Tolerance chart optimization for quality and cost

This paper introduces a mathematical model for tolerance chart balancing during machining process planning. The criteria considered in this study are based on the combined effects of manufacturing cost and quality loss, under the constraints of process capability limits, design functionality restrictions, and product quality requirements. Manufacturing cost is expressed in geometrical decreasing functions, which represent tolerances to be assigned. Process variability is expressed in quadratic loss functions, which represent the deviation between part measurement and the target value. Application of this model minimizes the total cost of manufacturing activities and quality issues relating to machining process planning, particularly in the early stages of planning.     

Robust computer-aided parameter and tolerance determination for an electronic circuit design

Conventionally, parameter design precedes tolerance design in the course of product design or process planning. To lower the production costs, as well as to improve quality, this study proposes the simultaneous determination of parameter and tolerance values when designing an electronic circuit. With the current development of CAD (Computer-Aided Design) software for electronic circuit design, engineers can determine parameter and tolerance values without providing transfer functions for circuit analysis. In this study, a computer experiment is performed by using CAD software (PSpice) to obtain outputs that will be converted into the total cost, which includes the quality loss, the tolerance cost and the failure cost. Then, Response Surface Methodology (RSM) is employed to minimize the total cost and to find the optimal parameter and tolerance values statistically. Consequently, a parameter and tolerance design for quality improvement and cost reduction can be achieved for any complex electronic circuit during the early stages 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.     

Process parameters determination for precision manufacturing

Conventional process planning in manufacturing operations presents fixed process means and process tolerances for all operations and allows actual outputs to be distributed around these fixed values, as long as the final outputs fall within acceptable specifications. Some approaches attempt to maximize the process tolerances of all manufacturing operations for part production. Other approaches intend to minimize the tolerance cost or quality loss based on known functions. Most of them consider process mean and process tolerance as independent decision variables in process planning, with the condition that the resultant working dimensions are equal to the design target values of blueprint dimensions. These approaches assume that there is no process drift or deterioration. However, these conventional approaches are inappropriate for small‐volume, high‐value and precision processing, particularly of a complex part. Hence this study introduces an alternative approach to the tolerance‐balancing problem that does not provide specific objective functions, which determines process means and process tolerances simultaneously and adjusts them sequentially. Copyright © 2000 John Wiley & Sons, Ltd.     

Simultaneous tolerance synthesis for manufacturing and quality

Tolerance allocation affects product design, manufacturing, and quality. No existing technique has been found by the authors that takes product design, manufacturing, and quality into account simultaneously. This paper introduces a new concurrent engineering method for tolerance allocation. A nonlinear optimization model was constructed to implement the method. The model minimizes the combination of quality loss and manufacturing cost simultaneously in a single objective function by setting both process tolerances and design tolerances simultaneously. The purpose of the model is to balance manufacturing cost and quality loss to achieve near-optimal design and process tolerances simultaneously for minimum combined manufacturing cost and quality loss over the life of the product. Compared to other models, this model shows significant improvements. Electronic Publication     

Determination of optimal lot sizing parameters and a controllable process mean for a production system

Several mathematical models have been developed separately for determining production and recycled lot quantities to minimize total production cost and the determination of optimal process mean setting to minimize total quality cost. For a single stage discrete part production system, this paper presents a mathematical model that combines these two inter-related aspects. The production process has a controllable parameter, the process mean, which determines the output lot quality. One-sided tolerance is used to decide the quality of finished goods. Bad units are reworked before they can be reprocessed with the fresh input. For such a situation, the model determines production lot size, recycling lot quantity, and a process mean while minimizing total system cost. The model has been validated using sample data from a pharmaceutical company. Results indicate that the production lot size and the recycled quantity have an inverse relationship with process mean and, a direct relationship with process variance.     

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.     

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.     

Optimal process parameter determination for computer‐aided manufacturing

Producing high‐quality products at low cost is one of the key factors to survival for manufacturing sectors in today's intense global competition environment. One way to gain competitiveness is to integrate product design and process planning into one activity. This study attempts to determine optimal process parameters for a manufacturing process under given design parameters. The process parameters to be determined in this study include process means and process tolerances for particular manufacturing process sequences. The problem is formulated in constrained non‐linear optimization, considering both quality‐ and manufacturing‐related costs. The proposed application evaluates alternative product designs and process sequences so that the best associated process parameters can be determined during the early stages of design and planning. This makes the link between CAD and CAM systems more useful and effective. As a result, optimal integration of product design and process planning with minimal production costs and maximal product quality is possible. Copyright © 1999 John Wiley & Sons, Ltd.     

