Concurrent process tolerance design based on minimum product manufacturing cost and quality loss

In a concurrent design environment, a robust optimum method is presented to directly determine the process tolerances from multiple correlated critical tolerances in an assembly. With given distributions of multiple critical assembly dimensions, the Taguchi quadric quality loss function is first derived. The quality loss is then expressed as the function of pertinent process tolerances. A nonlinear optimal model is established to minimize the summation of manufacturing costs and product quality loss. An example illustrates the proposed model and the solution method .     

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.     

Determining the optimum process mean for a mixed quality loss function

In 1999, Wen and Mergen adopted the step loss function of a product to balance the costs of out-of-specification occurrences and to determine the optimum process mean. They considered a normal quality characteristic and assumed a known standard deviation for the process in their model. This paper proposes a modified Wen and Mergen [1] model with a mixed quality loss function to determine the optimum process mean. The quality loss of the product per item includes a quadratic loss within specifications and an out-of-specification piecewise linear loss.     

Simultaneous process mean and process tolerance determination with adjustment and compensation for precision manufacturing process

Conventional process planning of manufacturing operations presets fixed process means and process tolerances for all operations and allows outputs to be distributed around these fixed values, as long as the final outputs meet acceptable specifications. Most of these approaches consider process means and process tolerances to be independent decision variables in process planning with the resultant process means equal or close to the design targets of the blueprint dimensions. Furthermore, these approaches assume that process variability is small in comparison to the quality requirement, and that the phenomena of process shifting or deterioration are not factors of manufacturing operations. For these reasons, conventional approaches to process planning are inappropriate for high value, and precision manufacturing process, particularly of a complex part. Hence, this study introduces a process optimization model which considers process means and process tolerances simultaneously, with sequential operation adjustment to reduce process variability, and with part compensation to offset process shifting.     

Product and process dimensioning and tolerancing techniques. A state-of-the-art review

Dimensioning and tolerancing are important engineering processes in the different phases of a product development cycle. The two main phases in a product cycle where dimensioning and tolerancing techniques are extensively employed are in the areas of product design and process planning. Tolerance and dimension assignment in both product design and process planning has an equally important role in keeping the production cost down and, hence, requires equal attention as far as research into these areas are concerned. Another important motivating factor for research is that manual dimension and tolerance assignment is often tedious, time-consuming and requires a considerable amount of skill and experience on the part of the engineer, resulting in inconsistencies and errors. Extensive research, in the area of dimensioning and tolerancing in both product design and process planning, has been carried out with the advancement in computers since the 1970s. The purpose of this paper is to review the state-of-the-art dimensioning and tolerancing techniques in both product design and process planning and explore the opportunities for future research in these areas.     

Optimal determination of production run and initial settings of process parameters for a deteriorating process

This paper presents a generalized model for the optimal determination of a production run and the initial settings of the process mean and process variance for a deteriorating production process. It is assumed that the process deteriorates due to tool wear-out. The probability that the process deterioration starts at a random point in time follows an exponential distribution. Quality loss from the target values is measured using Taguchi’s quadratic loss function. The time dependent maintenance cost and the salvage value of the equipment are included. The expressions for determining the optimal process mean and process variance are developed. Numerical examples are provided to demonstrate the application of the proposed model.     

Dimensional and geometrical tolerance balancing in concurrent design

In conventional design, tolerancing is divided into two separated sequential stages, i.e., product tolerancing and process tolerancing. In product tolerancing stage, the assembly functional tolerances are allocated to BP component tolerances. In the process tolerancing stage, the obtained BP tolerances are further allocated to the process tolerances in terms of the given process planning. As a result, tolerance design often results in conflict and redesign. An optimal design methodology for both dimensional and geometrical tolerances (DGTs) is presented and validated in a concurrent design environment. We directly allocate the required functional assembly DGTs to the pertinent process DGTs by using the given process planning of the related components. Geometrical tolerances are treated as the equivalent bilateral dimensional tolerances or the additional tolerance constraints according to their functional roles and engineering semantics in manufacturing. When the process sequences of the related components have been determined in the assembly structure design stage, we formulate the concurrent tolerance chains to express the relations between the assembly DGTs and the related component process DGTs by using the integrated tolerance charts. Concurrent tolerancing which simultaneously optimizes the process tolerance based on the constraints of concurrent DGTs and the process accuracy is implemented by a linear programming approach. In the optimization model the objective is to maximize the total weight process DGTs while weight factor is used to evaluate the different manufacturing costs between different means of manufacturing operations corresponding to the same tolerance value. Economical tolerance bounds of related operations are given as constraints. Finally, an example is included to demonstrate the proposed methodology.     

