Analyzing Dispersion Effects from Replicated Factorial Experiments

Article

Nair, Vijayan N.; Pregibon, Daryl   (1988, ASQC and the American Statistical Association)   AT&T Bell Laboratories, Murray Hill, NY

Technometrics    Vol. 30    No. 3
QICID: 9354    August 1988    pp. 247-257
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Article Abstract

Recent developments in quality engineering methods have led to considerable interest in the analysis of dispersion effects from designed experiments. A commonly used method for identifying important dispersion effects from replicated experiments is based on least squares analysis of the logarithm of the within-replication variance (Bartlett and Kenbdall 1946). Box and Meyer (1986) introduced a pooling technique for unreplicated two-level experiments. We extend this to replicated two-level experiments and compare its performance with the least squares analysis. We show that both of these methods can be obtained as special cases of maximum likelihood estimation under normal theory. The pooling technique is generally biased and is not recommended for model identification. The least squares analysis performs well as a model identification tool, but the estimators can be inefficient. In such cases we recommend that the parameters of the identified submodel be estimated by maximum likelihood. We derive some properties of the maximum likelihood estimator in balanced designs. An experiment for the robust design of leaf springs for trucks is used to illustrate the results.

Keywords

Robust design,Efficiency,Least squares,Maximum likelihood estimate (MLE),Identification,Quality improvement (QI)


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