Concurrent optimal allocation of design and process tolerances for mechanical assemblies with interrelated dimension chains

Concurrent tolerance allocation has been the focus of extensive research, yet very few researchers have considered how to concurrently allocate design and process tolerances for mechanical assemblies with interrelated dimension chains. To address this question, this paper presents a new tolerance allocation method that applies the concept of concurrent engineering. The proposed method allocates the required functional assembly tolerances to the design and process tolerances by formulating the tolerance allocation problem into a comprehensive model and solving the model using a non-linear programming software package. A multivariate quality loss function of interrelated critical dimensions is first derived, each component design tolerance is formulated as the function of its related process tolerances according to the given process planning, both manufacturing cost and quality loss are further expressed as functions of process tolerances. And then, the objective function of the model, which is to minimize the sum of manufacturing cost and expected quality loss, is established and the constraints are formulated based on the assembly requirements and process constraints. The purpose of the model is to balance manufacturing cost and quality loss so that concurrent optimal allocation of design and process tolerances is realized and quality improvement and product cost reduction is achieved. The proposed method is tested on a practical example.     

Concurrent optimization of assembly tolerances for quality with position control using scatter search approach

Tolerance allocation to individual parts in any assembly should be a vital design function with which both the design and manufacturing engineers are concerned. Generally design engineers prefer to have tighter tolerances to ensure the quality of their design, whereas manufacturing engineers prefer loose tolerances for ease of production and the need to be economical. This paper introduces a concurrent tolerance approach, which determines optimal product tolerances and minimizes combined manufacturing and quality related costs in the early stages of design. A non-linear multivariable optimization model is formulated here for assembly. A combinatorial optimization problem by treating cost minimization as the objective function and stack-up conditions as the constraints are solved using scatter search algorithm. In order to further explore the influence of geometric tolerances in quality as well as in the manufacturing cost, position control is included in the model. The results show how position control enhances quality and reduces cost.     

Concurrent optimal allocation of geometric and process tolerances based on the present worth of quality loss using evolutionary optimisation techniques

Concurrent tolerancing becomes an optimisation problem to find out the optimum allocation of the process tolerances in the given design function constraints. In traditional optimisation methods, finding out the optimum solution for this advanced tolerance design problem is complex. The proposed algorithms (elitist non-dominated sorting genetic algorithm) and differential evolution extensively do better than the previous algorithms for attaining the optimum result. The aim of this paper is to suggest a model for optimal tolerance allocation by considering both tolerance cost and the present worth of quality loss such that the total manufacturing cost/loss is minimised. The suggested model takes into account the time value of money for quality loss and product degradation over time and consists of two new parameters: the planning horizon and the product user’s discount rate. From the outcome of this study, a longer planning horizon results in an increase in both tolerance cost and quality loss; however, a larger value of discount rate gives up a decrease in both tolerance cost and quality loss. Finally, a practical example is brought into reveal the effectiveness of the suggested method.     

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.     

Tolerance analysis and synthesis for cam mechanisms

Tolerance is one of the most important parameters in product and process design, so tolerancing plays a key role in design and manufacturing. Tolerance synthesis is in a period of extensive study due both to increased demands for quality products and to increasing automation of machining and assembly. Optimum tolerance design and synthesis ensures good quality product at low cost. This paper presents an analytical methodology for tolerance analysis and synthesis for a disk cam-translating follower system. Both dimensional ( size) and geometric tolerances ( position and profile ) on the components are considered. Tolerance analysis is performed on individual tolerances as well as on total tolerance accumulation. With the lowest manufacturing cost as its objective function a nonlinear optimization model is formulated for tolerance synthesis and solved by a sequential quadratic programming ( SQP) algorithm. An example is provided to illustrate the optimization model and solution procedure.     

Parameter and tolerance design in the engineering modelling stage

Generalized parameter and tolerance design problems have been formulated as nonlinear optimization problems under a broader set of assumptions. A new approach for parameter design and tolerance design problems is outlined. This approach integrates engineering models and numerical optimization methods so it can work in the early stage of design where a good engineering model is available to simulate the real product or process. The new approach is also able to handle multiple quality characteristics and constraints. Several important theoretical results have been derived by the authors for tolerance design problems that could serve as guidelines for optimal tolerance design and tolerance distribution.     

