Computer‐aided tolerance synthesis with statistical method and optimization techniques

Most tolerance design optimization problems have focused on developing exact methods to reduce manufacturing cost or to increase product quality. The inherent assumption with this approach is that assembly functions are known before a tolerance design problem is analyzed. With the current development of CAD (Computer‐Aided Design) software, design engineers can address the tolerance design problem without knowing assembly functions in advance. In this study, VSA‐3D/Pro software, which contains a set of simulation tools, is employed to generate experimental assembly data. These computer experimental data will be converted into other forms such as total cost and Process Capability Index. Total cost consists of tolerance cost and quality loss. Then, empirical equations representing two variables can be obtained through a statistical regression method. After that, mathematical optimization and sensitivity analysis are performed within the constrained ‘desired design and process’ space. Consequently, tolerance design via computer experiments enables engineers to optimize design tolerance and manufacturing variation to achieve the highest quality at the most cost effective price during the design and planning stage. Copyright © 2001 John Wiley & Sons, Ltd.     

Robust tolerance design by computer experiment

Tolerance design affects the quality and cost of a product cycle time. Most of the literature on tolerance design problems has focused on developing exact methods to minimize manufacturing cost or quality loss. The inherent assumption in this approach is that the assembly function is known before a tolerance design problem is analysed. With the current development in CAD (Computer-Aided Design) software, design engineers can proceed with the tolerance design problems, without knowing assembly functions in advance. In this study, the Monte Carlo simulation is employed using VSA-3D/Pro software to obtain experimental data. Then the design of experiments (DOE) approach is adopted for data analysis in order to select critical components for cost reduction and quality improvement. Implementing the discussed computer experiments, a tolerance design analysis which improves quality and reduces cost can be performed for any complex assembly via computer during the early stage of design.     

Robust product development for multiple quality characteristics using computer experiments and an optimization technique

Conventional parameter or tolerance designs focus on developing exact methods to minimize quality loss or manufacturing cost. The inherent assumption is that the response functions which represent the link between controllable variables and response values of quality characteristics are known before a design is developed. Moreover, parameter and tolerance values are assumed to be independent controllable variables in previous works; namely, they are determined separately in design activities. Currently, advanced computer software, such as computer-aided engineering, can help engineers to handle design problems with unknown response functions, at the stage of product design and process planning. Therefore, in this study, the software ANSYS was employed to obtain simulation data which represent the response values of quality characteristics. These response values will be used to fit a set of response functions for later analysis. However, previous works in computer simulation for design and planning usually lack consideration of the noise impact from an external design system. To approximate a realistic design environment, various levels of controllable variables, in conjunction with artificial noises created from uncontrollable variables, are used to generate simulated data for statistical analysis via Response Surface Methodology (RSM). Then, an optimization technique, such as mathematical programming, is adopted to integrate these response functions into one formulation so that optimal parameter and tolerance values are concurrently determined, with multiple quality characteristics taken into consideration. A bike-frame design was used to demonstrate the presented approach, followed by multiple quality characteristics of interest: material cost, bike-frame weight, structure reliability, and rigidity dependability. The goal is to minimize material cost and bike frame weight and to maximize structure reliability and rigidity dependability. This approach is useful for solving any complex design problems in the early stages, while providing enhanced functionality, quality, economic benefits, and a shorter design cycle.     

Simultaneous Optimization of Robust Parameter and Tolerance Design Based on Generalized Linear Models

Robust parameter design (RPD) and tolerance design (TD) are two important stages in design process for quality improvement. Simultaneous optimization of RPD and TD is well established on the basis of linear models with constant variance assumption. However, little attention has been paid to RPD and TD with non‐constant variance of residuals or non‐normal responses. In order to obtain further quality improvement and cost reduction, a hybrid approach for simultaneous optimization of RPD and TD with non‐constant variance or non‐normal responses is proposed from generalized linear models (GLMs). First, the mathematical relationship among the process mean, process variance and control factors, noise factors and tolerances is derived from a dual‐response approach based on GLMs, and the quality loss function integrating with tolerance is developed. Second, the total cost model for RPD‐TD concurrent optimization based on GLMs is proposed to determine the best control factors settings and the optimal tolerance values synchronously, which is solved by genetic algorithm in detail. Finally, the proposed approach is applied into an example of electronic circuit design with non‐constant variance, and the results show that the proposed approach performs better on quality improvement and cost reduction. Copyright © 2012 John Wiley & Sons, Ltd.     

