Robust Design with Engineering Models Described by Implicit Mathematical Functions

Functional performance variations of products and systems are often used to measure the qualities of products and systems considering the changes in the design parameter values caused by uncertainties. A robust design approach has been developed in this research to minimize the functional performance variations considering the design parameter uncertainties by identifying the boundaries of the functional performance variations through optimization. In this work, a mathematical model is developed to describe the relationships among functional performance, design configurations and parameters, and design parameter uncertainties. A multi-level optimization model is established to identify: (1) The optimal design configuration, (2) the optimal values of design parameters, and (3) the boundaries of functional performance variations. Sensitivity analysis considering the impact of parameter uncertainties on functional performance variation boundaries has also been conducted. A case study on the design of a truss system has been conducted. Case study results show that the sensitivities of functional performance variation boundaries to the design parameter uncertainties can be reduced significantly using the new robust design approach.

Increasing competition in the global marketplace demands products be adaptable to the changes of functional requirements, operation environments, and technology advancement. Adaptable design can be employed for developing adaptable products and systems that can be changed, such as reconfigured and upgraded, during product operation stage. In addition, since product and operating parameters are normally subject to influence of uncertainties that lead to variations of functional performance, robust design needs to be carried out to identify the design whose functional performance is the least sensitive to the variations of product and operating parameters. This research aims at developing a robust adaptable design approach such that the product is adaptable to various changes in requirements and parameters during the product operation stage, meanwhile the product functional performance measures are the least sensitive to parameter variations. First, the requirements, parameters, and variations of these parameters are defined as numerical functions of a time parameter. Then, mathematical models are established to describe the relationships among product design/operating parameters, functional performances, and variations of these parameters and performances. Furthermore, an optimization-based model is developed to achieve the robust adaptable design. A case study has also been developed to demonstrate the effectiveness of the newly developed robust adaptable design method.

For solving the existing problems of assembly quality of B-pillar, a robust design approach was utilized to optimize locator layout of Reinf Pillar and Side Beam Threshold so that the assembly deviation of B-Pillar was minimized. Taguchi orthogonal experiment was carried out to perform the idea by taking the locators coordinate as design parameters, taking the manufacturing and positioning deviation of par ts as noise factors. The gap value between Reinf Pillar and Side-body Panel was considered as the measurement index. Furthermore, based on the establishment of robust evaluation function and signal-to-noise ratio formula, the robust layout scheme was determined. The 3DCS(Dimensional Control Systems), a tolerance simulation software, was running, and the simulation analysis results show that robust design greatly reduces the assembly gap, effectively solving the problem of large assembly deviation and quality fluctuation of B-Pillar.

Traditional reliability model, which is based on fault state logic of product composition units, has inherent limitations, e.g., it can't map the failure caused by cumulative error of performance degradation or parameter drift, and can't associate reliability requirements or product failure time with product design parameters so that little use is got to support testability or PHM function design, etc. In order to overcome these shortcomings, this paper proposesa physics of failure based reliability modeling framework, which is aimed at describing the nature of failure dynamics, of which failure was that the output performance variation driven by mechanisms to go beyond design specifications. This modeling framework includes simulation analysis of the expected dominant failure mechanisms (including device degradation or parameter drift, etc.) by way of classical stress-damage modeling, and study of failure mechanism impact on the product's output with fault injection when the corresponding mechanism taken place. Complete description of the failure dynamics closely links product failure events, design parameters and external conditions together, and it facilitates the reliability and PHM design effort. In this paper, a formal model and its simulation analysis approach were presented, and a case study of an electronic module was also given. This modeling approach is more applicable for digital product design scenario as generally complex simulation calculation is needed in this way.

*This paper addresses the need and usage of an innovative design tool called robust design that could be employed during the whole product lifecycle management (PLM) to facilitate the business success for the long run. Quality in itself is an important business strategy for the long-term success. Many quality failures can be traced back to the design deficiencies, which must be addressed using robust design approaches very early in the design cycle. VR&D, over the last 15 years, has been developing and providing a number of tools that could be used to improve productivity and quality in product development. This paper will address the development of a framework for performing a robust design approach called Design For Six Sigma (DFSS). It will describe strategies and tools that can be used to successfully implement a robust design approach The VisualDOC optimization software system will provide the necessary software tools for implementing the proposed framework.

