The Robustness of experimental designs against errors in the factor levels

Vuchkov, Ivan N.; Boyadjieva, Lidia N.

doi:10.1080/00949658308810635

Cited by 10 publications

(5 citation statements)

References 8 publications

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“…It is also possible that there are some known or unknown deviations from the planned experimental conditions. For robustness against such deviations see for example Vuchkov and Boyadjieva (1983) and Carroll et aI. (1993).…”

Section: Discussionmentioning

confidence: 99%

Robust Planning and Analysis of Experiments

Müller

1997

Lecture Notes in Statistics

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Section: Discussionmentioning

confidence: 99%

Robust Planning and Analysis of Experiments

Müller

1997

Lecture Notes in Statistics

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“…A related notion of robustness deals with errors in the factor levels. Vuchkov and Boyadjieva (1983) consider this problem and attempt to determine design families that are robust. The interested reader should first read Box (1963) in which the effect of errors in factor levels is considered in both first and second order models.…”

Section: Rsm Design Robustnessmentioning

confidence: 99%

Response Surface Methodology

Myers¹,

Montgomery²

1996

IIE Transactions

1,108

525

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Approved for Public Release: Distribution Unlimited 17. OiSTAiSuTiON STATEMENT (of the ob.trocl -ntoted IA Block 20, It different 1-m. Roporl) If. SUPPLEMENTARY NOTES 19. KEY *ORDS (Comntin~ue onrvrse 00.... It necateottv aid Identity by block number) Response Surface, Review, Design, Analysis. 20 ABSTRACT (Contln..e an roers*9 old* It flec*esorYan id hentity by block number)This paper provides a thorough review of response surface methodology since 1966. The review covers topics pertaining to the design and analysis of response surfaces. Multirespone techniques associated with optimization and lack of fit testing are also covered.

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“…In Section 2 we discuss how the analysis of the data is a ected if the actual design is not known and introduce a measure for design robustness that is easer to calculate and interpret than those used previously by Draper and Beggs (1970) and Vuchkov and Boyadjieva (1983). We show that when the actual design can be recorded exactly and prior information about the errors in setting the factor levels is available, other generalizations of the D-optimality criterion than that used by Pronzato (1998Pronzato ( , 2002 are more appropriate.…”

Section: Introductionmentioning

confidence: 99%

“…However, they also recognize that ÿnding an analytical proof for any optimality conditions when there are two or more factors is very di cult and recommend searching numerically for a solution. Vuchkov and Boyadjieva (1983) point out that in general the errors in the factor levels introduce heterogeneity in the variance of the response and propose the robustness of the design to such errors to be measured by the maximum element of the covariance matrix for the response or by its trace. Pronzato (1998Pronzato ( , 2002 also considers the case when the planned (or target) design in the experiment cannot be achieved due to errors in the factor levels.…”

Section: Introductionmentioning

confidence: 99%

Design of experiments in the presence of errors in factor levels

Donev

2004

Journal of Statistical Planning and Inference

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This paper is concerned with the statistical properties of experimental designs where the factor levels cannot be set precisely. When the errors in setting the factor levels cannot be measured, design robustness is explored. However, when the actual design could be measured at the end of the investigation, its optimality is of interest. D-optimality could be assessed in di erent ways. Several measures are compared. Evaluating them is di cult even in simple cases. Therefore, in general, simulations are used to obtain their values. It is shown that if D-optimality is measured by the expected value of the determinant of the information matrix of the experimental design, as has been suggested in the past, on average the designs appear to improve with the variance of the error in setting the factor levels. However, we argue that the criterion of D-optimality should be based on the inverse of the information matrix. In this case it is shown that the experiment could be better or worse than the planned one. It is also recognized that setting the factor levels with error could lead to an increased risk of losing observations, which on its own could reduce considerably the optimality of the experimental designs. Advice on choosing the design region in such a way that such a risk is controlled to an acceptable level is given.

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The Robustness of experimental designs against errors in the factor levels

Cited by 10 publications

References 8 publications

Robust Planning and Analysis of Experiments

Robust Planning and Analysis of Experiments

Response Surface Methodology

Design of experiments in the presence of errors in factor levels

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