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Statements

Subject Item: dbr:Orthogonal_array
rdf:type: yago:Location100027167 yago:Object100002684 yago:GeographicalArea108574314 dbo:MartialArtist yago:Tract108673395 yago:PhysicalEntity100001930 yago:YagoLegalActorGeo yago:PublicSquare108619620 yago:YagoPermanentlyLocatedEntity yago:YagoGeoEntity yago:WikicatLatinSquares yago:Region108630985
rdfs:label: 직교 배열 Orthogonales Feld 直交表 Orthogonal array
rdfs:comment: In mathematics, an orthogonal array is a "table" (array) whose entries come from a fixed finite set of symbols (typically, {1,2,...,n}), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t-tuples of the symbols, formed by taking the entries in each row restricted to these columns, appear the same number of times. The number t is called the strength of the orthogonal array. Here is a simple example of an orthogonal array with symbol set {1,2} and strength 2: 조합론에서 직교 배열(直交配列, 영어: orthogonal array)은 좌표들의 부분 집합으로 제한하였을 때 모든 가능한 벡터들이 균등하게 분포되어 있는, 주어진 유한 집합 위의 벡터들의 유한 집합이다. 直交表（ちょっこうひょう）とは、どの2列をとっても、その水準のすべての組み合わせが同数回現れる配列(表)のことである。これを「その2列はバランスしている」あるいは「直交している」と呼ぶ。この性質を使って、実験計画法において因子と水準の割り付け表に用いられる。一般的な多元配置の実験では、一つの因子のみを変化させた条件で行うため、膨大な数の実験を行わなければならない。直交表で割り付けた実験は、複数の因子を変化させるが、どの因子・水準の組み合わせも同回数だけ実験するようにし、その因子の主効果を求められる。最小限の実験数に抑えられるという利点がある。直交表を用いる実験は、交互作用に重きをおかず、主効果のみの実験を行う目的の場合に適する。 Orthogonale Felder (eng.: Orthogonal Arrays) sind Tabellen, die im Rahmen der statistischen Versuchsplanung zur Erstellung von Versuchsplänen verwendet werden. Ein orthogonales Feld (genauer gesagt ein orthogonales Feld mit festen Elementen) von -Elementen, bezeichnet mit ist eine -Matrix, deren Spalten die Eigenschaft haben, dass in jedem Spaltenpaar jedes der möglichen geordneten Elementpaare gleich oft vorkommt.
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dbo:abstract: 直交表（ちょっこうひょう）とは、どの2列をとっても、その水準のすべての組み合わせが同数回現れる配列(表)のことである。これを「その2列はバランスしている」あるいは「直交している」と呼ぶ。この性質を使って、実験計画法において因子と水準の割り付け表に用いられる。一般的な多元配置の実験では、一つの因子のみを変化させた条件で行うため、膨大な数の実験を行わなければならない。直交表で割り付けた実験は、複数の因子を変化させるが、どの因子・水準の組み合わせも同回数だけ実験するようにし、その因子の主効果を求められる。最小限の実験数に抑えられるという利点がある。直交表を用いる実験は、交互作用に重きをおかず、主効果のみの実験を行う目的の場合に適する。 조합론에서 직교 배열(直交配列, 영어: orthogonal array)은 좌표들의 부분 집합으로 제한하였을 때 모든 가능한 벡터들이 균등하게 분포되어 있는, 주어진 유한 집합 위의 벡터들의 유한 집합이다. In mathematics, an orthogonal array is a "table" (array) whose entries come from a fixed finite set of symbols (typically, {1,2,...,n}), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t-tuples of the symbols, formed by taking the entries in each row restricted to these columns, appear the same number of times. The number t is called the strength of the orthogonal array. Here is a simple example of an orthogonal array with symbol set {1,2} and strength 2: Notice that the four ordered pairs (2-tuples) formed by the rows restricted to the first and third columns, namely (1,1), (2,1), (1,2) and (2,2), are all the possible ordered pairs of the two element set and each appears exactly once. The second and third columns would give, (1,1), (2,1), (2,2) and (1,2); again, all possible ordered pairs each appearing once. The same statement would hold had the first and second columns been used. This is thus an orthogonal array of strength two. Orthogonal arrays generalize, in a tabular form, the idea of mutually orthogonal Latin squares. These arrays have many connections to other combinatorial designs and have applications in the statistical design of experiments, coding theory, cryptography and various types of software testing. Orthogonale Felder (eng.: Orthogonal Arrays) sind Tabellen, die im Rahmen der statistischen Versuchsplanung zur Erstellung von Versuchsplänen verwendet werden. Ein orthogonales Feld (genauer gesagt ein orthogonales Feld mit festen Elementen) von -Elementen, bezeichnet mit ist eine -Matrix, deren Spalten die Eigenschaft haben, dass in jedem Spaltenpaar jedes der möglichen geordneten Elementpaare gleich oft vorkommt.
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