## 2 Materials and Methods
### Results  
Using the Cochran Q test previously described, it can be shown that there are significant differences between the alternatives (a)-(q) for all four questions: (1)-(4). The \(p\)-values for each question are all below \(10^{-7}\). For a deeper analysis of what categories (a)-(q) actually have a significant difference, the MRD is applied. In Figure 1, the results from the survey are shown. Some observations can be made. * In research today (left chart, blue bars), the most popular areas are simulation (e) and digital twins (f). For simulation (e), the MRD test shows that there is a significant difference (\(\alpha=0.05\)) to all other categories except (c) and (f). * In the industry today (left chart, red bars), the most popular areas are tolerance analysis and evaluation (c), followed by tolerance specification (a) and simulation (e). For (c), the MRD shows that there is a significant difference (\(\alpha=0.05\)) to all other categories. * For the future (right chart), digital twins (f) are considered highly important in both research and the industry. This is also true for simulation (e), new manufacturing methods (k), and Industry 4.0 (n). For research and digital twins (f)), the MRD shows that there is a significant difference (\(\alpha=0.05\)) to all other categories except (e). For the industry and (f), the MRD test shows that there is a significant difference (\(\alpha=0.05\)) to all other categories except (e), (g), (k), and (n). To see the differences between the situation today and future needs, the differences between the answers are compared (see Figure 2). This illustrates the increased need of (f) (digital twins), g (zero-defect manufacturing), k (new manufacturing methods), and n (Industry 4.0), especially in the industry. For digital twins (f) it can be noted that the increased need for industrial development is not matched by an equally large increase in future research. Digital twins are already a hot research topic, as seen in the left part of Figure 1, and the challenge is the applicability of the digital twin framework in the industry. This will be the focus of a more in-depth interview study, presented in the following sections. Other interesting observations from the survey can be reached if the data is filtered based on the affiliation of the respondents (see Figure 3). Figure 1: Responses to questions (1)–(4). The left part shows what areas are believed important today in research (blue) and the industry (red). The right part shows what areas are believed to be important in the future. Figure 2: Gap between the future’s and today’s research and development needs in research (blue bars) and the industry (red bars). By filtering data into groups, the sample size for each group decreases, and therefore, not all differences are statistically significant. The z-test introduced in Section 2.2 is used to test for significance. Significant differences, using \(\alpha=0.10\), are encircled in Figure 3.  
Some observations about the future:  
* For research in the future, digital twins are highly valued in both academia and the industry. The significant differences are found in (c) (tolerance analysis and evaluation, (e) (simulation), and (g) (zero-defect manufacturing), which all are considered to be more important among employees in academia. On the other hand, (a) (tolerance specification) and (j) (new materials) are considered more important among industrialists than academics. * For the industry in the future, the top priority is, again, digital twins. There is a higher level of agreement between people from academia and the industry in this area compared to research in the future, with significant differences only in (a) (tolerance specification), (b) (tolerances synthesis), and (o) (robust design). In general, it can, based on the study, be concluded that digital twins are one of the most important areas within variation management.