Tolerance optimization using the Lambert W function: An empirical approach

M. S. Govindaluri, S. Shin, B. R. Cho*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (SciVal)


This paper explores the integration of the Lambert W function to a tolerance optimization problem with two unique features. First, the Taguchi loss function has been a popular tool for quantifying a quality loss incurred by the customer. This paper utilizes an empirical approach based on a well-established regression analysis, which may be more appealing to engineers and better capture the customer's perception of product performance. Second, by trading off manufacturing and rejection costs incurred by a manufacturer and quality loss incurred by the customer, this paper shows how the Lambert W function, widely used in physics, can be efficiently applied, which is perhaps the first attempt in the literature related to tolerance optimization and synthesis. Using the concept of the Lambert W function, this paper derives a closed-form solution, which may serve as a means for quality practitioners to make a quick decision on their optimal tolerances 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)3235-3251
Number of pages17
JournalInternational Journal of Production Research
Issue number16
Publication statusPublished - Aug 15 2004
Externally publishedYes

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


Dive into the research topics of 'Tolerance optimization using the Lambert W function: An empirical approach'. Together they form a unique fingerprint.

Cite this