Increasing competition in the global marketplace demands products be adaptable to the changes of functional requirements, operation environments, and technology advancement. Adaptable design can be used for developing adaptable products that can be easily changed, such as reconfigured or upgraded, in the product operation stage. In addition, since the uncertainties in product parameters and environment parameters usually lead to the variations of functional performance, robust design has to be carried out to identify the design whose functional performance is the least sensitive to the variations of product and environment parameters. In this research, a robust adaptable design method is developed to identify the product whose parameter values can be changed in the product operation stage. First, a mathematical model is established to describe the relationships among product functional performances, parameters, and variations of these parameters. Then, an optimization-based design model is developed to achieve the robust adaptable design. A case study has also been developed to demonstrate the effectiveness of the newly developed robust adaptable design method.

An optimal concurrent product design and service planning approach through simulation-based evaluation considering the whole product life-cycle span

This article presents a tolerance modelling and robust design approach to support concurrent engineering. This method allows the designer to synthetically specify dimensional and geometric tolerance, considering assembly functional requirements (AFRs) and manufacturing costs. First, features of ISO/TC 213 are used as the basis for the construction of tolerance network and tolerance model for assembly. Second, the manufacturing cost-tolerance model for cylindrical and planar features is established. This model addresses not only dimensional tolerances but also geometric tolerances and nominal parameters. Finally, the robust tolerance optimization model is established, and genetic arithmetic is used to obtain robust tolerance values. The proposed approach is consistent with the philosophy of concurrent engineering, in which AFRs are satisfied and manufacturing cost is reduced. A design instance is introduced to show the validity of this method.

The paper aims to explore how organizations in the transition phase of co-location to multi-locations production environment applied Robust Design approach to accommodate the complexity of manufacturing and assembly operation in multi-location production environment. By using a single case study method on a home appliances Research and Development (R&D) Company, this paper examines the detail of design and operational transformations within the organization at pre and post implementation stage of Robust Design. The paper starts with enlightenment of issues faced by the company that drove the move to explore the application of Robust Design, follows by illustrations on how Robust Design concept is re-configured and executed across the product design process within the company. The paper subsequently reviews operational impact driven by the implementation of Robust Design, this is followed by discussion and recommendation for improvement. Result from the case study suggested that top management commitment is the key success factor for the implementation of Robust Design in Research and Development firm. In addition, the case study offers an alternative and effective approach to develop a robust system within design and development environment.

Flexure-based compliant mechanisms are the preferred motion guiding systems for small range, nano-precision positioning applications because of excellent characteristics like friction-free continuous motion. These mechanisms are commonly used in nano fabrication equipment and ultra precision instruments. However, machining imperfections induced geometric errors in the mechanisms are known to cause undesirable parasitic motion and significant loss of precision. A systematic design approach to minimize the sensitivity of the flexure mechanisms to geometric errors induced by machining tolerances is presented here. Central to the design approach is the screw systems based analytical model to study the spatial motion characteristics of flexure mechanisms. Using this model, the parasitic motion is classified into those errors which can be corrected by calibration (extrinsic) and those which are coupled with the mechanism motion and cannot be corrected by apriori calibration (intrinsic). Metric to quantify the intrinsic parasitic motion results naturally from the screw systems analysis, and is used to represent the precision capability of the flexure mechanism. The analytical model enables the selection of geometric parameters of flexure joints of the mechanism via an optimization scheme with the aim of minimizing the parasitic motion metric. The statistical nature of the machining tolerances is accounted for by sampling the random variables at every iteration step of the optimization, leading to a stochastic formulation. The robust design approach is illustrated using a one DOF rotational flexure mechanism that is used in nano-imprint lithography equipment. Numerical results of the optimization indicate up to 40% improvement in the precision capability of the mechanism without any change in the manufacturing tolerance limits. Further, it is shown via eigenscrew analysis of mechanism compliance that the robustness resulting from the optimal flexure joint design can be attributed to the improved compliance distribution.

