A weighted three-point-based methodology for variance estimation

Thaweepat Buranathiti, Jian Cao*, Wei Chen, Z. Cedric Xia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


It is widely accepted that variations in manufacturing processes are inevitable and should be taken into account during analysis and design processes. However, estimating uncertainty propagation in an end-product caused by these variations is a very challenging task, especially when a computationally expensive effort is already needed in deterministic models, such as simulations of sheet metal forming. The focus of this article is on the variance estimation of a system response using sensitivity-based methods. A weighted three-point-based strategy for efficiently and effectively estimating the variance of a system response is proposed. Three first-order derivatives of each variable are used to describe the non-linear behaviour and estimate the variance of a system. A methodology for determining the optimal locations and weights of the three points along each axis is proposed and illustrated for the cases where each variable follows either a normal distribution or a uniform distribution. An extension of the weighted three-point-based strategy is introduced to take into account the interaction between parameters. In addition, an extension is given for mean estimation of the system response without requiring more data. The considerable improvement in accuracy compared with the traditional first-order approximation is demonstrated in a number of test problems. The proposed method requires significantly less computational effort than the Monte Carlo method.

Original languageEnglish (US)
Pages (from-to)557-576
Number of pages20
JournalEngineering Optimization
Issue number5
StatePublished - Jul 1 2006


  • First-order approximation
  • Mean estimation
  • Uncertainty propagation
  • Variance estimation
  • Weighted three-point-based strategy

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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