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The quality of a system for any given function is affected by the variability of the output response related to that function. The variation of the output response is typically an aggregate of many variations from components of the system. In order to study how the variation of the components is transmitted to the output response, it is desirable to derive variance transmission equation (VTE) that describes the variance structure between components and the response. Based on the availability of system transfer function (STF) for a given function or application, three approaches are discussed to develop the variance transmission equation: Taylor series approximation, response surface model, and design of experiments methods. The developed variance transmission equation is incorporated in the tolerance design model that is used to find an economic balance between the desired quality and the cost associated with variance. Using a case study for a passive filter network, we illustrate how to improve the quality of a device using tolerance design through variance transmission equation. The results demonstrate the quality improvement of the system using the proposed economic optimization model.

This paper uses the Taguchi method on the tolerance design of a hinge mechanism with the aim of obtaining a design that is insensitive to variations in manufacturing tolerance and joint clearance. The contribution of each control factor in the mechanism to the variations was also quantified. From the analysis of the response table and diagram, it was concluded that the dimension r₁, r₂, r₄ and β had a significant effect on the quality of the mechanism, contributing a total of 82.36% to product variation and were consequently named the key dimensions. The tolerance of these factors must therefore be tightened to improve the quality of the mechanism. Through a series of confirmation experiments, it was revealed that tightening the tolerance resulted in an increase in the S/N (signal to noise) ratio by 1.851 db and a reduction in product variation by 19.25% from the original 80.75%. The proposed method does not require complex mathematical derivatives, but simply the input and output relationship of the system. The method proposed in this study can be applied to all types of mechanism.

Tolerance design technique balances the expected quality loss due to variations of the system performance and the cost due to controlling these variations. Measures of quality are discussed and quality loss function is used for tolerance design. The goal is to minimize the total loss that consists of the quality loss to the customer and the cost increase to the producer. The design methodologies are presented for the tolerances of products before shipping to the customer and the tolerances of lower-level characteristics. The approaches to tolerance design for components and subsystems are also demonstrated using the variation transfer function. Examples are given as illustrations of the methodology.

Tolerance design is one of the key activities in the product creation process. It not only directly effects product quality but also has significant impact on manufacturing process and product cost. The tolerance design should never be overlooked in the product creation process. Though the importance of the tolerance design is well understood in the engineering community, a well established process for the tolerance design in the product creation process is still lacking. The practice of the tolerance design in most automotive industries is not consistent, and it largely depends on individual experience. Best practice and valuable knowledge is not captured in a systematic manner, and most often the new design does not benefit from best-in-class design knowledge. Most engineers can only go back to the very previous design for reference due to the lack of knowledge base tools. Therefore, optimal tolerance design could be missed. In addition, most tolerance design at earlier product lifecycle only concentrates on product functionality itself. Some serious manufacturing issues could be overlooked at the beginning and are only uncovered until it is too late. In addition to the delay of the product launch, the cost of fixing these manufacturing problems is often very expensive. Moreover, lack of a tool or process to look at system level tolerance interactions causes designers to miss optimal tolerance for each individual part design. In this paper, a tolerance design process is proposed in order to optimize product tolerance for function, manufacturing cost, and quality. This process will capture the knowledge of product tolerance design and optimize this knowledge to re-apply to every new product design. Also, with the help of feature-based design and knowledge-based technology, manufacturing process, cost, product quality, etc. could be considered at the earliest stage of the design cycle. Therefore, the quality and cost of design will be better understood and controlled compared to an ad hoc tolerance design process.

A new method for parameter design, where the cost is influenced remarkably by the parameter central value, had been put forward by me in 1996. In this paper, the quality loss function is improved based on it so that a synthetic method, in which parameter design and tolerance design can be made in progress at the same time, can be constructed. The synthetic method can theoretically achieve the minimum quality loss value and it is verified by a calculating case of mechanical design that the synthetic method can obtain a smaller quality loss value than Taguchi's classic method