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Estimating the error of an effect in unreplicated 2‐level fractional factorial designs
Author(s) -
Wang Wenhao,
Lawson John
Publication year - 1988
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.4680040214
Subject(s) - fractional factorial design , estimator , factorial experiment , mathematics , replicate , statistics , design of experiments , variance (accounting) , bayesian probability , distribution (mathematics) , prior probability , mathematical analysis , accounting , business
Abstract Saturated fractional factorial experimental designs and orthogonal main effect plans are extremely valuable tools in quality engineering. However, one problem with these designs is that there are no replicate runs to be used for estimating experimental error. This note develops an estimator of the experimental error based on the hypothesis that not all factor effects will be non‐zero. A joint Bayesian prior distribution is presented for the experimental error variance of an effect, σ 2 , and the probability that each effect is non‐zero. From this prior distribution a posterior marginal distribution for σ 2 is derived along with a direct estimate of σ 2 . This method is compared with the traditional methods of estimating σ 2 in unreplicated designs through a numerical example.