Plackett-Burman 설계

Plackett–Burman design

Plackett-Burman 설계는 영국 공급부에서 근무하던 중 Robin L. Plackett과 J. P. Burman이 1946년에 제시한 실험 설계다.[1]그들의 목표는 제한된 수의 실험을 사용하여 이러한 의존성 추정치의 분산을 최소화하는 방법으로 각각 L 수준을 취하는 다수의 독립 변수(요인)에 대한 일부 측정된 양의 의존성을 조사하기 위한 실험 설계를 찾는 것이었다.요인 간의 상호작용은 무시할 수 있는 것으로 간주되었다.이 문제에 대한 해결책은 모든 실험 런(표 참조)에서 모든 요인 쌍에 대한 수준 조합이 동일한 횟수로 나타나는 실험 설계를 찾는 것이다.완전 요인 설계는 이 기준을 충족하지만, 아이디어는 더 작은 설계를 찾는 것이었습니다.

12개의 런과 11개의 2-수준 요인에[2] 대한 Plackett-Burman 설계 임의의 두 X에i 대해 각 조합( -, -+, +-, ++)은 세 번 나타난다. 즉, 동일한 횟수.
달리다 X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11
1 + + + + + + + + + + +
2 − + − + + + − − − + −
3 − − + − + + + − − − +
4 + − − + − + + + − − −
5 − + − − + − + + + − −
6 − − + − − + − + + + −
7 − − − + − − + − + + +
8 + − − − + − − + − + +
9 + + − − − + − − + − +
10 + + + − − − + − − + −
11 − + + + − − − + − − +
12 + − + + + − − − + − −

두 가지 수준(L = 2)의 경우, Plackett과 Burman은 1933년에 Raymond Paly가 발견한 방법을 원소가 모두 1 또는 -1인 직교 행렬(Hadamard matrix)을 생성하는 데 사용했다.Paley의 방법은 대부분의 N에 대한 N 크기의 행렬이 4의 배수와 같은 것을 찾는 데 사용될 수 있다.특히 N = 92를 제외한 모든 N에서 최대 100까지 작동했다.그러나 N이 2의 검정력인 경우 결과 설계는 부분 요인 설계와 동일하므로 Plackett-Burman 설계는 N이 4의 배수지만 2의 검정력이 아닐 때 주로 사용된다(예: N = 12, 20, 24, 28, 36).[3]N개 미만의 모수(전체 평균 포함)를 추정하려는 경우 행렬의 열 부분 집합을 사용하게 된다.

두 단계 이상의 경우에 대해, Plackett과 Burman은 이전에 Raj Chandra Bose와 K가 주었던 디자인을 재발견했다. 인도 통계 연구소의 키센.[4]Plackett 및 Burman은 L = 3, 4, 5 또는 7에 대해 일부 정수 검정력에 대한 수준 L의 수와 동일한 실험 횟수를 갖는 설계에 대한 세부사항을 제공한다.

요인 간의 교호작용이 무시할 수 없는 경우, 이들은 Plackett-Burman 설계에서 주효과와 혼동되는 경우가 많으며, 이는 설계가 특정 주효과와 특정 교호작용을 구별하는 것을 허용하지 않는다는 것을 의미한다.이것을 앨리어싱 또는 교란이라고 한다.

확장 사용

1993년, 데니스 린은 Plackett-Burman 설계의 반을 통한 건설 방법을 설명했는데, 나머지 열의 절반을 차지하기 위해 하나의 열을 사용했다.[5]결과 행렬(이 열 제외)은 거의 존재하지 않는다는 가정 하에 유의미한 첫 번째 순서 효과를 찾기 위한 "과포화 설계"[6]이다.

Box-Behnken 설계는 Plackett-Burmans로 각각 평면 행렬과 시드 행렬에 사용된 부분 요인 설계와 불완전한 블록을 대체함으로써 더 작거나 매우 큰 설계로 만들 수 있다.예를 들어, 30개의 변수에 대한 2차 설계에는 30개의 열 PB 계획 행렬이 0과 1이 필요하며, 계획 행렬에 PB 시드 행렬이 나타나는 곳마다 -1과 +1(15개 또는 16개 변수)을 사용하여 각 줄의 PB 시드 행렬을 대체하고, -1, 0, +1을 사용하여 557개의 런 설계를 생성하여 전체 2차 모드의 496개 매개변수를 추정한다.l. 축 점을 추가하면 일변량 입방 및 사분위 효과를 추정할 수 있다.

