# Integrated Tolerance and Fixture Layout Design for Compliant Sheet Metal Assemblies
### Tolerance-Cost Optimization  
Managing uncertainty is a key activity in product development to realize products with high reliability, robustness, and safety [4; 5]. In this regard, tolerancing aims to assure product quality, e.g., functionality or aesthetics, by managing and limiting the unavoidable geometric part variations caused by manufacturing uncertainty [4; 6]. Tolerance design, which corresponds to the last step in a robust product design [1], consists of three main tasks, viz. tolerance specification, tolerance allocation, and tolerance analysis [7]. While tolerance types and references are chosen for the functional relevant geometry elements in tolerance specification, tolerance allocation is used to assign suitable tolerance values to them [7]. In the early years of tolerancing, experience, handbooks or best practices [8], graphical and simple analytical approaches, such as equal or proportional scaling [9; 10], as well as the repetitive application of tolerance and sensitivity analysis [11], could meet the former requirements [12; 13].  
However, the steadily increasing cost and quality pressure required the development of more sophisticated approaches to automatically find the combination of tolerance values that lead to minimum costs, but can also assure high product quality [12; 13]. Tolerance-cost optimization--also known under the terms optimal/least-cost tolerance allocation/design/synthesis--accelerates the usually manual, trial-and-error based search by turning the task into a mathematical optimization problem in order to find the optimal compromise between cost and quality [12]. In the beginning, its applicability was mainly limited by the low computing powers and the lack of powerful optimization algorithms [12]. The development of soft-computing, nature-inspired meta-heuristic algorithms, in combination with the significantly increased computer technology, has finally paved the way for its practical application to complex engineering systems [12; 13].  
At the same time, the general idea of concurrent and simultaneous engineering has lead to a joint consideration of the previously separated optimization-based tolerance allocation methods from the design and manufacturing [12; 13]. As a consequence, design-driven approaches have successively adopted additional manufacturing aspects, which lead to a shift to a process-oriented tolerance allocation [12; 14].  
In this regard, the research scope mainly depends on the addressed type of assembly process [12; 15]. The total variation of assemblies, where the parts are located and fixed through part-to-part mating surfaces, is mostly influenced by the individual geometrical part variations [15; 16]. Further cost aspects, such as quality loss, including tool degradation and maintenance planning [15; 17; 18] and environmental costs [19], can additionally be considered in tolerance-cost optimization. Research in the field of process-oriented tolerancing summarily shows that the joining technique itself, the assembly and the fixture layout, and its tolerances have a significant impact on the results of optimal tolerance allocation.