A general model for process-setting with an asymmetrical linear loss function

In many industries, unbalanced tolerance design is a common occurrence. It occurs when the deviation of a quality characteristic in one direction is more harmful than the deviation in the opposite direction. The failure mode in the two directions is usually different. Taguchi redefines quality using Gauss’s quadratic function as the loss that a product imparts to society from the time the product is shipped. However, using a quadratic loss function when the actual loss function is nonquadratic may yield incorrect input parameter levels. In certain situations, a linear loss function is more appropriate in industrial applications. Furthermore, automatic inspection and measurement technology is widely used by many industries; the nonconforming quality characteristic would be detected automatically. Thus, rather than use a quadratic loss function, we assume a truncated asymmetrical linear loss function to describe unbalanced tolerance design. The purpose of this paper is to find out the optimal setting of the process mean such that the expected quality loss is minimised. The results show that the process mean should be slightly offset from the target value.     

Unbalanced Tolerance Design and Manufacturing Setting with Asymmetrical Linear Loss Function

Taguchi has developed many loss functions, and many of the situations are approximated by the quadratic function. Using a quadratic loss function when the actual loss function is non-quadratic may cause the incorrect input parameter levels to be chosen. In certain situations, a linear loss function is more appropriate in industrial applications. If tolerance design is unbalanced, setting the process mean at the nominal will not minimise the expected quality loss. Thus, two specific models of linear loss function are discussed for unbalanced tolerance design. One is an asymmetrical linear loss function and the other is a truncated asymmetrical linear loss function. The optimal process means for these two loss functions are also compared with each other. The results show that the process mean should be shifted a little from the nominal such that the expected quality loss is minimised.     

Target Selection for an Indirectly Measurable Quality Characteristic in Unbalanced Tolerance Design

a production process should be measured or controlled by another measurable variable. The immeasurable quality characteristic is a function of the directly measurable variable. For this type of quality characteristic, if the tolerance design is unbalanced, or if the relationship between the measurable variable and immeasurable quality characteristic is nonlinear, setting the process mean at the target value of the measurable variable will not minimise the expected quality loss. In this paper, the optimal process mean of the measurable variable is determined such that the expected quality loss is minimised for the above conditions. The results are compared with those of a directly measurable variable.     

Simultaneous process mean and process tolerance determination with asymmetrical loss function

Process design involves process mean and process tolerance determination. Process mean determination is finding the best settings for product quality, without affecting manufacturing cost. However, process tolerance determination is a manufacturing process selection which generally affects manufacturing cost and product quality. In this study, asymmetric quality loss is considered in measuring product quality, and tolerance cost is adopted in representing manufacturing cost. To reflect the combined effect of process mean and process tolerance completely, failure cost is added to the category of manufacturing cost. Then, based on the sum of these three costs, a simultaneous optimization of process mean and process tolerance is determined for process planning in the early stages of development.     

Concurrent tolerancing for design and manufacturing based on the present worth of quality loss

The quality loss function developed by Taguchi provides a monetary measure for the deviation of the product quality characteristic from the target value. Product use causes degradation on its quality characteristic, and since such a deviation can be changing over time, so can the quality loss. However, most studies on concurrent tolerancing theory do not consider the quality loss caused by the degradation. In this paper, the present worth of expected quality loss expressed as the function of the pertinent process tolerances in a concurrent tolerancing environment is derived to capture the quality loss due to product degradation over time as a continuous cash flow function under continuous compounding. A new tolerance optimization model, which is to minimize the summation of manufacturing cost and the present worth of expected quality loss, is established to realize the concurrent tolerance allocation for products with multiple quality characteristics. An example of the bevel gear assembly involving concurrent allocation of design and process tolerances is given, demonstrating that the proposed model is feasible in practice.     

Optimal Parameter and Tolerance Design with a Complete Inspection Plan

The need to remain competitive has led manufacturing sectors to consider tolerances as the key to achieving low cost and high quality. To produce quality products at low cost in today’s manufacturing industry, an integration of product design and process planning is essential. Process tolerance is one of the most important parameters that link product design and process planning. The process mean is also a critical parameter for further quality improvement and cost reduction under the permissible process setting adjustment within design tolerance limits. This study discusses an approach to integrate the product and process design via the optimisation of process mean and process tolerance.     

