Dynamic Robust Parameter Design Using Response Surface Methodology based on Generalized Linear Model
Abstract
Purpose: When designing an input-output system susceptible to noise, engineers assume a functional relation between the input and the output. The Taguchi method, which uses a dynamic, robust parameter design (RPD) to evaluate the robustness of the input-output relation against noise, is employed. This study aims to address extending the scope of use of a dynamic RPD.
Methodology/Approach: A target system in a typical dynamic RPD can be interpreted as one in which the relation between the input and the output is a linear model, and the output error follows a normal distribution. However, an actual system often does not conform to this premise. Therefore, we propose a new analysis approach that can realize a more flexible system design by applying a response surface methodology (RSM) based on a generalized linear model (GLM) to dynamic RPD.
Findings: The results demonstrate that 1) a robust solution can be obtained using the proposed method even for a typical dynamic RPD system or an actual system, and 2) the target function can be evaluated using an adjustment parameter.
Research Limitation/implication: Further analysis is required to determine which factor(s) in the estimated process model largely contribute(s) to changes in the adjustment parameter.
Originality/Value of paper: The applicability of typical dynamic RPD is limited. Hence, this study’s analytical process provides engineers with greater design flexibility and deeper insights into dynamic systems across various contexts.
Category: Research paper
Keywords: robust parameter design; dynamic system; generalized linear model; response surface methodology; Taguchi method
Full text article
References
Enkawa, T. and Miyakawa, M., 1992. SQC Theory and Practice. Tokyo, Japan: Asakura Publishing.
Kawamura, T. and Takahashi, T., 2013. A Statistical Modeling and Optimization of Dynamic Parameter Design. Journal of the Japanese Society for Quality Control, [e-journal] 43(3), pp.364-371. https://doi.org/10.20684/quality.43.3_364.
Kume, S. and Nagata, Y., 2013. Robust Parameter Design for Signal-Response Systems Using Generalized Linear Model. Asian Network for Quality Congress 2013, The Swiss Hotel Le Concorde Hotel, Bangkok, 16-18 October 2013.
Lee, Y. and Nelder, J. A., 1998. Generalized Linear Models for the Analysis of Quality-improvement Experiments. The Canadian Journal of Statistics, [e-journal] 26(1), pp.95-105. https://doi.org/10.2307/3315676.
Lee, Y. and Nelder, L. A., 2003. Robust Design via Generalized Linear Models. Journal of Quality Technology; [e-journal] 35(1), pp.2-12. https://doi.org/10.1080/00224065.2003.11980187.
Mikami, E. and Yano, H., 2004. Studies of a Method of Detecting Thermoresistant Bacteria. Journal of Quality Engineering Society, [e-journal] 12(6), pp.37-44. https://doi.org/10.18890/qes.12.6_37.
Myers, R. H. and Montgomery, D. C., 1997. A Tutorial on Generalized Linear Models. Journal of Quality Technology, [e-journal] 29(3), pp.274-291. https://doi.org/10.1080/00224065.1997.11979769.
Myers, W. R., Brenneman, W. A. and Myers, R. H., 2005. A Dual-Response Approach to Robust Parameter Design for a Generalized Linear Model. Journal of Quality Technology, [e-journal] 37(2), pp.130-138. https://doi.org/10.1080/00224065.2005.11980311.
Nagata, Y., 2009. Statistical Quality Control - A Step-by-Step Guidebook. Tokyo, Japan: Asakura Publishing.
Nair, V. N., 1992. Taguchi’s Parameter Design: A Panel Discussion. Technometrics, [e-journal] 34(2), pp.127-161. https://doi.org/10.2307/1269231.
Nelder, J. A. and Wedderburn, R. W. M., 1972. Generalized Linear Models. Journal of the Royal Statistical Society, [e-journal] Series A, 135(3), pp.370-384. https://doi.org/10.2307/2344614.
Smyth, G. K., 1989. Generalized Linear Models with Varying Dispersion. Journal of the Royal Statistical Society, Series B, [e-journal] 51(1), pp.47-60. https://doi.org/10.1111/J.2517-6161.1989.TB01747.X.
Smyth, G. K. and Verbyla, A. P., 1999. Adjusted Likelihood Methods for Modelling Dispersion in Generalized Linear Models. Environmetrics, [e-journal] 10(6), pp.696-709. https://doi.org/10.1002/(SICI)1099-095X(199911/12)10:6<695::AID-ENV385>3.0.CO;2-M.
Tatebayashi, K., 2004. Introduction to Taguchi Method. Tokyo, Japan: JUSE Press.
Yoshino, S., 1995. Optimization of Bean Sprouting Condition by Parameter Design. Journal of Quality Engineering Society, [e-journal] 3(2), pp.17-22. https://doi.org/10.18890/qes.3.2_17.
Authors
Copyright (c) 2024 Kosuke Oyama, Ohkubo Masato, Yasushi Nagata
This work is licensed under a Creative Commons Attribution 4.0 International License.
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access. This journal is licensed under a Creative Commons Attribution 4.0 License - http://creativecommons.org/licenses/by/4.0.
Authors who publish with the Quality Innovation Prosperity agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.