Abstract

In robust design (RD) modeling, the response surface methodology (RSM) based on the least-squares method (LSM) is a useful statistical tool for estimating functional relationships between input factors and their associated output responses. Neural network (NN)-based models provide an alternative means of executing input-output functions without the assumptions necessary with LSM-based RSM. However, current NN-based estimation methods do not always provide suitable response functions. Thus, there is room for improvement in the realm of RD modeling. In this study, a new NN-based RD modeling procedure is proposed to obtain the process mean and standard deviation response functions. Second, RD modeling methods based on the feed-forward back-propagation neural network (FFNN), cascade-forward back-propagation neural network (CFNN), and radial basis function network (RBFN) are proposed. Third, two simulation studies are conducted using a given true function to verify the proposed three methods. Fourth, a case study is examined to illustrate the potential of the proposed approach. In conclusion, a comparative analysis of the three feed-forward NN structure-based modeling methods and conventional LSM-based RSM proposed in this study showed that the proposed methods were significantly lower in the expected quality loss (EQL) and various variability indicators.

Highlights

  • In recent decades, robust design (RD) has been considered essential for improvement of product quality, as the primary purpose of RD is to seek a set of parameters that make a product insensitive to various sources of noise factors

  • RD modeling methods based on the feed-forward back-propagation neural network (FFNN), cascade-forward back-propagation neural network (CFNN), and radial basis function network (RBFN) are proposed

  • Based on the pattern of connection, Neural network (NN) typically fall into two distinct categories: feed-forward networks, in which the connection flows unidirectionally from input to output, and recurrent networks, in which the connections among layers run in both directions

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Summary

Introduction

Robust design (RD) has been considered essential for improvement of product quality, as the primary purpose of RD is to seek a set of parameters that make a product insensitive to various sources of noise factors. Arungpadang and Kim [41] developed a feed-forward NN-based RSM to model the functional relationship between input variables and output responses to improve the precision of estimation without increasing the number of experimental runs. RD modeling methods based on the feed-forward back-propagation neural network (FFNN), cascade-forward back-propagation neural network (CFNN), and radial basis function network (RBFN) are proposed These are applied to estimate the process mean and standard deviation response functions. The optimal numbers of hidden neurons in the FFNN and CFNN structures and the dispersion constant “spread” in the RBFN are identified to finalize the optimal structures of the corresponding NNs. The DR functions can be separately estimated using the proposed estimation methods from the optimal NN structures with their control factors and output responses.

NN Structures
Proposed NN-Based Estimation Method 1
Number of Hidden Neurons
Integration into a Learning Algorithm
Generalization and Overfitting Issues
Proposed NN-Based Estimation Method 2
Proposed NN-Based Estimation Method 3
Simulation Studies
Simulation Study 1
Simulation Study 2
Case Study
Conclusions and Further Studies
Full Text
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