Combined parameter and tolerance design optimization with quality and cost

The need to remain competitive for survival in the current world market has led manufacturing sectors to consider the low cost and high quality of product and process design. Production of quality products at low cost in today's manufacturing industry requires simultaneous consideration of product design and process planning, particularly in the early stage of design and planning. During product design, parameter design determines the design target (design setting) and tolerance design determines design tolerance. During process design, the parameter design determines the process mean (process setting) and tolerance design determines process tolerance. This study provides a mathematical relationship to link the elements of design target, design tolerance, process mean and process tolerance in one equation. By following this equation, manufacturability for all possible combinations of product and process design can be ensured, which increases the flexibility of both product design and process planning. With this in mind, an analysis model that includes manufacturing cost and quality loss simultaneously has been developed to determine the optimal values of design tolerance, process mean and process tolerance. The proposed model provides a method of combining the optimization of parameter and tolerance design over product/process in the early stage of design.     

Parameter tolerance design for electrical circuits

Realistic circuit design requires that unavoidable tolerances on component parameters be taken into account, particularly in situations where a circuit is to be mass-produced. Since specifications are normally imposed on circuit performance, parameter tolerances can have the undesirable effect of reducing manufacturing yield (i.e. the percentage of circuits which meet specifications) to values below unity, thereby effectively increasing circuit cost. Approaches have been developed to electrical circuit design which incorporate aspects of parameter tolerance variations at the various stages of design, thus enabling tolerance effects to be assessed and minimized. There are two principal approaches: statistical and deterministic. The first uses probabilistic techniques to predict variations in circuit performance, whereas the second uses deterministic (i.e. non-stochastic) methods. Within each group, three types of problems are important: first, the maximization of yield, secondly, the minimization of circuit unit cost and, thirdly, the minimization of performance variability. This paper discusses some important advances in the statistical approach to tolerance design. Monte Carlo analysis is almost invariably an important component of the procedure: random fluctuations in parameter values are simulated according to some probability density function and inserted into a computer circuit simulation program which computes corresponding circuit performance variations. The procedure — also referred to as tolerance analysis — not only allows the designer to predict expected performance fluctuations but also presents him with information regarding the relative location of acceptable and non-acceptable circuits in component parameter space. The Monte Carlo method can handle without difficult any number of component parameters and performance functions; moreover, statistical dependence among parameters is readily handled. The algorithm presented here is experimentally validated through successful design of practical circuits and is applicable to both discrete and integrated circuits. Strategies which ensure computational efficiency of the methods are discussed and a cost/benefit analysis carried out for a typical circuit.     

Circuit Design Optimization Based on Quality Cost Estimation

The variations in component parameter values embodied in an electronic circuit can result in it failing to conform to its specification. Such failures can cause the manufacturer to incur significant quality costs, arising from factors including warranty returns and legal liabilities. It can be difficult to predict both the probability that a circuit will fail to meet its specification and the consequent quality costs. It can also be difficult to determine which component parameter variations are most significant in causing faults. In this paper we introduce the concept of functional capability, which is a variation on the familiar process capability, as a measure of the performance variation found in a circuit relative to the specified range of acceptable performance. Based on this capability measure, along with a failure modes and effects analysis and a cost model, we are able to relate functional capability to quality costs. In addition, we introduce a capability breakdown which allows the effect of different parameter variations to be readily visualized so that the designer may focus effort where it will be most effective in reducing quality costs. The resulting technique is primarily intended to aid the design of printed circuit board level analogue and mixed signal circuits, particularly in safety critical applications. The paper illustrates the technique through analysis of a simple circuit and the analysis of a commercial mixed signal circuit. It also shows how the technique may be integrated within a capable design, manufacture and test analysis process. Copyright © 2005 John Wiley & Sons, Ltd.     

Variational geometry based pre-inspection of a pattern of holes

Tolerance is an important factor that affects product quality, cost and production time. However tolerance design still relies heavily on experience, which cannot satisfy the requirements of advanced manufacturing. In this work, a tolerance pre-inspection approach for a pattern of holes (POH) is proposed. The approach conducts tolerance pre-inspection based on the variational geometry generated with mathematical models of translational and rotational variations in three-diamensional (3D) CAD systems. Using this approach, the effect of POH tolerance design can be explicitly simulated, visualized and inspected in a 3D CAD system at the early design stage. The approach is implemented and some test results are given.     

