tactility experiment 25 Annex D (informative) Optimizing a cus

16、tomer PVC formulation. 34 Annex E (informative) Genetic algorithms for DNA sequencing experiment. 44 Bibliography . 52 SANS 29901:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO/TR 29901:2007(E) iv ISO 2007 All rights reservedForeword

17、 ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical

18、 committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of elec

19、trotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the

20、 member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. In exceptional circumstances, when a technical committee has collected data of a different kind from that which is normally published as an International Standa

21、rd (“state of the art”, for example), it may decide by a simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely informative in nature and does not have to be reviewed until the data it provides are considered to be no longer valid or useful. A

22、ttention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO/TR 29901 was prepared by Technical Committee ISO/TC 69, Applications of statistical methods. SANS

23、29901:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO/TR 29901:2007(E) ISO 2007 All rights reserved vIntroduction The Six Sigma and international statistical standards communities share a philosophy of continuous improvement and many

24、analytical tools. The Six Sigma community tends to adopt a pragmatic approach driven by time and resource constraints. The statistical standards community arrives at rigorous documents through long-term international consensus. The disparities in time pressures, mathematical rigor and statistical so

25、ftware usage have inhibited exchanges, synergy and mutual appreciation between the two groups. The present document takes one specific statistical tool (full factorial designs with four factors, 24 designs) and develops the topic somewhat generically (in the spirit of International Standards) but th

26、en illustrates it through the use of five detailed and distinct applications. The generic description focuses on the commonalities across 24 designs. These commonalities hold more generally for arbitrary numbers of factors, but a value of four was chosen for this Technical Report. The annexes contai

27、ning the five illustrations follow the basic framework but also identify the nuances and peculiarities in the specific applications. Each example offers at least one “wrinkle” to the problem, which is generally the case for real Six Sigma applications. It is thus hoped that practitioners can identif

28、y with at least one of the five examples, if only to remind them of the basic material on factorial designs that was encountered during their Six Sigma training. Each of the five examples is developed and analysed using statistical software of current vintage. The explanations throughout are devoid

29、of mathematical detail such material can be readily obtained from the many design and analysis of experiments textbooks available (such as those given in the Bibliography). SANS 29901:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .SANS 2

30、9901:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .TECHNICAL REPORT ISO/TR 29901:2007(E) ISO 2007 All rights reserved 1Selected illustrations of full factorial experiments with four factors 1 Scope This Technical Report describes the st

31、eps necessary to specify, to use and to analyse 24full factorial designs through illustration, with five distinct applications of this methodology. Depending on the application, a number of factors other than four may be considered in the experiment. NOTE 1 Each of these five illustrations is simila

32、r in that sufficient resources were available to implement the design. Other commonalities among the five examples are noted (e.g. study objective, two levels for factors, response variable(s), factors effecting the response). The individual illustrations have some salient features that are distinct

33、 such as presence/absence of repetitions, centre points, interactions, or different types of response variables. Each illustration takes place in a different environment such as marketing, software, manufacturing, telecommunications and chemical processing. NOTE 2 For the purposes of this Technical

34、Report, the selection of four factors with two levels (aside from centre points) was made in advance. Furthermore, the detailed use of response surface designs as a follow-up or augmentation of the existing designs was excluded from this Technical Report, although their use is noted in some of the i

35、llustrations. Likewise, Taguchi designs and blocking designs were not included. NOTE 3 Full factorial experiments are often employed by individuals (so-called “black belts” or “green belts”) associated with Six Sigma methods. Six Sigma methods are concerned with problem solving and continuous improv

36、ement. A full factorial experiment with four factors is one of many tools available to Six Sigma practitioners, but hitherto has not been addressed in detail in ISO International Standards. 2 Normative references The following referenced documents are indispensable for the application of this docume

37、nt. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 3534-1:2006, Statistics Vocabulary and symbols Part 1: General statistical terms and terms used in probability ISO 3534-2, Statistic

38、s Vocabulary and symbols Part 2: Applied statistics ISO 3534-3:1999, Statistics Vocabulary and symbols Part 3: Design of experiments SANS 29901:2010This s tandard may only be used and printed by approved subscription and freemailing clients of the SABS .ISO/TR 29901:2007(E) 2 ISO 2007 All rights res

39、erved3 Terms and definitions For the purposes of this document, the terms and definitions in ISO 3534-1, ISO 3534-2, ISO 3534-3 and the following apply. 3.1 analysis of variance ANOVA technique which subdivides the total variation of a response variable into meaningful components associated with spe

40、cific sources of variation NOTE Adapted from ISO 3534-3:1999, definition 3.4. 3.2 binomial distribution discrete distribution having the probability mass function !() (1)!( )!x nxnPX x p pxn x= where x = 0, 1, , n and with indexing parameters n = 1, 2, , and 0 0 NOTE Adapted from ISO 3534-1:2006, de

41、finition 2.50. 3.11 predictor variable variable that can contribute to the explanation of the outcome of an experiment NOTE Adapted from ISO 3534-3:1999, definition 1.3. 3.12 randomization process used to assign treatments to experimental units so that each experimental unit has an equal chance of b

42、eing assigned a particular treatment NOTE Adapted from ISO 3534-3:1999, definition 1.29. 3.13 replication performance of an experiment more than once for a given set of predictor variables NOTE Adapted from ISO 3534-3:1999, definition 1.27. 3.14 split-plot design design in which a group of experimen

43、tal units (plot) to which the same level assigned to the principal factor is subdivided (split) so as to study one or more additional principal factors within each level of that factor NOTE Adapted from ISO 3534-3:1999, definition 2.3.6. SANS 29901:2010This s tandard may only be used and printed by

44、approved subscription and freemailing clients of the SABS .ISO/TR 29901:2007(E) 4 ISO 2007 All rights reserved4 Symbols and abbreviated terms The symbols and abbreviated terms used in this Technical Report are as follows: y Response variable A, B, C, D Factors AB, AC, AD, BC, BD, CD 2-way interactio

45、ns ABC, ACD, BCD 3-way interactions ABCD 4-way interactions +1/1 High and low settings 24Four factors each with two levels Standard deviation 5 Generic description of full factorial designs 5.1 Overview of the structure of the four factor examples in Annexes A through E This Technical Report provide

46、s general guidelines on the design, conduct and analyses of two-level full factorial designs and illustrates the steps with five distinct applications given in Annexes A through E. Each of these five examples follows the basic structure given in Table 1. The steps given in Table 1 apply to design an

47、d analysis of experiments in general, although this Technical Report focuses on 24full factorial designs. Each of the seven steps is explained in general below. Specific explanations of the substance of these steps is provided in the examples in Annexes A through E. Table 1 Basic steps in experiment

48、al design 1 State the overall objective(s) of the experiment 2 Describe the response variable(s) 3 List the factors that might affect the response(s) 4 Select a “full” factorial design 5 Analyse the results Numerical summaries and graphical displays 6 Present the results 7 Perform a confirmation run

49、 5.2 Overall objective(s) of the experiment Experiments are conducted for a variety of reasons. The primary motivation for the experiment should be clearly stated and agreed to by all parties involved in the design, conduct, analysis and implications of the experimental effort. There may be secondary objectives which could be addressed with the full factorial experiment. The ultimate outcome of the experiment could be to take immediate action on factor levels or to obtain a predictive model, both of which dictate some elem