Integrating the Lambert W function to a tolerance optimization problem

Sangmun Shin, Madhumohan S. Govindaluri, Byung Rae Cho

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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
Volume21
Issue number8
DOIs
Publication statusPublished - Dec 2005

Fingerprint

Sensitivity analysis
Costs
Numerical methods
Physics
Optimization problem
Tolerance
Manufacturing
Closed-form solution

Keywords

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

ASJC Scopus subject areas

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

Cite this

Integrating the Lambert W function to a tolerance optimization problem. / Shin, Sangmun; Govindaluri, Madhumohan S.; Cho, Byung Rae.

In: Quality and Reliability Engineering International, Vol. 21, No. 8, 12.2005, p. 795-808.

Research output: Contribution to journalArticle

@article{10530fa6bf354c7db2d90ad5d4c2890c,
title = "Integrating the Lambert W function to a tolerance optimization problem",
abstract = "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.",
keywords = "Lambert W function, Optimal specification limits, Optimization, Tolerance design",
author = "Sangmun Shin and Govindaluri, {Madhumohan S.} and Cho, {Byung Rae}",
year = "2005",
month = "12",
doi = "10.1002/qre.687",
language = "English",
volume = "21",
pages = "795--808",
journal = "Quality and Reliability Engineering International",
issn = "0748-8017",
publisher = "John Wiley and Sons Ltd",
number = "8",

}

TY - JOUR

T1 - Integrating the Lambert W function to a tolerance optimization problem

AU - Shin, Sangmun

AU - Govindaluri, Madhumohan S.

AU - Cho, Byung Rae

PY - 2005/12

Y1 - 2005/12

N2 - 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.

AB - 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.

KW - Lambert W function

KW - Optimal specification limits

KW - Optimization

KW - Tolerance design

UR - http://www.scopus.com/inward/record.url?scp=28844479344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28844479344&partnerID=8YFLogxK

U2 - 10.1002/qre.687

DO - 10.1002/qre.687

M3 - Article

AN - SCOPUS:28844479344

VL - 21

SP - 795

EP - 808

JO - Quality and Reliability Engineering International

JF - Quality and Reliability Engineering International

SN - 0748-8017

IS - 8

ER -