Plackett-Burmans는 특정 열을 추정할 모수와 동일시하여 교호작용 또는 고차 효과와 함께 범주형 및 숫자 설계를 혼합하여 구성할 수도 있으며, 추정할 모형 모수의 수보다 4 런 이상이 필요하지 않다.범주형 변수 A와 다음 열에 할당된 a-1 열을 기준으로 정렬하십시오. 여기서 A = 1 + int(a/i /(max(i) + 0.00001), i = 행 번호 및 a = A의 값 수입니다.다음 정렬은 다른 범주형 변수에 할당된 열과 필요한 경우 반복하는 열.그러한 설계는 크다면 D-최적성과 같은 표준 검색 기법으로는 비교할 수 없을 수 있다.예를 들어 평균 3개의 값을 갖는 변수 13개는 검색할 조합이 100만개를 훨씬 넘을 수 있다.13개 변수의 2차 모형에서 105개의 모수를 추정하려면, 10C10을62 훨씬 넘는, 즉 3C10513 또는 약 10개의484 행렬에 대한 고려에서 공식적으로 제외하거나 X'X를 계산해야 한다.

4-48회 주행, 반분율을 표시하도록 정렬

P.B.4 + + +  + – –  – + –  – – +  P.B.8 + + + + + + +  + + – – – – +  + – + + – – –  + – – – + + –  – + + – + – –  – + – + – + –  – – + – – + +  – – – + + – +  P.B.12 + + + + + + + + + + +  + + + + – – – + – – –  + + – – – + – – + – +  + – + – + + + – – – –  + – – + – – + – + + –  + – – – + – – + – + +  – + + – – – + – – + +  – + – + + + – – – + –– + – – + – + + + – –  – – + + + – – – + – +  – – + – – + – + + + –  – – – + – + + + – – +  P.B.16 + + + + + + + + + + + + + + +  + + + – – – – – – – – + + + +  + + – + – – – – + + + – – – +  + + – – + + + + – – – – – – +  + – + + + – – + + – – + – – –  + – + – – + + – – + + + – – –  + – – + – + + – + – – – + + –  + – – – + – – + – + + – + + –  –+ + + – + – + – + – – + – –  – + + – + – + – + – + – + – –  – + – + + – + – – + – + – + –  – + – – – + – + + – + + – + –  – – + + – – + + – – + – – + +  – – + – + + – – + + – – – + +  – – – + + + – – – – + + + – +  – – – – – – + + + + – + + – +  P.B.20 + + + + + + + + + + + + + + + + + + +  + + + – + – + – – – – + + – – + – – +  + + – + – + – – – –+ + – – + – – + +  + + – + – – – – + + – – + – – + + + –  + + – – – – + + – – + – – + + + + – –  + – + + + + – + – + – – – – + + – – –  + – + – + – – – – + + – – + – – + + +  + – + – – + + + + – + – + – – – – + –  + – – + – – + + + + – + – + – – – – +  + – – – + + – – + – – + + + + – + – –  – + + + + – + – + – – – – + + – – + –  – + + + – + – + –– – – + + – – + – +  – + + – – + – – + + + + – + – + – – –  – + – – + + + + – + – + – – – – + + –  – + – – + – – + + + + – + – + – – – +  – – + + – – + – – + + + + – + – + – –  – – + – – – – + + – – + – – + + + + +  – – – + + + + – + – + – – – – + + – +  – – – + + – – + – – + + + + – + – + –  – – – – – + + – – + – – + + + + – + +  P.B.24 + + + + ++ + + + + + + + + + + + + + + + + +  + + + – + – + + – – + + – – + – + – – – – – +  + + + – – + + – – + – + – – – – – + + + + – –  + + – + + – – + + – – + – + – – – – – + + + –  + + – + – + + – – + + – – + – + – – – – – + +  + + – – – – – + + + + – + – + + – – + + – – –  + – + + – – + – + – – – – – + + + + – + – + –  + – + – + + – – + + – – + – + –– – – – + + +  + – + – + – – – – – + + + + – + – + + – – + –  + – – + + – – + – + – – – – – + + + + – + – +  + – – + – + – – – – – + + + + – + – + + – – +  + – – – – + + + + – + – + + – – + + – – + – –  – + + + + – + – + + – – + + – – + – + – – – –  – + + + – + – + + – – + + – – + – + – – – – +  – + + – – + – + – – – – – + + + + – + – + + –  – + –+ – – – – – + + + + – + – + + – – + + –  – + – – + + – – + – + – – – – – + + + + – + +  – + – – + – + – – – – – + + + + – + – + + – +  – – + + + + – + – + + – – + + – – + – + – – –  – – + + – – + + – – + – + – – – – – + + + + +  – – + – – – – – + + + + – + – + + – – + + – +  – – – + + + + – + – + + – – + + – – + – + – –  – – – – + + + + – + – + +– – + + – – + – + –  – – – – – – + + + + – + – + + – – + + – – + +  P.B.28 + + + + + + + + + + + + + + + + + + + + + + + + + + –  + + + – – + + + – + + – – + + + + – – – – – – – – + +  + + + – – – – – – – – + + + + – – + + + – + + – – + +  + + – + + – – + + + + – – – – – – – – + + + + – – + +  + + – + – – + + – – – + – – + + – + – – + – + – + – –+ + – + – – + – + – + – + + – + – – + + – – – + – – –  + + – – – + – – + + – + – – + – + – + – + + – + – – –  + – + + – + – – + + – – – + – – + + – + – – + – + – –  + – + – + + – + – – + + – – – + – – + + – + – – + – –  + – + – + – + + – + – – + + – – – + – – + + – + – – –  + – + – + – + – + – + – + – + – + – + – + – + – + – +  + – – + + + + – – –– – – – – + + + + – – + + + – + +  + – – + + + – + + – – + + + + – – – – – – – – + + + +  + – – – – – – – – + + + + – – + + + – + + – – + + + +  – + + + + – – + + + – + + – – + + + + – – – – – – – +  – + + + + – – – – – – – – + + + + – – + + + – + + – +  – + + + – + + – – + + + + – – – – – – – – + + + + – +  – + + – – + + + + – – – – – – – – + + ++ – – + + + +  – + – – + + – + – – + – + – + – + + – + – – + + – – –  – + – – + + – – – + – – + + – + – – + – + – + – + + –  – + – – + – + – + – + + – + – – + + – – – + – – + + –  – – + + – + – – + – + – + – + + – + – – + + – – – + –  – – + + – – – + – – + + – + – – + – + – + – + + – + –  – – + – + – + – + + – + – – + + – – – + – – + + – + –  – – –+ + + + – – + + + – + + – – + + + + – – – – – +  – – – + – – + + – + – – + – + – + – + + – + – – + + –  – – – – – + + + + – – + + + – + + – – + + + + – – – +  – – – – – – – + + + + – – + + + – + + – – + + + + – +  P.B.32 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +  + + + + – – – – – – – – – – – – – – – – + + + + + + + + + + +  ++ + – + – – – – – – – – + + + + + + + – – – – – – – + + + +  + + + – – + + + + + + + + – – – – – – – – – – – – – – + + + +  + + – + + – – – – + + + + – – – – + + + – – – – + + + – – – +  + + – + – + + + + – – – – + + + + – – – – – – – + + + – – – +  + + – – + + + + + – – – – – – – – + + + + + + + – – – – – – +  + + – – – – – – – + + + + + + + + – –– + + + + – – – – – – +  + – + + + + – – + + – – + + – – + + – – + – – + + – – + – – –  + – + + – – + + – – + + – – + + – – + + + – – + + – – + – – –  + – + – + – + + – – + + – + – – + + – – – + + – – + + + – – –  + – + – – + – – + + – – + – + + – – + + – + + – – + + + – – –  + – – + + – + + – + – – + – + + – + – – – + + – + – – – + + –  + – – + –+ – – + – + + – + – – + – + + – + + – + – – – + + –  + – – – + + – – + – + + – – + + – + – – + – – + – + + – + + –  + – – – – – + + – + – – + + – – + – + + + – – + – + + – + + –  – + + + + – + – + – + – + – + – + – + – – + – + – + – – + – –  – + + + – + – + – + – + – + – + – + – + – + – + – + – – + – –  – + + – + + – + – + – + – – + – + – + – + –+ – + – + – + – –  – + + – – – + – + – + – + + – + – + – + + – + – + – + – + – –  – + – + + + – + – – + – + + – + – – + – + – + – – + – + – + –  – + – + – – + – + + – + – – + – + + – + + – + – – + – + – + –  – + – – + – + – + + – + – + – + – – + – – + – + + – + + – + –  – + – – – + – + – – + – + – + – + + – + – + – + + – + + – + –  – – + + + – – ++ – – + + – – + + – – + – – + + – – + – – + +  – – + + – + + – – + + – – + + – – + + – – – + + – – + – – + +  – – + – + + + – – + + – – – – + + – – + + + – – + + – – – + +  – – + – – – – + + – – + + + + – – + + – + + – – + + – – – + +  – – – + + + + – – – – + + + + – – – – + + + – – – – + + + – +  – – – + – – – + + + + – – – – + + + + – + + – – – –+ + + – +  – – – – + – – + + + + – – + + – – – – + – – + + + + – + + – +  – – – – – + + – – – – + + – – + + + + – – – + + + + – + + – +  P.B.36 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + –  + + + + – + + + + – – + + – – – – – – + + + + – – – – – – + + – – + +  + + + – – + + – – – – – – + + + + – – – – – – + + – – + + + + +– + +  + + + – – – – – – + + – – + + + + + – + + + + – – + + – – – – – – + +  + + – + + + + – – + + – – – – – – + + + + – – – – – – + + – – + + + +  + + – + – – + – + – + + – – + + – + – – – + – + – – + + – – + – + – –  + + – + – – – + – + – – + + – – + – + – + + – + – – + – + – + + – – –  + + – – + + – + – – – + – + – – + + – – + – + – + + – + –– + – + – –  + + – – + – + – + + – + – – + – + – + + – – + + – + – – – + – + – – –  + – + + – + – – + – + – + + – – + + – + – – – + – + – – + + – – + – –  + – + + – – + + – + – – – + – + – – + + – – + – + – + + – + – – + – –  + – + – + + – + – – + – + – + + – – + + – + – – – + – + – – + + – – –  + – + – + + – – + + – + – – – + – + – – + + – – + – +– + + – + – – –  + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – +  + – – + + + + + – + + + + – – + + – – – – – – + + + + – – – – – – + +  + – – + + – – – – – – + + + + – – – – – – + + – – + + + + + – + + + +  + – – – – – – + + + + – – – – – – + + – – + + + + + – + + + + – – + +  + – – – – – – + + – – + + + + + – + + + + – – ++ – – – – – – + + + +  – + + + + + – + + + + – – + + – – – – – – + + + + – – – – – – + + – +  – + + + + – – + + – – – – – – + + + + – – – – – – + + – – + + + + + +  – + + + + – – – – – – + + – – + + + + + – + + + + – – + + – – – – – +  – + + – – + + + + + – + + + + – – + + – – – – – – + + + + – – – – – +  – + + – – – – – – + + + + – – – – – – + + –– + + + + + – + + + + – +  – + – + – – + + – – + – + – + + – + – – + – + – + + – – + + – + – – –  – + – – + + – – + – + – + + – + – – + – + – + + – – + + – + – – – + –  – + – – + – + – + + – – + + – + – – – + – + – – + + – – + – + – + + –  – + – – – + – + – – + + – – + – + – + + – + – – + – + – + + – – + + –  – – + + – + – – – + – + – – + + – – +– + – + + – + – – + – + – + + –  – – + + – – + – + – + + – + – – + – + – + + – – + + – + – – – + – + –  – – + – + – + + – + – – + – + – + + – – + + – + – – – + – + – – + + –  – – + – + – + + – – + + – + – – – + – + – – + + – – + – + – + + – + –  – – – + + + + – – – – – – + + – – + + + + + – + + + + – – + + – – – +  – – – + + – – + + + + + – + + + +– – + + – – – – – – + + + + – – – +  – – – + – + – – + + – – + – + – + + – + – – + – + – + + – – + + – + –  – – – – – + + + + – – – – – – + + – – + + + + + – + + + + – – + + – +  – – – – – + + – – + + + + + – + + + + – – + + – – – – – – + + + + – +  P.B.40 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + –  + + + + + + +– – + + – – + + – – – – – – – – + + + + – – – – + + – – – – + –  + + + + + – – + + – – + + – – – – – – – – + + + + – – – – + + – – – – + + + –  + + + – – + + – – + + – – – – – – – – + + + + – – – – + + – – – – + + + + + –  + + + – – – – + + – – – – + + + + + + + + – – + + – – + + – – – – – – – – + –  + + – + – + – + – – + + – – + + – – + – + – + –+ + – + – – + – + + – – + – +  + + – + – – + – + + – – + – + + – + – + – + – – + + – – + + – – + – + – + – +  + + – – + + – – + – + – + – + + – + – – + – + + – – + – + + – + – + – + – – +  + + – – + – + + – + – + – + – – + + – – + + – – + – + – + – + + – + – – + – +  + + – – + – + – + – + + – + – – + – + + – – + – + + – + – + – + – – + + – – +  +– + + – + – + – + – – + + – – + + – – + – + – + – + + – + – – + – + + – – +  + – + + – + – – + – + + – – + – + + – + – + – + – – + + – – + + – – + – + – +  + – + + – – + – + + – + – + – + – – + + – – + + – – + – + – + – + + – + – – +  + – + – + + – + – – + – + + – – + – + + – + – + – + – – + + – – + + – – + – +  + – + – + – + + – + – – + – + + – –+ – + + – + – + – + – – + + – – + + – – +  + – – + + – – + + – – – – – – – – + + + + – – – – + + – – – – + + + + + + + –  + – – + + – – – – – – – – + + + + – – – – + + – – – – + + + + + + + + – – + –  + – – – – + + + + + + + + – – + + – – + + – – – – – – – – + + + + – – – – + –  + – – – – + + – – – – + + + + + + + + – – + + – – + + – – – – – – – –+ + + –  + – – – – – – – – + + + + – – – – + + – – – – + + + + + + + + – – + + – – + –  – + + + + + + + + – – + + – – + + – – – – – – – – + + + + – – – – + + – – – –  – + + + + – – – – + + – – – – + + + + + + + + – – + + – – + + – – – – – – – –  – + + – – + + – – – – – – – – + + + + – – – – + + – – – – + + + + + + + + – –  – + + – – – – + + + + + ++ + – – + + – – + + – – – – – – – – + + + + – – – –  – + + – – – – – – – – + + + + – – – – + + – – – – + + + + + + + + – – + + – –  – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + +  – + – + – + – – + + – – + + – – + – + – + – + + – + – – + – + + – – + – + + +  – + – + – – + + – – + + – – + – + – + – + + – + – – + – + +– – + – + + – + +  – + – – + + – – + + – – + – + – + – + + – + – – + – + + – – + – + + – + – + +  – + – – + – + + – – + – + + – + – + – + – – + + – – + + – – + – + – + – + + +  – – + + – – + + – – + – + – + – + + – + – – + – + + – – + – + + – + – + – + +  – – + + – – + – + – + – + + – + – – + – + + – – + – + + – + – + – + – – + + +  – – + – + + –+ – + – + – – + + – – + + – – + – + – + – + + – + – – + – + + +  – – + – + + – – + – + + – + – + – + – – + + – – + + – – + – + – + – + + – + +  – – + – + – + – + + – + – – + – + + – – + – + + – + – + – + – – + + – – + + +  – – – + + + + + + + + – – + + – – + + – – – – – – – – + + + + – – – – + + – –  – – – + + + + – – – – + + – – – – + + + + + + ++ – – + + – – + + – – – – – –  – – – + + – – – – + + + + + + + + – – + + – – + + – – – – – – – – + + + + – –  – – – – – + + + + – – – – + + – – – – + + + + + + + + – – + + – – + + – – – –  – – – – – – – + + + + – – – – + + – – – – + + + + + + + + – – + + – – + + – –  P.B.44 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + +  + + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + –  + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – +  + + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – –  + + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – –+ + – –  + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + +  + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – +  + + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + –  + + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – +– – –  + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + +  + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – +  + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + +  + – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – +– –  + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – +  + – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – –  + – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + –  + – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – ––  + – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + –  + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – +  + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + +  + – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + –+ – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + +  – + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + +  – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + –  – + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – +– + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – –  – + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + +  – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – –  – + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – +  –+ – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + –  – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + –  – + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + +  – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – –  – –+ + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – +  – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + –  – – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + +  – – + – + + + – – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + –  – – +– – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – +  – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – –  – – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – – + – – + +  – – – + – + – – + + + – + + + + + – – – + – + + + – – – – – + – – – + + – + – + + – +  – – – +– – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – –  – – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + – – – – +  – – – – + – – – + + – + – + + – – + – – + – + – – + + + – + + + + + – – – + – + + + –  P.B.48 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ +  + + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + –  + + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – –  + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – +  + + + – – + – + – + + + – – + – – + + – + + – – – + – + – ++ – – – – + – – – – – + + + + – +  + + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + –  + + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – –  + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + +  + + – + + + – – + – – + + – ++ – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – –  + + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – –  + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + +  + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – ++ – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + +  + – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – –  + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – +  + – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – +– – – – – + + + + – + + + –  + – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + –  + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + +  + – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + –  + – – + – – + + – + + – – – + – + –+ + – – – – + – – – – – + + + + – + + + + – – + – + – + +  + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – +  + – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + –  + – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – –  + – –– – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – +  – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – –  – + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – +  – + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – –– + – – – – – + + + + +  – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + –  – + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + +  – + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – +  – + – + – + + + – – + – – + + – + + – –– + – + – + + – – – – + – – – – – + + + + – + + + + –  – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – –  – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + –  – + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + +  – + – – –– + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + +  – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – –  – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – –  – – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + +– + + + + – – + +  – – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + +  – – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – +  – – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – +  – – + – + – + + – – – – + – – – – – + + + + –+ + + + – – + – + – + + + – – + – – + + – + + –  – – + – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – –  – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + – –  – – – + + – + + – – – + – + – + + – – – – + – – – – – + + + + – + + + + – – + – + – + + + – +  – – – + – – – –– + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + –  – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – – + –  – – – – – – + + + + – + + + + – – + – + – + + + – – + – – + + – + + – – – + – + – + + – – – +

참조

  1. ^ R.L. Plackett과 J.P. Burman, "최적 다요소 실험의 설계", Biometric 33 (4), 페이지 305–25, 1946년 6월 도이:10.1093/바이오메트/33.4.305
  2. ^ Plackett-Burman은 통계적 방법의 NIST/SEMATECH 전자 핸드북을 설계한다.
  3. ^ Ledolter, Johannes; Swersey, Arthur J (2007). Testing 1-2-3: experimental design with applications in marketing and service operations. Stanford University Press. ISBN 978-0-8047-5612-9.
  4. ^ R. C. Bose & K. Kishen, "일반 대칭 요인 설계의 교란 문제에 대하여", Sankhya 5, 21 (1940) JSTOR 25047628
  5. ^ 린, D.K.J. 1993년"초포화 설계의 새로운 등급."테크노메트릭스 35, 28-31
  6. ^ V K 굽타, 라젠더 파사드, 바수데프 콜레, 랄 모한 바르, "과포화 디자인", 인도 농업통계연구소, 2011년 10월 18일

Public Domain이 글은 국립표준기술원 웹사이트 https://www.nist.gov의 공공 도메인 자료를 통합한 것이다.