## 3 Results
### WBI Examples  
To compute the _WBI_, the following data points for 13 April 2024, which provide a _WBI_ of 8, are analyzed. The parameter values are presented in Figure 9 (case 1). The second entry corresponds to 21 September 2023, with almost double the number of steps, fewer wakeups, and a low-stress level, as presented in Figure 9 (case 2). The calculated _WBI_ is 5. Although the values may initially suggest a stress level in the first case, the four components counterbalance each other, resulting in an overall equilibrium. The _HRC_ evaluates the average heart rate against established health standards using Equation (1). A value of zero suggests a potential stress level. The following three parameters could confirm this value. Otherwise, the value contribution will be balanced by the other three components. \[HRC_{2024-04-13}=0.25\times\left(\frac{117-47}{71}\right)=0.24\]  
The _PAC_ assesses the level of physical activity, represented by the number of steps taken, using Equation (2):  
\[PAC_{2024-04-13}=0.25\times\left(\ln(7161)+\ln(4781)+\ln(925)+\ln(152)\right)=7.30\]  
Figure 9: Two examples of computing WBI. The \(SQC\) measures the quality and duration of sleep, factoring in deep and shallow sleep times, using Equation (3). The zero value indicates poor sleep, but it does not mean that the job influences it. \[SQC_{2024-04-13}=0.25\times\frac{46}{381\times 22}=0.00137\approx 0\]  
The SI evaluates stress levels identified during the monitored day using Equation (4). A value of 0 indicates no stress during working hours. \[SC_{2024-04-13}=0.25\times 0=0\]  
The \(WBI\) calculation uses Equation (6) and results in a value of 8:  
\[WBI_{2024-04-13}=ROUND(0.24+7.30+0+0)=8\]  
In the second case, corresponding to the identification of stress levels during the working period, there were significant heart rate fluctuations relative to the average, a high level of passive activity, and restless sleep. This entry corresponds to 21 September 2023, for which the \(WBI\) was calculated at 5. All four components indicate low values: an \(HRC\) of 0.28, a \(PAC\) of 4.89, a \(DSC\) of 0, signaling significant sleep issues, and an \(SC\) of 0.25. In the following, two \(DSC\) scenarios are simulated to demonstrate the feasibility of the proposed Equation (11) for \(EGI\). The first case sends 20 negative messages out of 100 marked as S\({}_{1}\), while the second case sends 90 negative messages marked as S\({}_{2}\). Consequently, the analysis focuses on two specific days, i.e., 28 February 2023 and 21 September 2023, to explore the \(DSC\) and \(WBI\) correlations. This helps identify how the \(EGI\) responds to different combinations of \(DSC\) and \(WBI\): high \(DSC\)-high \(WBI\), high \(DSC\)-low \(WBI\), low \(DSC\)-high \(WBI\), and low \(DSC\)-low \(WBI\). The results demonstrate the effectiveness of Equation (11), which corresponds to the \(EGI\). By applying Equation (10), the \(DSC\) values are as follows for the days exemplified above:  
\[DSC_{date\_S1}=10-\frac{20}{100}\times 10=8\]  
\[DSC_{date\_S2}=10-\frac{90}{100}\times 10=1\]  
Using Equation (11) for 28 February 2023, the \(EGI\) values in the two scenarios are as follows:  
\[EGI_{2023-02-28\_S1}=ROUND\left(\frac{8+8}{2}\right)=8\]  
\[EGI_{2023-02-28\_S2}=ROUND\left(\frac{8+1}{2}\right)=4.5=5\]  
By employing Equation (11) for 21 September 2023, the \(EGI\) values in the two scenarios are as follows:  
\[PAC_{2024-04-13}=0.25\times\left(\ln(7161)+\ln(4781)+\ln(925)+\ln(152)\right)=7.30\]0  
\[PAC_{2024-04-13}=0.25\times\left(\ln(7161)+\ln(4781)+\ln(925)+\ln(152)\right)=7.30\]1  
These results show that the \(EGI\) produces low values corresponding to low well-being levels when both the \(WBI\) and the \(DSC\) have low values. This secures no risk of misinterpretation caused by poor physical condition or miscommunication. This means that Equation (11) accurately reflects situations where both well-being and satisfaction are low.