Tolerance optimization using the Lambert <i>W</i> function: an empirical approach

Govindaluri, Madhumohan S.; Shin, Sangmun; Cho, B. R.

doi:10.1080/00207540410001696311

Cited by 18 publications

(6 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The economic factor is often expressed in a quality loss function [111] and in most applications the Taguchi loss function is used. Govindaluri et al [97] consider the quality loss from the perspective of the customer and the manufacturing and rejection costs by the manufacturer. When incorporating Taguchi's quality loss function Cheng and Maghsoodloo [112] found that when a component's mean varies, only the quality loss associated with that component will be changed; whereas when a component's variance shifts, the optimal allowance, tolerance costs, and quality losses associated with each component will be affected.…”

Section: Digital Tolerancing Methods and Tolerance Optimisationmentioning

confidence: 99%

See 1 more Smart Citation

Design verification and validation in product lifecycle

2010

View full text Add to dashboard Cite

Section: Digital Tolerancing Methods and Tolerance Optimisationmentioning

confidence: 99%

“…The primary function of tolerance setting is to balance the product functionality with economic factors [97]. Excessively tight tolerances will add cost due to more complex processing stages whereas inadequately wide tolerances will result in insufficient quality and costly rework.…”

Section: Tolerance Analysis and Optimisationmentioning

confidence: 99%

Design verification and validation in product lifecycle

2010

View full text Add to dashboard Cite

“…In general, finding optimal tolerance settings require a numerical optimization, since closed-form solutions are usually difficult to obtain due to the complexity of functional forms. Recently, Govindaluri et al (2004) investigated possible roles of the Lambert W function, commonly used in Physics, in a tolerance optimization problem, and developed closed-form solutions by showing that the function is useful for simplifying mathematical complexities.…”

Section: Introductionmentioning

confidence: 99%

Designing the optimum configurations of circular and spherical product specifications for multiple quality characteristics

Cho

Phillips

Kovach

2005

J. Syst. Sci. Syst. Eng.

View full text Add to dashboard Cite

As an integral part of tolerance design in the context of design for six sigma, determining optimal product specifications has become the focus of increased activity, as manufacturing industries strive to increase productivity and improve the quality of their products. Although a number of research papers have been reported in the research community, there is room for improvement. Most existing research papers consider determining optimal specification limits for a single quality characteristic. In this paper, we develop the modeling and optimization procedures for optimum circular and spherical configurations by considering multiple quality characteristics. The concepts of multivariate quality loss function and truncated distribution are incorporated. This has never been adequately addressed, nor has been appropriately applied in industry. A numerical example is shown and comparison studies are made.

show abstract

“…Of late, the Lambert W function is used with increasing frequency to appear in a large variety of engineering sciences. Even though Corless et al (1996) reveal the consideration of Lambert W functions by Govindaluri et al (2004) and Shin et al (2010) to get optimal tolerances, assembly constraint was not considered. Trabelsi and Delchambre (2000) discussed the representation schemes of tolerance and tolerance analysis of assemblies to assess the cost and their assembly orders.…”

Section: Introductionmentioning

confidence: 99%

Least cost–tolerance allocation based on Lagrange multiplier

Kumar¹,

Padmanaban

Balamurugan

2016

Concurrent Engineering

View full text Add to dashboard Cite

Industry-related competitiveness and reduction in manufacturing cost can be achieved by selection of ideal tolerance. Implementing non-traditional techniques for tolerance allocation to various parts in a mechanical assembly is an enervating procedure. Analytical methods are implemented to obtain creditable design. The main objective of this article is to minimize the manufacturing cost, quality loss, and TRSS (root sum square tolerance) for complex mechanical assemblies. The proposed methodology deals with the reciprocal exponential function. Hence, it is used to solve the problem for obtaining the closed-form solution by Lagrange multiplier method which integrates Lambert W function. The illustrations used in the research article demonstrate the feasibility and effectiveness of the traditional approaches. The results obtained also show that tolerance can be allocated economically and precisely. Here, non-traditional optimization methods are correlated and finally their performances are analyzed.

show abstract

Tolerance optimization using the Lambert W function: an empirical approach

Cited by 18 publications

References 20 publications

Design verification and validation in product lifecycle

Design verification and validation in product lifecycle

Designing the optimum configurations of circular and spherical product specifications for multiple quality characteristics

Least cost–tolerance allocation based on Lagrange multiplier

Contact Info

Product

Resources

About