基于多重相关特征质量损失函数的公差优化设计

在重点推导了具有多重相关特征产品的质量损失与尺寸公差的函数关系的基础上,提出了多重相关特征产品的公差优化设计方法,建立了基于制造成本一质量损失的公差优化设计的综合模型,建立该模型的目的是寻求制造成本和质量损失之间的平衡,实现旨在提高产品质量和降低成本的公差优化设计。应用实例验证了所提出方法的有效性。     

The study of cost-tolerance model by incorporating process capability index into product lifecycle cost

To reduce the cost of manufacturing systems, many studies of cost minimization have been performed. Since tolerance design significantly affects the manufacturers’ cost, the optimization of cost-tolerance allocation will be an important issue for reducing these costs. Costs incurred in a product life-cycle include manufacturing cost and quality loss. However, most cost-tolerance optimization models frequently ignore the concept of quality loss and may not lead to an accurate analysis of the tolerance. Until now, process capability analysis has been the tool used to evaluate the adequacy of a production tool in meeting a quality target. Hence, the concept of process capability analysis should be included into the cost-tolerance optimization model. In this study, a flexible cost-tolerance optimization model will be constructed by integrating the process capability index into the product life-cycle cost function. The constructed cost-tolerance optimization model simultaneously considers the manufacturing cost of the components, the process capability of the manufacturing operations, and the quality loss of products. The decision-maker can apply the proposed cost-tolerance optimization model to determine a reasonable tolerance with minimum total cost including consideration of the process capability .     

Concurrent optimization of machining process parameters and tolerance allocation

With the advent use of sophisticated and high-cost machines coupled with higher labor costs, concurrent optimization of machining process parameters and tolerance allocation plays a vital role in producing the parts economically. In this paper, an effort is made to concurrently optimize the manufacturing cost of piston and cylinder components by optimizing the operating parameters of the machining processes. Design of experiments (DoE) is adopted to investigate systematically the machining process parameters that influence product quality. In addition, tolerance plays a vital role in assembly of parts in manufacturing industries. For the selected piston and cylinder component, improvements efforts are made to reduce the total manufacturing cost of the components. By making use of central composite rotatable design method, a module of DoE, a mathematical model is developed for predicting the standard deviation of the tolerance achieved by grinding process. This mathematical model, which gives 93.3% accuracy, is used to calculate the quality loss cost. The intent of concurrent optimization problem is to minimize total manufacturing cost and quality loss function. Genetic algorithm is followed for optimizing the parameters. The results prove that there is a considerable reduction in manufacturing cost without violating the required tolerance, cutting force, and power.     

Optimal tolerance design for products with correlated characteristics by considering the present worth of quality loss

The quality loss function proposed by Taguchi provides a quantitative measurement of product quality when product’s quality characteristic value deviates from the ideal target at an arbitrary time. However, product use causes degradation on its quality characteristic, and since such a deviation can be changing over time, so can its quality loss. The quality loss caused by degradation on quality characteristic has not been considered in most research. In this paper, the time value of money for quality loss and product degradation over time is integrated into the total cost model, and a new optimization model for the tolerance design of products with correlated characteristics is established. The discussions focus on the multivariate quality loss function as an extension of the Taguchi loss function, which is used to model quality loss due to product degradation as a continuous cash flow function under continuous compounding. The optimal tolerance design is achieved by minimizing the total cost, which is the sum of manufacturing cost and the present worth of expected quality loss. An illustrative example is presented to demonstrate the effectiveness of the proposed model.     

Process mean, process tolerance, and use time determination for product life application under deteriorating process

Robust design can significantly improve a producer’s competitive ability to deliver high-quality products with low development cycle time, quality loss, failure cost, and tolerance cost. However, during usage by a consumer, the functional performance of a product or some of its components may change as use time passes, leading to unexpected product failure that is usually costly in both time and money. The cost of these failures may influence the determination of optimal use time and optimal initial settings as compensation for the possible process mean changes during consumer usage. In addition to finding use time and initial settings for proper quality performance, the determination of process mean and tolerance also needs to be considered. As is known, changes in process means acquired quality loss and variability, while process tolerance has an effect on tolerance-related costs and quality loss. Because there exists a dependency among use time, initial setting of process mean, process mean, and process tolerance, these values must be determined simultaneously. Thus, in this paper, an optimization model with an acceptable reliability value is developed to minimize total cost, including quality loss, failure cost, and tolerance cost, by determining optimal use time, initial settings, process mean, and process tolerance, simultaneously. Applications of single and multiple components are presented to explain the proposed models. Finally, sensitivity analysis and model discussions on some decision variables are performed.     