Modelling and analysis of selective assembly using Taguchi's loss function

An assembly is the integrative process of joining components to make a completed product. It brings together the upstream process of design, engineering and manufacturing processes. The functional performance of an assembled product and its manufacturing cost are directly affected by the individual component tolerances. But, the selective assembly method can achieve tight assembly tolerance through the components manufactured with wider tolerances. The components are segregated by the selective groups (bins) and mated according to a purposeful strategy rather than being at random, so that small clearances are obtained at the assembly level at lower manufacturing cost. In this paper, the effect of mean shift in the manufacturing of the mating components and the selection of number of groups for selective assembly are analysed. A new model is proposed based on their effect to obtain the minimum assembly clearance within the specification range. However, according to Taguchi's concept, manufacturing a product within the specification may not be sufficient. Rather, it must be manufactured to the target dimension. The concept of Taguchi's loss function is applied into the selective assembly method to evaluate the deviation from the mean. Subsequently, a genetic algorithm is used to obtain the best combination of selective groups with minimum clearance and least loss value within the clearance specification. The effect of the ratio between the mating part quality characteristic's dimensional distributions is also analysed in this paper.     

Cost-tolerance analysis model based on a neural networks method

The purpose of tolerance design in product components is to produce a product with the least manufacturing cost possible, while meeting all functional requirements of the product. The product designer and process planner must fully understand the process accuracy and manufacturing cost of all kinds of manufacturing process to perform a good process plan job. Usually, the cost-tolerance model is constructed by a linear or non-linear regression analysis based on the data of the cost-tolerance experiment and to derive the correlation curve between the two. Though these correlation curves can show the relationship between manufacturing cost and tolerance, a fitting error is inevitable. In particular, there is considerable discrepancy in terms of the non-experimental data. A cost-tolerance analysis model based on a neural networks method is proposed. The cost-tolerance experimental data are used to set the training sets to establish a cost-tolerance network. Three representation modes of the cost-tolerance relationship are presented. First, the cost-tolerance relationship is derived from the grid points setting by the required tolerance accuracy. Second, a reasonable manufacturing cost of an unknown cost-tolerance experimental pair can be derived by the simulation of a cost-tolerance network. Third, an inference model based on a network's output is proposed to express the scope of the cost variation of various tolerances by means of a cost band. Comparison is also made with the high-order polynomial power function and exponential function cost-tolerance curves adopted by Yeo et al . Analytical results prove that the application of the cost-tolerance analysis model based on neural networks yields better performance in controlling the average fitting error than all conventional fitting models. The representation model using a cost band can identify precisely the possible cost variation range and reduce the chances of error in the tolerance design and cost estimation. It can thus provide important references for tolerance designers and process planners.     

Economic considerations on parameter design

A simultaneous consideration of process mean and variance in product design stages has been considered one of the most significant of Taguchi's contributions. Among his quality improvement methods, parameter design has drawn a great deal of particular attention from researchers. The ultimate objective of Taguchi's parameter design is to find control factor settings to achieve an on‐target process mean with a minimum variance. There is no doubt regarding the virtue of the minimum variance. However, considering a variety of economic aspects related to product specifications as well as a quality loss, the on‐target process mean may not necessarily be economical. This paper investigates the parameter design problem from an economic point of view and proposes an alternative procedure to achieve the most economical process mean as well as the minimum variance by taking product specifications and an asymmetric quality loss into consideration. It is shown through an illustrative example that a significant cost saving can be accrued from the proposed procedure. Copyright © 2000 John Wiley & Sons, Ltd.     

Concurrent process planning for finish milling and dimensional inspection of sculptured surfaces in die and mould manufacturing

With the introduction of computer-aided tools, traditional manufacturing tasks such as design, machining and inspection are now highly automated. However, due to the complexity and enormous knowledge involved in each process, most of these activities are still dealt with separately. Recent development of concurrent engineering emphasizes the importance of bringing manufacturing knowledge into the early design stage for optimum product and process design. In this paper, a knowledge-based CAD/CAM system which integrates process planning for finish milling and dimensional inspection of sculptured surfaces in die and mould manufacturing is presented. Optimum production plans are determined by minimizing the integral cost of machining and inspection. NC path generation and inspection planning are then verified by dynamic geometric simulations which provide the designer with the evaluations of machinability and inspectability. The implied significance is that strong inter-dependency may exist among various design life-cycle activities and that optimum solutions can be obtained by taking into account the interactions of the life-cycle events.     

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.