Formal Solution of N-Type Taguchi Parameter Design Problems With Stochastic Noise Factors

1991 ◽  
Author(s):  
Nestor F. Michelena ◽  
Alice M. Agogino
Keyword(s):  
Performance Characteristic ◽  
Degrees Of Freedom ◽  
Formal Solution ◽  
Parameter Design ◽  
Absolute Deviation ◽  
Design Problems ◽  
Problem Reduction ◽  
Stochastic Parameters ◽  
Noise Factors ◽  
Monotonicity Analysis

Abstract The Taguchi method of product design is a statistical experimental technique aimed at reducing the variance of a product performance characteristic due to uncontrollable factors. The goal of this paper is to provide a monotonicity analysis based methodology to facilitate the solution of N-type parameter design problems. The obtained design is robust, i.e., the least sensitive to variations on uncontrollable factors (noise). The performance characteristic is unbiased in the sense that its expected value equals a target or specification. The proposed loss function is based on the absolute deviation of the characteristic with respect to the target, instead of the common square error approach. Conditions, like those imposed by monotonicity analysis, on the monotonic characteristics of the performance function are proven, despite the objective function is not monotonic and contains stochastic parameters. These conditions allow the qualitative analysis of the problem to identify the activity of some constraints. Identification of active sets of constraints allows a problem reduction strategy to be employed, where the solution to the original problem is obtained by solving a set of problems with fewer degrees of freedom. Results for the case of one uncontrollable factor are independent of the probability measure on the factor. However, conclusions for the multi-parametric case must take into account the characteristics of the probability space on which the random parameters are defined.

Formal Solution of N-Type Robust Parameter Design Problems with Stochastic Noise Factors

1994 ◽  
Vol 116 (2) ◽  
pp. 501-507 ◽  
Author(s):  
N. F. Michelena ◽  
A. M. Agogino
Keyword(s):  
Performance Characteristic ◽  
Degrees Of Freedom ◽  
Formal Solution ◽  
Parameter Design ◽  
Robust Parameter Design ◽  
Absolute Deviation ◽  
Design Problems ◽  
Robust Parameter ◽  
Noise Factors ◽  
Monotonicity Analysis

The Taguchi method of product design is a statistical experimental technique aimed at reducing the variance of a product performance characteristic due to uncontrollable factors. The goal of this paper is to provide a monotonicity analysis based methodology to facilitate the solution of N-type parameter design problems. The design obtained is robust in that the sensitivity to variations of uncontrollable factors (noise) has been minimized. The performance characteristic is unbiased in the sense that its expected value equals a target or specification. The proposed loss function is based on the absolute deviation of the characteristic with respect to the target, instead of the common square error approach. Conditions, like those imposed by monotonicity analysis, on the monotonic characteristics of the performance function are proven even for problems where the objective function is not monotonic and contains stochastic parameters. These conditions allow the qualitative analysis of the problem to identify the activity of some constraints. Identification of active sets of constraints allows a problem reduction strategy to be used, where the solution to the original problem is obtained by solving a set of problems with fewer degrees of freedom. Results for the case of one uncontrollable factor are independent of the probability measure on the factor. However, conclusions for the multiparametric case must take into account the characteristics of the probability space on which the random parameters are defined.

Alternatives of Taguchi's Approach for Dynamic Robust Design Problems

1998 ◽  
Vol 05 (02) ◽  
pp. 115-131 ◽  
Author(s):  
Kwok-Leung Tsui
Keyword(s):  
Response Function ◽  
Robust Design ◽  
Dynamic Responses ◽  
Response Model ◽  
Function Model ◽  
Design Problems ◽  
Loss Model ◽  
Modeling Approaches ◽  
Noise Factors ◽  
Model Approach

Robust Design is an important method for improving product quality, manufacturability, and reliability at low cost. Most research in robust design has been focused on problems with static responses. This paper deals with the robust design problems with dynamic responses. The objective of the paper is to investigate and compare three modeling approaches: the loss model, the response function model, and the response model approaches. Taguchi16 proposes the loss model approach which models the loss measures as functions of the control factor effects. Miller and Wu10 propose the response function model approach which models the loss measures as functions of the effects of both control and noise factors. Tsui18 proposes the response model approach which directly models the response as a function of the effects of control, noise, and signal factors. In this paper, we identify and derive the relationships between the effect estimates of the three approaches and show that the loss model approach creates unnecessary biases for the factorial effect estimates and may lead to non-optimal solutions. The three modeling approaches are compared in a real example.

A Framework for Algorithms in Globally Optimal Design

1989 ◽  
Vol 111 (3) ◽  
pp. 353-360 ◽  
Author(s):  
P. Hansen ◽  
B. Jaumard ◽  
S. H. Lu
Keyword(s):  
Combinatorial Optimization ◽  
Optimal Design ◽  
Branch And Bound ◽  
General Framework ◽  
Ad Hoc ◽  
Design Problems ◽  
Branch And Bound Algorithms ◽  
Monotonicity Analysis

Many problems of globally optimal design have been solved in the literature using monotonicity analysis and a variety of tests, often applied in an ad hoc way. These tests are developed here, expressed mathematically and classified according to the conclusions they yield. Moreover, many new tests, similar to those used in combinatorial optimization, are presented. Finally, a general framework is proposed in which branch-and-bound algorithms for globally optimal design problems can be expressed.