一种宽带高隔离度SPDT开关的设计与实现

 采用多个PIN管设计并制作了一种串/并联结构的宽带高隔离度微带单刀双掷（single pole double throw,SPDT）开关。首先建立了所用型号的PIN管开路、短路的等效电路模型;然后借助于CAD软件Serenade进行了电路仿真和参数优化,得到了很好的仿真结果;最后设计出电路制版图并制作了经济实用的微带开关,经过实验测量达到了技术指标要求。     

参数化CAD中参数有效范围的算法研究

为了解决在参数化CAD系统中由于参数赋值不合理而导致的几何实体重建失败的问题,提出了确定一类二维参数化CAD模型中参数有效范围的代数算法。该算法可以实时求解所有简单多边形中距离约束参数的有效取值范围,并利用几何变换简化求解规模,提高求解效率。研究结果表明,该算法提供的有效取值范围内的任一赋值,均可保证重建后几何实体的拓扑形状不发生改变,在一定程度上提高了参数化CAD软件的设计效率和人机交互的智能化水平。同时对算法复杂度进行了分析,该算法的复杂度为O(n~2)。     

Sequential optimization of parameter and tolerance design for multiple dynamic quality characteristics

System design, parameter design and tolerance design are the three stages of design process as presented by G. Taguchi. Systems design identifies the basic elements of the design to provide new or improved products to customers. Parameter design determines the optimal parameter settings, which will minimize variation from the target performance of the product. Tolerance design finally identifies the components of the design, which are sensitive in terms of affecting the quality of the product, and establishes tolerance limits that will give the required level of variation in the design. Most studies have focused primarily on optimizing the parameter design or tolerance design for multiple static quality characteristics. In this paper, a mathematical formula corresponding to the model is derived from Taguchi's quadratic quality loss function to minimize the expected total cost for the parameter design of multiple dynamic quality characteristics. When the optimal parameter design is not sufficient to reduce the output variation, the first-order Taylor series expansion is then used to analyse the variations of noise factors for optimizing the tolerance design. It concludes with an example demonstrating this approach.     

Product data quality validation system for product development processes in high-tech industry

Among various product data, 3D CAD data plays a key role in current product design and manufacturing processes including industrial design, detail design, CAE, inspection, mould-making, production, and so on. If 3D CAD data has geometrical or topological errors by user mistakes or modelling software bugs and those errors are not cleaned by the data creator in an early stage, the data will be transferred to the downstream operators and they have to fix the errors before starting their own work. Because 3D data is quite complex, it is very difficult to recognise the data errors manually in a modelling system before a big problem is encountered which blocks the next operation. In this case, it generally causes time delay and high cost for data correction and the effect will be bigger when the process is close to the back-end. In this research, we develop a fully automated product data quality validation and management system to support the product development processes of high-tech products like televisions, camcorders, mobile telephones, home appliances, etc. The system automatically validates the 3D data in real time and gives 3D error reports to the creator to correct modelling failures in their steps. Also, project managers can check or control the data delivery based on the data quality for each step.     

Collaborative design environment between ECAD and MCAD engineers in high-tech products development

In order to make more competitive electronic products, major electronics companies struggle to design products with a thin shape and complex convergence functionalities without any lead-time and cost increase. Also, the development mission of a project is changed continuously to catch up with the competitor’s products in a short time and the importance of aesthetic design is getting bigger and bigger in these days. In many cases, shape changes bring the electrical layout changes of a notebook computer main board and vise versa. Those development environmental changes make the engineers harder and harder and require more collaboration between electrical and mechanical engineers to reduce development time and design errors occur from early design stage. In this paper, a collaborative design environment consists of a web-based project management system and automated printed circuit board (PCB) generation and validation system is proposed. The web system is used for project management and design data exchange including electrical CAD (ECAD) data and related technical documents between ECAD and mechanical CAD (MCAD) engineers. By using this project management web portal, engineers can share the design information with design change history. ECAD data in Intermediate Data Format can be automatically validated in 2D domain while sending the ECAD data via web system. To generate a full 3D quality product model with PBA in MCAD side, an automated 3D PCB generation and assembly clearance checking module is developed.     

