## 4 Discussion
### Limitations  
In this study, we used the DOE method and examined the control elements with an fractional factorial I-optimal response surface test design. The test design used had the resolution IV, i.e., the effects of the main factors (A, B, C, etc.) were neither mixed with each other nor with effects of the two-factor interactions (AB, AC, etc.). However, effects of the main factors were mixed with three-factor interactions (ABC, ACD, etc.), as well as effects of the two-factor interactions among themselves. This type of design is used to identify factors that have a significant effect on the evaluation parameters. The mathematical models created and optimization calculations performed in this study provide initial guidance. In a follow-up study, detailed investigations with the significant factors will be conducted with a full factorial design. The important factors will be evaluated on more levels and with a significantly increased number of experiments in order to further increase the accuracy of the mathematical models.  
The main field of application of the DOE is chemical and process engineering [59]. However, the DOE is also being used more and more in the field of human factors [78]. Compared with chemical and process engineering, signal-to-noise ratios (SNRs) for human test participants must be expected to be higher owing to human variabilities such as age, affinity for technology, and prior VR experience. The SNR presented in Tables 6 and 9 indicates that the tests had high scatter in some cases. In our estimation, these are mainly due to the different prior experiences of the test participants with the VR systems. In addition, the standard deviation of questionnaires in the field of usability and user experience is high [79].  
This also made it difficult to perform confirmatory runs. Tables 7 and 10 show the results of the confirmation runs, in which four additional test participants evaluated the optimized control elements. The theoretical parameter values calculated using the mathematical models for these control elements deviated for both the joystick and rotary control for the dimensions of the User Experience Questionnaire. However, the calculated 95% prediction intervals were partially outside the scale of the questionnaire. The upper limits of the 95% prediction interval were above a value of three for all UEQ dimensions, and thus above the scale. In addition, it could be assumed that some test participants tended towards the middle [80; 81]. Consequently, extreme values of the questionnaire were selected less frequently. However, during the optimization calculations, the design of the control elements was calculated to precisely achieve these extreme values. Therefore, the mathematical model for the mental workload for operating the rotary control could not be confirmed. According to the optimization calculation, the optimized rotary control should achieve a score of zero. However, this score is unlikely in practice. The optimized rotary control achieved a score of 2.63 in the confirmation runs. This corresponded to a low mental workload.  
Overall, the experiments showed that although the response behavior of the test participants could not be precisely modeled mathematically, the models were sufficient to calculate suitable control elements that achieved good results on the questionnaires. Comparatively high values were achieved for the UEQ and SUSQ. The positioning times (time on task) and positioning accuracy were even better than those predicted by the mathematical models. Generally, these human performance data, such as positioning accuracy or the time on task, can be better represented mathematically than factors for perception, such as mental workload.