Design and optimization of concurrent tolerance in mechanical assemblies using bat algorithm

Concurrent designing of tolerance has become a vital concern in product and process development due to the relationship between quality, functionality and product cost. It is one of the well explored areas in combinatorial optimization. In this paper, a recently developed optimization algorithm, called Bat algorithm (BA), is used for optimizing the tolerance based on concurrent objectives to minimize the manufacturing cost, present worth of expected quality loss and quality loss. The mechanical assemblies such as Bevel gear assembly (A), Gear box assembly (B) and Suction union assembly (C) are considered to demonstrate the proposed algorithm. It is found that the BA has produced better results than other methods in initial generations for concurrent tolerance problems.     

Optimal tolerance design of assembly for minimum quality loss and manufacturing cost using metaheuristic algorithms

Tolerance allocation is a design tool for reducing overall cost of manufacturing while meeting target levels for quality. An important consideration in product design is the assignment of design and manufacturing tolerances to individual component dimensions so that the product can be produced economically and functions properly. The allocation of tolerances among the components of a mechanical assembly can significantly affect the resulting manufacturing costs. In this work, the tolerance allocation problem is formulated as a non-linear integer model by considering both the manufacturing cost of each component by alternate processes and the quality loss of assemblies so as to minimise the manufacturing cost. Metaheuristics techniques such as genetic algorithm and particle swarm optimisation are used to solve the model and obtain the global optimal solution for tolerance design. An example for illustrating the optimisation model and the solution procedure is provided. Results are compared with conventional technique and the performances are analysed.     

公差稳健优化设计的研究

为了解决产品加工成本与质量稳健的协调性问题,提出了一种新的公差稳健优化设计数学模型.依据公差稳健设计的思想,考虑产品质量的模糊性,以封闭环误差分布概率密度函数的方差和优质品概率之比为设计目标,建立了公差优化设计产品质量稳健性损失成本目标函数,并研究了优质品率和封闭环误差分布方差的确定方法.以加工成本和产品质量稳健性损失成本为目标,以模糊装配可靠度、可取公差极限范围为约束条件,建立了公差多目标优化数学模型.举例说明了文中所述的公差稳健优化设计方法的应用,采用遗传算法实现了公差的多目标优化设计.实例表明,该方法能够协调零件的加工成本和产品质量的稳健性损失成本,使优化指标的综合性能最佳.     

Manufacturing environment-oriented robust tolerance optimization method

Tolerance design has a great impact on the cost and quality of a product. Previous research focused on process tolerances or robust tolerance design with little consideration on real manufacturing context. This paper presents a nonlinear method for robust tolerance design based on the real manufacturing context in three stages. The objective function to be minimized is the total manufacturing cost. The constraint equations for the optimization model are also deduced, which select suitable manufacturing processes based on the manufacturing environment. Simulation annealing (SA) is used for the nonlinear optimization. The approach is finally illustrated by a practical example. The results of the comparison with different models indicate that the proposed approach is more effective with the manufacturing resource. The robust and reliable tolerance can be obtained.     

Tolerance chart balancing with a complete inspection plan taking account of manufacturing and quality costs

This paper introduces a mathematical model of tolerance chart balancing for machining process planning under complete inspection. The criteria considered in this study are based on the combined effects of manufacturing cost and quality loss, under constraints such as process capability limits, product design specifications, and product quality requirements. Manufacturing costs include the machining cost, part cost, inspection cost, reworking cost, and replacement cost. The machining 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 the part measurement and the target value. An example is presented to demonstrate the proposed model. A comparison made with previous methods shows that the proposed model minimizes the total cost of manufacturing activities and quality-related issues in machining process planning, particularly in the early stages. Moreover, the applications are not be limited to machining process planning but can also be used in other forms of production planning.     

