Measured quantity value estimator for multiplicative nonlinear measurement models

Ye Chow Kuang, Arvind Rajan, Melanie Po Leen Ooi, Serge N. Demidenko

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


An estimate of a measurand using a nonlinear function of uncorrelated input quantities can be done by either applying the nonlinear function to the means of the input quantities (Method 1) or calculating the mean of a set of values obtained from propagating individual measurement values through the nonlinear function (Method 2). This paper proposes an improvement over the standard Method 2 procedures when the input quantities are assumed to be statistically independent and the nonlinear function has a general sum-of-product form, which covers many common measurement models. This paper shows that the proposed new approach (called Method 2S), if applicable, always produces a mean-squared error smaller than that of the conventional Method 2 procedures. The proposed approach improves the efficiency of Type-A evaluation as well as the Monte Carlo method. It also well complements the mainstream practices in the measurement uncertainty evaluation.

Original languageEnglish
Article number7857051
Pages (from-to)715-722
Number of pages8
JournalIEEE Transactions on Instrumentation and Measurement
Issue number4
Publication statusPublished - 1 Apr 2017


  • Estimation
  • Guide to the Expression of Uncertainty in Measurement (GUM)
  • independence
  • measurement
  • measurement data handling
  • nonlinear systems
  • Type-A procedure
  • uncertainty

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