Simultaneous optimal selection of design and manufacturing tolerances with different stack-up conditions using genetic algorithms

Tolerance design is one of the most critical aspects of product design and development process as it affects both the product's functional requirements and manufacturing cost. Unnecessarily tight tolerances lead to increased manufacturing cost, while loose tolerances may lead to malfunctioning of the product. Traditionally, this important phase of product development is accomplished intuitively to satisfy design constraints, based on handbooks' data and/or skill and experience of the designers. Tolerance design carried out in this manner does not necessarily lead to an optimum design. Research in this area indicates that, in general, tolerance design is carried out sequentially in two steps; (1) tolerance design in CAD to obtain design or functional tolerances and (2) tolerance design in CAPP to obtain manufacturing tolerances. Such a sequential approach to tolerance design suffers from several drawbacks, such as more time consumption, suboptimality and unhealthy working atmosphere. This paper reports on an integrated approach for simultaneous selection of design and manufacturing tolerances based on the minimization of the total manufacturing cost. The nonlinear multivariable optimization problem formulated in this manner may result in a noisy solution surface, which can effectively be solved with the help of a global optimization technique. A solution methodology using genetic algorithms and applying penalty function approach with proper normalization of the penalty terms for handling the constraints is proposed. The application of the proposed methodology is demonstrated on a simple mechanical assembly with different tolerance stack-up conditions.     

Reliability improvement of electronic circuits based on physical failure mechanisms in components

Traditionally the position of reliability analysis in the design and production process of electronic circuits is a position of reliability verification. A completed design is checked on reliability aspects and either rejected or accepted for production. This paper describes a method to model physical failure mechanisms within components in such a way that they can be used for reliability optimization, not after, but during the early phase of the design process. Furthermore a prototype of a CAD software tool is described, which can highlight components likely to fail and automatically adjust circuit parameters to improve product reliability.     

CAD navigation and diagnostics by linking ATE and EDA

This paper describes a specific methodology and software that links automated test equipment (ATE) and electronic design automation (EDA) tools to identify and diagnose failures at the layout level. The ATE software, named wafer fail layout map (WFLMAP), works in concert with the EDA integrated circuits (IC) design database and provides computer-aided design (CAD) navigation and correlation between the tester failure data and IC design data. With this approach, layout-level defect diagnosis is achieved at the individual chip level, as well as at the wafer level. This method can also be used for improved design for manufacturing (DFM).     

Economic Design of CSP-1 Plan Under the Dependent Production Process and Linear Inspection Cost

Chen and Chou presented the economic design of type I continuous sampling plan (CSP-1 plan) under the linear inspection cost. However, it can be argued that the production process is seldom independent. In this paper, we further propose the problem concerning the economic design of CSP-1 plan under the dependent production process and linear inspection cost. A solution procedure is developed to find the unique combination (i*, f*) that will meet the average outgoing quality limit (AOQL) requirement while also minimizing the total expected cost per unit produced during one inspection cycle.     

Optimal robust and tolerance design for computer experiments with mixture proportion inputs

Computer experiments often have inputs that are proportions/fractions of components in a mixture. In these mixture computer experiments, it can be of interest to perform robust and tolerance design on the mixture proportions since the proportions are subjected to noise variations. Traditionally, manufacturing of mixture products is controlled via interval tolerances for mixture amounts. In this paper, an optimal tolerance region for proportions, which gives optimal quality cost among all possible tolerance regions for mixture proportions with the same acceptance probability, is proposed for integrated parameter and tolerance design in mixture computer experiments. Real examples are given to demonstrate the improvements that can be achieved with the optimal tolerance region.     

Economic parameter design for ultra-fast laser micro-drilling process

The basic requirement in this type of micro-drilling process is to achieve high product quality with the minimum machining cost, which can be realised through parameter design. In this paper, we propose a new economic parameter design under the framework of Bayesian modelling and optimisation. First of all, the Bayesian seemingly unrelated regression (SUR) models are utilised to develop the relationship models between input factors and output responses in the laser micro-drilling process. After that, simulated response values which reflect the real laser micro-drilling process are obtained by using the Gibbs sampling procedure. Moreover, a novel rejection cost function and a quality loss function are constructed based on the simulated responses. Finally, an optimisation scheme integrating the rejection cost (i.e. rework cost and scrap cost) function and the quality loss function is implemented by using multi-objective genetic algorithm to find feasible economic parameter settings for laser micro-drilling process.     

基于双响应面法的公差设计研究

探讨了产品综合成本的构成,以此为基础提出了以产品综合成本最低为目标的公差稳健设计模型,并利用双响应面法(Response Surface Methodology ,RSM) 来实现公差的稳健优化设计。