Inspection Allocation Planning for a Multiple Quality Characteristic Advanced Manufacturing System

Producing products with multiple quality characteristics is always one of the concerns for an advanced manufacturing system. To assure product quality, finite automatic inspection systems should be used. Inspection planning to allocate inspection stations should then be performed to manage the limited inspection resource. Except for finite inspection station classes, in this work, the limited number of inspection stations, of each inspection station class, is considered for solving the inspection allocation problem in a multiple quality characteristic advanced manufacturing system. Since the product variety in batch production or job shop production increases to satisfy the changing requirements of the various customers, the tolerances specified will vary from time to time. This inspection allocation problem is solved using a unit cost model in which the manufacturing capability, inspection capability, and tolerance specified are concurrently considered for a multiple quality characteristic product. The situation of unbalanced tolerance design is also considered. The inspection allocation problem can then be solved according to customer requirements. Since determining the optimal inspection allocation plan seems to be impractical, as the problem size becomes large, two decision criteria (i.e. sequence order of workstation and tolerance interval) are employed separately to develop two different heuristic solution methods in this work. The performance of each method is measured in comparison with the enumeration method that generates the optimal solution. The result shows that a feasible inspection allocation plan can be determined efficiently. ID="A1"Correspondance and offprint requests to: Dr Yau-Ren Shiau, Department of Industrial Engineering, Feng-Chia University, 100 Wenhwa Road, Seatwen, PO Box 25–097, Taichung 407, Taiwan     

一种基于制造环境的统计公差分析方法

在并行公差设计理论的基础上,提出基于制造环境的面向装配的统计公差分析方法,使得在公差设计中,考虑实际加工环境的加工状况,即各种加工方法的工序能力。在此基础上,建立基于工序能力的统计公差分析模型。在假定过程平均漂移为均匀分布和正态分布两种情况下,计算出制造偏差的概率密度函数,进而推导出线性装配相应函数的概率统计特性值,为统计公差优化设计奠定了基础．     

Repeatability/Linearity Study and Measurement Loss Cost Analysis of an Automatic Gauge

Computer-aided inspection (CAI) has become one of the fundamental steps in advanced manufacturing by employing automatic gauges. However, it is necessary to provide a more practical way to evaluate CAI on-line efficiency. Since a gauge capability study should be conducted before applying any automatic gauge, the necessary off-line gauge assesment for CAI is introduced in this paper. An R&R (repeatability/reproducibility) study is commonly conducted in the gauge capability study, but in this paper, an R&L (repeatability/linearity) study of a machine vision system is investigated and introduced. The ANOVA approach and regression approach are applied and compared to study the linearity effect. The measurement loss cost includes extra costs (i.e. costs of discarding, reworking, inspection, and quality loss) that arise from measurement error. These costs are analysed by interpreting the relationships between manufacturing capability, gauge capability, and the tolerance. As most gauge capability studies were conducted for the bilateral tolerance inspection, unbalanced tolerance inspection is considered here. The way that the relative costs contribute to the measurement loss cost is also studied. Rather than using a constant measurement error determined by previous observations, the measurement error model is embedded in the relative cost models. Users can then evaluate CAI on-line efficiency by incorporating the measurement error when the tolerances are rapidly changed to satisfy customer requirements.     

基于广义装配原理的产品生长型设计

通过研究生物生长与产品设计之间的相似性,提出了基于广义装配原理的生长型设计过程,研究了广义装配原理的三个理论构成。首先,在产品生长阶段,为实现生长过程中的自然选择,提出了以复杂度理论为控制因素的设计推理策略;其次,提出了功能公差设计理论,通过加工成本以及基于多因素的模糊质量损失成本体现广义装配成本,在确保产品功能的同时,以较低的装配与制造成本为公差的分配策略;在产品进化阶段,为保证产品良好的装配性能,采用了虚实结合设计技术。将以装配质量因素为核心的产品复杂度、精度以及制造、装配成本等众多设计因素并行集成于生长型设计过程中,实现了以全生命周期装配质量保障为核心的产品生长型设计。