The recently completed volume of Quality and Reliability Engineering International is its 25th anniversary. The mission of the journal is to provide information on new developments in many aspects of the discipline to professionals with research articles, review papers, and applications and case study papers. It is appropriate to look back over this anniversary volume and identify some important themes, highlight some of the significant papers that contribute to those themes, and discuss what we hope to see in the future. Statistical Process Control (SPC) and related topics continue to be an important area of research and applications. The journal published many noteworthy papers in this area, including the papers on adaptive procedures by Li et al.1 and Kooli and Liman2, run-to-run control3, integration of SPC with other techniques4, 5, design of control charts6, 7, and methods for identifying the change point in high-yield processes8. Reliability engineering and the associated statistical methods continue to be a key focus area for the journal. Koka et al.9 present an interdisciplinary approach to reliability in design and Samet10 discusses fault-tolerant computing. Accelerated life testing techniques are discussed by Liu and Tang11 and Pan12. Remenyte-Prescott and Andrews13 present a new real-time method for the efficient analysis of non-coherent fault trees. Anderson-Cook et al.14 investigate resource allocation for a complex system with aging components. Designed experiments and robust design are an integral part of both product design and process improvement. Methodology for robust product or process design is considered by Shaibu et al.15, Steenackers et al.16 and Rodriguez et al.17. Hazelrigg18 discusses many interesting aspects of engineering design. Other extremely useful papers include Gaudard et al.19 on the interaction between data mining and designed experiments, Guo et al.20 on the general balanced metric for mixed-level fractional factorial designs, Wesley et al.21 on prediction variance in split-plot designs, Guo et al.22 on optimal fold-over designs for mixed-level fractional factorial designs, and Jones and Johnson23 on designs for computer experiments. The journal also presented several interesting case studies, including Monroe and Pan24, Carmignani25, Magniez et al.26, Johnson et al.27 and Aksoy and Orbak28. Case studies are an important part of this journal. We have a high standard for these papers. They must represent the best of contemporary practice either through the application of new methodology or the application of existing methods in unique environments. Quality and reliability engineers are knowledge workers. They accumulate, generate and deploy knowledge with the express objective of improving products, processes, services and society. Case studies facilitate the generation and widespread adoption of new methods or provide insight about how existing methods can be used in novel situations. These types of papers can perform a valuable service to our profession. We encourage potential authors of case studies to contribute to our journal.

The paper describes a computational simulation approach for durability, damage tolerance (D&DT) and reliability of composite wind turbine blade structures in presence of uncertainties in material properties. This computer-based prediction methodology combines composite mechanics with finite element analysis, damage and fracture tracking capability, probabilistic analysis and a robust design algorithm to reduce weight of turbine bales without loss in structural durability and reliability. A composite turbine blade was first assessed with finite element based multi-scale progressive failure analysis to determine failure modes and locations as well as the fracture load. Analysis D&DT results were validated with static test performed at Sandia National Laboratories. The work was followed by detailed weight analysis to identify contribution of various materials to the overall weight of the blade. The methodology ensured that certain types of failure modes, such as delamination progression, are contained to reduce risk to the structure. Probabilistic analysis indicated that composite shear strength has a great influence of the blade ultimate load under static loading. Weight was reduced by 12% with robust design without loss in reliability or D&DT. It was achieved by replacing a small volume of key materials with foam.

A commercial spacecraft should survive on orbit for more than 10 years under the severe circumstances without any maintenance. To realize this subject, not only performance but also other design factors such as reliability, mass, robustness, cost, etc. should be taken into consideration. From point of the thermal design, it is very important to obtain the robust thermal control subsystem with matrix heat pipe layout while minimizing the mass (weight). A new thermal optimization method without compromising the thermal robustness and the mass of thermal subsystem is highly anticipated. This paper proposes a robust thermal design approach for optimizing the heat pipe shape to minimize the mass of the spacecraft panel. We apply a combination of Design of Experiments (DOE), Response Surface Methodology (RSM) and Monte Carlo Simulation to determine the robust design parameters that minimize the mass of the heat pipe structure. Dimensions of the heat pipe design parameters were determined with rationally in a short time and practical robust optimization method was established.

Optimal small satellite orbit design based on robust multi-objective optimization method

A general approach, called robust optimal design, is developed in a companion paper and applied here to a comprehensive, nonlinear, activated sludge treatment system. The treatment system robustness is related to the sensitivity of steady-state effluent biochemical oxygen demand and total suspended solids concentrations to changes in 55 uncertain model parameter values. Treatment system designs with lower sensitivity of the effluent water quality measures are likely to be more robust than designs with higher sensitivity. The robust optimal design approach is used to generate alternative designs that represent the trade-off between total system cost and robustness. The robust design trends are generally more consistent with recommended design practice than are typical minimum-cost design trends. In particular, improvements in the robustness of effluent biochemical oxygen demand concentration are associated with higher activated sludge mean solids-residence times, whereas typical minimum-cost designs are associated with low solids-residence times. The robustness of the alternative designs is evaluated further using a nonlinear worst-case analysis. The robust optimal design framework should be applicable to many design problems where uncertainty in parameter values is significant.