Small sample performance of some statistical setup adjustment methods

Enrique Del Castillo, Rong Pan, Bianca M. Colosimo

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The setup adjustment problem occurs when a machine experiences an upset at setup that needs to be compensated for. In this article, feedback methods for the setup adjustment problem are studied from a small-sample point of view, relevant in modern manufacturing. Sequential adjustment rules due to Grubbs (Grubbs, F. E. (1954). An optimum procedure for setting machines or adjusting processes. Industrial Quality Control July) and an integral controller are considered. The performance criteria is the quadratic off-target cost incurred over a small number of parts produced. Analytical formulae are presented and numerically illustrated. Two cases are considered, the first one where the setup error is a constant but unknown offset and the second one where the setup error is a random variable with unknown first two moments. These cases are studied under the assumption that no further shifts occur after setup. It is shown how Grubbs' harmonic rule and a simple integral controller provide a robust adjustment strategy in a variety of circumstances. As a by-product, the formulae presented in this article allow to compute the expected off-target quadratic cost when a sudden shift occurs during production (not necessarily at setup) and the adjustment scheme compensates immediately after its occurrence.

Original languageEnglish (US)
Pages (from-to)923-941
Number of pages19
JournalCommunications in Statistics Part B: Simulation and Computation
Issue number3
StatePublished - Aug 2003
Externally publishedYes


  • Integral control
  • Process adjustment
  • Stochastic approximation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation


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