A stratified sampling model in spherical feature inspection using coordinate measuring machines

Kai-Tai Fang*, Song-Gui Wang, Gang Wei

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

7 Citations (Scopus)


A coordinate measuring machine (CMM) is a computer-controlled device that uses a probe to obtain measurements on a manufactured part's surface. In the process of collecting, analyzing and interpreting CMM data, many statistical problems arise. One of them is to choose a model describing the relationship between the location and shape parameters of the part and CMM data and representing the effects of the various sources of randomness of these data. This article suggests a linear model for a stratified sampling scheme, which is one of the most commonly discussed in the CMM literature, in fitting a spherical surface. A feasible generalized least-squares estimator of the part's spherical parameter set is given and its property is studied. Our theoretical results indicate that stratified sampling performs better than random sampling. A similar conclusion was also obtained by Caskey et al. (1990, Design Manufacturing Systems Conf. 779–786) and Xu (1992, M.S. thesis, University of Texas - EI Paso, Mechanical and Industrial Engineering Department, unpublished) using the Monte Carlo experiments for some quite different situations.
Original languageEnglish
Pages (from-to)25-34
Number of pages10
JournalStatistics and Probability Letters
Issue number1
Early online date4 Dec 2000
Publication statusPublished - 1 Jan 2001
Externally publishedYes

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Computer aided design
  • Coordinate measuring machine
  • Linear model
  • Random effect
  • Stratified sampling


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