ASTM E1325-2015 Standard Terminology Relating to Design of Experiments《实验设计相关标准术语》.pdf
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1、Designation: E1325 02 (Reapproved 2008)E1325 15 An American National StandardStandard Terminology Relating toDesign of Experiments1This standard is issued under the fixed designation E1325; the number immediately following the designation indicates the year oforiginal adoption or, in the case of rev
2、ision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This standard includes those statistical items related to the area of design of experiments for whi
3、ch standard definitionsappearsappear desirable.2. Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and Statistics3. Significance and Use3.1 This standard is a subsidiary to Terminology E456.3.2 It provides definitions, descriptions, discussion, and comparison of terms.4.
4、Terminologyaliases, nin a fractional factorial design, two or more effects which are estimated by the same contrast and which, therefore,cannot be estimated separately.DISCUSSION(1) The determination of which effects in a 2n factorial are aliased can be made once the defining contrast (in the case o
5、f a half replicate) or definingcontrasts (for a fraction smaller than 12) are stated.The defining contrast is that effect (or effects), usually thought to be of no consequence, about whichall information may be sacrificed for the experiment.An identity, I, is equated to the defining contrast (or def
6、ining contrasts) and, using the conversionthat A2 = B2 = C2 = I, the multiplication of the letters on both sides of the equation shows the aliases. In the example under fractional factorial design,I = ABCD. So that: A = A2BCD = BCD, and AB = A2B2CD = CD.(2) With a large number of factors (and factor
7、ial treatment combinations) the size of the experiment can be reduced to 14, 18, or in general to 12kto form a 2 n-k fractional factorial.(3) There exist generalizations of the above to factorials having more than 2 levels.balanced incomplete block design (BIB), nan incomplete block design in which
8、each block contains the same number k ofdifferent versions from the t versions of a single principal factor arranged so that every pair of versions occurs together in thesame number, , of blocks from the b blocks.DISCUSSIONThe design implies that every version of the principal factor appears the sam
9、e number of times r in the experiment and that the following relationshold true: bk = tr and r (k 1) = (t 1).For randomization, arrange the blocks and versions within each block independently at random. Since each letter in the above equations representsan integer, it is clear that only a restricted
10、 set of combinations (t, k, b, r, ) is possible for constructing balanced incomplete block designs. For example,t = 7, k = 4, b = 7, = 2. Versions of the principal factor:1 This terminology is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of
11、Subcommittee E11.10 on Sampling /Statistics. The definitions in this standard were extracted from E456 89c.Current edition approved April 1, 2008Oct. 1, 2015. Published May 2008October 2015. Originally approved in 1990. Last previous edition approved in 20022008 asE1325 02.E1325 02 (2008). DOI: 10.1
12、520/E1325-02R08.10.1520/E1325-15.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM
13、 standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all
14、 cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1colwidth=“19.00*“/COLSPECBlock 1 1 2 3 62 2 3 4 73 3 4 5 14 4 5 6 25 5 6 7 3
15、6 6 7 1 47 7 1 2 5completely randomized design, na design in which the treatments are assigned at random to the full set of experimental units.DISCUSSIONNo block factors are involved in a completely randomized pletely randomized factorial design, na factorial experiment (including all replications)
16、run in a completely posite design, na design developed specifically for fitting second order response surfaces to study curvature, constructed byadding further selected treatments to those obtained from a 2n factorial (or its fraction).DISCUSSIONIf the coded levels of each factor are 1 and + 1 in th
17、e 2n factorial (see notation 2 under discussion for factorial experiment), the (2n + 1) additionalcombinations for a central composite design are (0, 0, ., 0), (6a, 0, 0, ., 0) 0, 6a, 0, ., 0) ., (0, 0, ., 6 a). The minimum total number of treatmentsto be tested is (2n + 2n + 1) for a 2n factorial.
18、Frequently more than one center point will be run. For n = 2, 3 and 4 the experiment requires, 9, 15,and 25 units respectively, although additional replicate runs of the center point are usual, as compared with 9, 27, and 81 in the 3n factorial. Thereduction in experiment size results in confounding
19、, and thereby sacrificing, all information about curvature interactions. The value of a can be chosento make the coefficients in the quadratic polynomials as orthogonal as possible to one another or to minimize the bias that is created if the true formof response surface is not quadratic.confounded
20、factorial design, na factorial experiment in which only a fraction of the treatment combinations are run in eachblock and where the selection of the treatment combinations assigned to each block is arranged so that one or more prescribedeffects is(are) confounded with the block effect(s), while the
21、other effects remain free from confounding.NOTE 1All factor level combinations are included in the experiment.DISCUSSIONExample: In a 23 factorial with only room for 4 treatments per block, the ABC interaction (ABC: (1) + a + b ab + c ac bc + abc) can besacrificed through confounding with blocks wit
22、hout loss of any other effect if the blocks include the following.following:Block 1 Block 2Treatment (1) aCombination ab b(Code identification shown in discus-sion under factorial experiment)acbccabcBlock 1 Block 2Treatment (1) aCombination ab b(Code identification shown in discus-sion under factori
23、al experiment)acbccabcThe treatments to be assigned to each block can be determined once the effect(s) to be confounded is(are) defined. Where only one term is tobe confounded with blocks, as in this example, those with a positive sign are assigned to one block and those with a negative sign to the
24、other.There are generalized rules for more complex situations. A check on all of the other effects (A, B, AB, etc.) will show the balance of the plus andminus signs in each block, thus eliminating any confounding with blocks for them.The treatments to be assigned to each block can be determined once
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