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2024 | Buch

Intrinsic Essence of Robust Design Kapitel lesen Erstes Kapitel lesen

Robust Design and Assessment of Product and Production by Means of Probabilistic Multi-objective Optimization

verfasst von: Maosheng Zheng, Jie Yu

Verlag: Springer Nature Singapore

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book develops robust design and assessment of product and production from viewpoint of system theory, which is quantized with the introduction of brand new concept of preferable probability and its assessment. It aims to provide a new idea and novel way to robust design and assessment of product and production and relevant problems.

Robust design and assessment of product and production is attractive to both customer and producer since the stability and insensitivity of a product’s quality to uncontrollable factors reflect its value. Taguchi method has been used to conduct robust design and assessment of product and production for half a century, but its rationality is criticized by statisticians due to its casting of both mean value of a response and its dispersion into one index, which doesn’t characterize the issue of simultaneous optimization of above two independent sub-responses sufficiently for robust design, so an appropriate approach is needed.

The preference or role of a response in the evaluation is indicated by using preferable probability as the unique index. Thus, the rational approach for robust design and assessment of product and production is formulated by means of probabilistic multi-objective optimization, which reveals the simultaneous optimization of both mean value of a response and its dispersion in manner of joint probability.

Besides, defuzzification and fuzzification measurements are involved as preliminary approaches for robust assessment, the latter provides miraculous treatment for the 'target the best' case flexibly.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Intrinsic Essence of Robust Design
Abstract
This chapter discusses the fundamental questions: the essence of robust design, and the fundamental requirements to conduct the robust design.
Maosheng Zheng, Jie Yu
Chapter 2. Relevant Contents of System Theory and Probability Theory
Abstract
Relevant substances of system theory and probability theory for our subsequent use are concisely presented in this chapter, so as to extract guidable and valuable ideas. The system optimization and wholeness are stressed for a system; the joint probability reflects the concurrent occurring of two independent events in a system.
Maosheng Zheng, Jie Yu
Chapter 3. Concise Description of Probabilistic Multi-objective Optimization from Viewpoint of System Theory
Abstract
This chapter concisely describes the scientific connotation and essence of multi—objective optimization from viewpoint of system theory, which is the simultaneous optimization of multiple objectives. From the perspectives of set theory and probability theory, the basic methods of “simultaneous optimization of multiple objectives” in a system are the mutual methods such as “intersection” and “joint probability”. Furthermore, the concept of “preferable probability” and its evaluation method are given briefly, and thus the fundamental methodology of probabilistic multi—objective optimization is regulated, which characterizes the simultaneity of multi—objective optimization and treats both beneficial type of utility indexes and unbeneficial type of utility indexes of performance indicators equivalently and conformably.
Maosheng Zheng, Jie Yu
Chapter 4. Robust Design of a Single Objective as Dual Sub-objectives Optimization
Abstract
This chapter aims to develop a probabilistic approach of robust design with one objective, which is based on the probabilistic multi-objective optimization. In the treatment, the arithmetic mean value of performance utility indicator of the objective of an alternative is taken as one sub-objective, and the dispersion of performance utility indicator is taken as other sub-objective, the dual sub-objectives contribute their part of partial preferable probabilities to the alternative individually. Thus it becomes an optimization problem of dual sub-objectives simultaneously. Furthermore, three cases, i.e., the larger the better, the smaller the better and target the best, are formulated respectively. Moreover, ranking sequence of total preferable probabilities of alternatives is used to complete the optimization option. Subsequently, some application examples are given.
Maosheng Zheng, Jie Yu
Chapter 5. Robust Design and Assessment of Product and Production with Multiple Objectives
Abstract
Each objective can decompose dual sub-objectives, i.e., the mean value and the dispersion of the objective in principle, so multi-objective robust design problem can be seen as the “dual multi-objective optimization” reasonably; the evaluation for the part of partial preferable probability of mean value is conducted according to the type of the attribute, while the evaluation for the part of partial preferable probability of the dispersion is conducted as an unbeneficial type of attribute; the total preferable probability of a candidate scheme is the product of the complete parts of partial preferable probabilities of all possible response attributes, which is the unique indicator of the corresponding alternative in the comprehensive competition, the optimal candidate scheme is with highest total preferable probability.
Maosheng Zheng, Jie Yu
Chapter 6. Robust Design with Sequential Uniform Algorithm for Optimization by Means of PMOO
Abstract
Regulation of optimum parameters in sequential uniform design of subsequent optimization is developed by means of probabilistic multi-objective optimization (PMOO) in term of total preferable probability. A series of temportary candidate “optimum statuses” which were produced in the subsequent optimization of sequential uniform algorithm is used to form a “special point set”; the objective responses of “special point set” are evaluated once more with PMOO, the total preferable probability is comparatively evaluated to determine the final optimum status and parameters of the entire sequential uniform design process. Comparatively, the final optimum status is with the highest total preferable probability. Besides, under condition of “target value being the best”, both discrepancy of average value \(\overline{Y}\) of a response from its target value Y0, \(\varepsilon \equiv \left| {\overline{Y} - Y_{0} } \right|\), and averaged deviation γ of actual response value Y from the target value Y0 are taken as the dual individual sub-objectives to conduct the simultaneous optimization. Two examples are given to illuminate the procedure.
Maosheng Zheng, Jie Yu
Chapter 7. Robust Design and Assessment of Product and Production with Fuzzy Number
Abstract
In this chapter, the robust design and assessment of product and production with fuzzy number are conducted by means of probabilistic approach for multi—objective optimization (PMOO) with defuzzification routine, the fundamental idea and algorithm of fuzzy theory are taken as the footstone to conduct the regulation, the “intersection” of the “desired data” and “available data” of performances can be used to determine the utility of the corresponding attribute in the scheme selection. Besides, a nimble fuzzification approach of robust design for “target the best” case is developed by means of combination of probabilistic approach for multi—objective optimization (PMOO) with fuzzy theory flexibly for the convenience, the membership of an actual performance index with respect to its target value can be taken as the utility in the assessment by means of PMOO directly; the “fuzzification” procedure is a brand new approach. Furthermore, typical examples are given to illustrate the new regulations.
Maosheng Zheng, Jie Yu
Chapter 8. Concluding Remarks
Abstract
This chapter gives a summary of the whole book, mainly the intrinsic essence of robust design and appropriate strategy.
Maosheng Zheng, Jie Yu
Metadaten
Titel
Robust Design and Assessment of Product and Production by Means of Probabilistic Multi-objective Optimization
verfasst von
Maosheng Zheng
Jie Yu
Copyright-Jahr
2024
Verlag
Springer Nature Singapore
Electronic ISBN
978-981-9726-61-5
Print ISBN
978-981-9726-60-8
DOI
https://doi.org/10.1007/978-981-97-2661-5

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