Integrating the Lambert W function to a tolerance optimization problem

Sangmun Shin, Madhumohan S. Govindaluri, Byung Rae Cho*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


This paper explores the integration of the Lambert W function to a tolerance optimization problem with the assessment of costs incurred by both the customer and a manufacturer. By trading off manufacturing and rejection costs, and a quality loss, this paper shows how the Lambert W function, widely used in physics, can be efficiently applied to the tolerance optimization problem, which may be the first attempt in the literature related to tolerance optimization and synthesis. Using the concept of the Lambert W function, a closed-form solution is derived, which may serve as a means for quality practitioners to make a quick decision on their optimal tolerance without resorting to rigorous optimization procedures using numerical methods. A numerical example is illustrated and a sensitivity analysis is performed.

Original languageEnglish
Pages (from-to)795-808
Number of pages14
JournalQuality and Reliability Engineering International
Issue number8
Publication statusPublished - Dec 2005
Externally publishedYes


  • Lambert W function
  • Optimal specification limits
  • Optimization
  • Tolerance design

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


Dive into the research topics of 'Integrating the Lambert W function to a tolerance optimization problem'. Together they form a unique fingerprint.

Cite this