过程均值偏移随机的EWMA控制图优化设计

针对过程均值偏移随机的情况,提出一种统计经济最优的指数加权移动平均控制图优化设计方法。该方法将过程受控、失控未检出、失控被检出并进行恢复这三个阶段定义为一个周期,分析了三个阶段的平均时长及质量成本构成,通过计算产品质量特性超出规格界限的概率量化缺陷产品所造成的质量损失,以单位时间内期望成本最小为目标建立指数加权移动平均控制图优化模型并设计了遗传算法,优化了样本容量、采样间隔、平滑界限和控制界限等参数。通过与休哈特均值控制图、传统指数加权移动平均控制图等进行对比验证了该模型的优越性。     

A graph theoretic approach linking design dimensioning and process planning

The purpose of this paper and its companion (Part 2) is to present a rigorous graph theoretic model to link designing with process planning. This paper shows how to generate process plans from design dimension trees. It is the foundation for the companion paper, Part 2, which shows how part dimensioning (during designing) can be guided by knowledge of the datum-hierarchy tree structure underlying process plans. Design dimensions are represented as a design dimension tree, which is the basis for defining an ideal (optimal) datum-hierarchy tree of a process plan. The ideal datum-hierarchy tree, in turn, is used to define measures of process planning efficiency. These measures can be utilised to compare actual process plans and improve manufacturing processes. An example is presented to illustrate the concepts and method.     

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.     

公差设计多目标模型及其粒子群优化算法研究

为解决成本一公差设计模型中忽视产品质量的问题，以新型的田口质量观和Pareto最优解集概念为基础，提出了一种公差设计多目标模型。该模型将加工成本和质量损失分别作为设计目标，并以统计法公差装配成功率为约束条件，获得了比极值公差法更加宽松的公差限。改进了传统的粒子群优化算法，利用Pareto最优性重新定义粒子，然后采用快速非支配排序技术进行粒子的适应度排序，使其能够有效地对多目标模型进行求解。该算法对具体工程实例求解时，一次运行就可求得令人满意的Pareto最优解集，设计者可以根据生产实际和市场需求从中进行选取。通过对求得的Pareto进行最优前沿的分析，可得到该类零件公差设计的特性，其结果验证了公差诒计的一船规徨．     

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。     

Using target costing concept in loss function and process capability indices to set up goal control limits

This paper depicts the relationship among the loss function, process capability indices and control charts to establish goal control limits by extending the target costing concept. The specification limits derived from the reflected normal loss function is linked through the C _pm value, computed either directly from the raw data or given by management or engineers, to conventional control charts to obtain goal control limits. The target value can be taken into consideration directly. The advantages of applying the target costing philosophy are also discussed. This paper explains, from a quantitative approach, that reducing process variation is not enough to solve quality problems. In fact, reducing process variation should be used along with bringing the process mean to the target value.A list of symbols K: The maximum-loss parameter in the reflected normal loss function - : The shape parameter in the reflected normal loss function, /4 - T: The target value - : The distance from the target value to the point where K first occurs (tolerance or specification limit) - E(L(y)): The expected loss associated with the reflected normal loss function - : The average value (mean) of a population - : The standard deviation of a population - _T : The standard deviation from the target value of a population - : The estimated standard deviation of - : The new process standard deviation when 2 are applied - n: The sample size of the subgroup - d ₂: The parameter used to estimate , determined by n - D ₄, D ₃, and A ₂: The parameters in and R control charts, determined by n - c ₄: the parameter used to estimate , determined by n - B ₄, B ₃, and A ₃: The parameters in and S control charts, determined by n - L(y): The general loss function - L ₁(y): The general loss function when the quality improvement is implemented - h: The parameter used to determine L ₁(y), where L ₁(y)=hK - f(y): The probability density function