Response surface modeling and optimization in multiresponse experiments using seemingly unrelated regressions

Harry K. Shah, Douglas Montgomery, W. Matthew Carlyle

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


Response surface methodology (RSM) is widely used for optimizing manufacturing processes and product designs. Most applications of RSM involve several response variables. In a typical RSM study, the experimenter will build an empirical model such as the second-order model to each response and use these models to determine settings on the design variables that produce optimal or at least acceptable values for the responses. In most multiple-response RSM problems, the experimenter fits a model to each response using ordinary least squares (OLS). This article illustrates another estimation technique useful in multiple-response RSM problems, seemingly unrelated regressions (SUR). This technique can be very useful when response variables in a multiple-response RSM problem are correlated. Essentially, SUR produces more precise estimates of the model parameters than OLS when responses are correlated. This improved precision of estimation can lead to a more precise estimate of the optimum operating conditions on the process.

Original languageEnglish (US)
Pages (from-to)387-397
Number of pages11
JournalQuality Engineering
Issue number3
StatePublished - Mar 1 2004


  • Correlated responses
  • Multiresponse experiments
  • Ordinary least squares (OLS)
  • Response surface methodology
  • Seemingly unrelated regression (SUR)

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


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