An Adaptive One-Factor-at-a-Time Method for Robust Parameter Design: Comparison With Crossed Arrays via Case Studies

2007 ◽  
Vol 130 (2) ◽  
Author(s):  
Daniel D. Frey ◽  
Nandan Sudarsanam
Keyword(s):  
Case Studies ◽  
Experimental Error ◽  
Fractional Factorial ◽  
Parameter Design ◽  
Robust Parameter Design ◽  
Control Factors ◽  
Starting Point ◽  
Robust Parameter ◽  
Crossed Arrays ◽  
Noise Factors

This paper presents a conceptually simple and resource efficient method for robust parameter design. The proposed method varies control factors according to an adaptive one-factor-at-a-time plan while varying noise factors using a two-level resolution III fractional factorial array. This method is compared with crossed arrays by analyzing a set of four case studies to which both approaches were applied. The proposed method improves system robustness effectively, attaining more than 80% of the potential improvement on average if experimental error is low. This figure improves to about 90% if prior knowledge of the system is used to define a promising starting point for the search. The results vary across the case studies, but, in general, both the average amount of improvement and the consistency of the results are better than those provided by crossed arrays if experimental error is low or if the system contains some large interactions involving two or more control factors. This is true despite the fact that the proposed method generally uses fewer experiments than crossed arrays. The case studies reveal that the proposed method provides these benefits by exploiting, with high probability, both control by noise interactions and also higher order effects involving two control factors and a noise factor. The overall conclusion is that adaptive one-factor-at-a-time, used in concert with factorial outer arrays, is demonstrated to be an effective approach to robust parameter design providing significant practical advantages as compared to commonly used alternatives.

scholarly journals Robust parameter design with covariates of multiple noise factors

2015 ◽  
Vol 1 (2) ◽  
pp. 77-88 ◽  
Author(s):  
Kensuke Goto ◽  
Hironao Sato ◽  
Masami Miyakawa ◽  
Yasushi Nagata
Keyword(s):  
Parameter Design ◽  
Robust Parameter Design ◽  
Robust Parameter ◽  
Noise Factors

Constraint Dominance Methods Applied to the Design of a Linear Motor

2003 ◽  
Author(s):  
Ashish D. Deshpande ◽  
James R. Rinderle
Keyword(s):  
Optimal Solution ◽  
Design Problems ◽  
Basic Principles ◽  
Electric Actuator ◽  
Critical Design ◽  
Effective Decision ◽  
Effective Decision Making ◽  
Actuator Design ◽  
Monotonicity Analysis ◽  
Insight Into

Reasoning about relationships among design constraints can facilitate objective and effective decision making at various stages of engineering design. Exploiting dominance among constraints is one particularly strong approach to simplifying design problems and to focusing designers’ attention on critical design issues. Three distinct approaches to constraint dominance identification have been reported in the literature. We lay down the basic principles of these approaches with simple examples and we apply these methods to a practical linear electric actuator design problem. The identification of dominance along with the use of Interval Propagation and Monotonicity Analysis leads to an optimal solution for a particular design configuration of the linear actuator. Identification of dominance also provides insight into the design of linear actuators, which may lead to effective decisions at the conceptual stage of the design.

Synergy and transitivity in constraint dominance methods: Demonstration with linear motor design problem

2006 ◽  
Vol 20 (4) ◽  
pp. 383-397
Author(s):  
ASHISH DESHPANDE ◽  
JAMES R. RINDERLE
Keyword(s):  
Design Problem ◽  
Optimal Solution ◽  
Design Problems ◽  
Electric Actuator ◽  
Constraint Reasoning ◽  
Effective Decision ◽  
Determination Methods ◽  
Effective Decision Making ◽  
Propagation Methods ◽  
Monotonicity Analysis

Reasoning about relationships among design constraints can facilitate objective and effective decision making at various stages of engineering design. Exploiting dominance among constraints is one particularly strong approach to simplifying design problems and to focusing designers' attention on critical design issues. Three distinct approaches to constraint dominance identification have been reported in the literature. We lay down the basic principles of these approaches with simple examples, and we apply these methods to a practical linear electric actuator design problem. With the help of the design problem we demonstrate strategies to synergistically employ the dominance identification methods. Specifically, we present an approach that utilizes the transitive nature of the dominance relation. The identification of dominance provides insight into the design of linear actuators, which leads to effective decisions at the conceptual stage of the design. We show that the dominance determination methods can be synergistically employed with other constraint reasoning methods such as interval propagation methods and monotonicity analysis to achieve an optimal solution for a particular design configuration of the linear actuator. The dominance determination methods and strategies for their employment are amenable for automation and can be part of a suite of tools available to assist the designer in detailed as well as conceptual design.

Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design

1988 ◽  
Author(s):  
P. Y. Papalambros
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Design Problems ◽  
Local Optima ◽  
Solution Strategies ◽  
Active Constraints ◽  
Active Sets ◽  
Trade Offs ◽  
Design Variables ◽  
Monotonicity Analysis

Abstract Solution strategies for optimal design problems in nonlinear programming formulations may require verification of optimality for constraint-bound points. These points are candidate solutions where the number of active constraints is equal to the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs and it would be desirable to identify them early, or exclude them in a strategy using active sets. Potential constrained-bound solutions are usually identified based on the principles of monotonicity analysis. This article discusses some cases where these points are in fact global or local optima.

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