## 3 Linking Early Robust Design and Optimal Parameter and Tolerance Design
### Comparison of Characteristic Aspects  
In the following, the characteristics of approaches for early robust design, parameter optimization, and tolerance optimization are compared, taking into account the associated terminology. For the comprehensive collection of influencing factors, the 7 M of the Ishikawa diagram known from quality management [64; 65] were considered first. This collection is completed by a cross-check with the aspects developed within the PSI framework, which enables a comprehensive description of design activities under various conditions [66]. Inspired by [PERSON]'s P-diagram [5], the collected factors are categorized in input, output, control as well as noise factors and are shown as a black box in Figure 2.  
Table 2 compares the domains early robust design, robust parameter optimization and tolerance-cost optimization by means of these aspects. The focus here is not on a precise classification of all terms used in the respective domains or a sharp differentiation, which is not feasible anyway due to the large variety of partially combining approaches. Instead, the aim is to give a common understanding of the essential aspects of the three domains so that engineers from different domains can gain an insight into the other one and thus understand the interrelations. Accordingly, Table 2 is limited to the two widely used methods of robust parameter optimization (with mean shift and robustness objective) and tolerance-cost optimization (with cost objective) highlighted in Figure 1.  
First of all, the comparison of the characteristics shows a significant difference between early robust design and the subsequent domains primarily due to the different levels of part and product geometry definition, which is also represented by the changing _dimension_. Along with the increasing detailed _functional system description_, the _extent_ of the optimization in late design stages is narrowed down and more specific. However, the apparently lower _number of perspectives_ respectively complexity within the optimization domains is compensated by an increasing _level of detail_, see Table 2 section _domain characteristics_. Moreover, the _engineers_ and the _environments or departments_ dealing with approaches from the respective domains change, starting with concept developers up to multidisciplinary tolerance experts incorporating manufacturing and inspection knowledge. The individual engineers are increasingly supported by computer-aided _facilities_ and _specific methods_ as product development progresses, see Table 2 section _control factors_. This goes along with a change of the inherent _uncertainties_, transforming from primarily epistemic uncertainties regarding conceptual design decisions to aleatory or irreducible uncertainties, e.g., resulting from the virtual mapping accuracy of reality [67]. Accordingly, a high degree of primarily _informal knowledge_ and design knowledge or experience is necessary for a successful concept and early robust design, see Table 2 section _noise factors_. This results from the poor _availability of formal knowledge_ in early development stages. It is also reflected in the primary available _information_ that forms the starting point for the respective approaches in the domains. They are increasingly specific and comprehensive. However, this concretization also leads to an increasing restriction of the scope for action or improvement. While in early robust design, only the requirements are considered as rather qualitative _boundary conditions_, the optimizations are subject to clear quantitative constraints, see Table 2 section _input_. Figure 2: Aspects considered in the comparison of the approaches. Accordingly, _quantitative objectives_ as well as _objective metrics_ are clearly defined in optimization, see Table 2 section _output_.