# A Novel Approach for the Definition of an Integrated Visual Quality Index for Residential Buildings
## 3 Methods
### Structure of the Index  
The visual quality index is composed of two parts, defined as quantitative and qualitative. The quantitative part is given by the value of five metrics (sDA, sDGP, UGR, E\({}_{\text{m}}\), and CCT) calculated in relation to a reference year. Each metric is assigned a relative weight (\(\omega\)) that represents the importance of the measured aspect in relation to the overall visual comfort of the inhabitants. The weights are shown in Table 3 and were proposed on the basis of the following considerations: daylight and electric lights were given the same importance; in each field, more importance was given to illuminance rather than to glare; and finally, color temperature was considered less important than the other parameters. This is consistent with the study of [PERSON] et al. [22], who state that solar access is the most important parameter, and that artificial lighting hours have a significant influence on visual comfort and inhabitants may be more tolerant to glare in residential spaces rather than in offices. In order to summarize in a single value the trend of each metric throughout the year, a method was exploited that is widely used also in other field of IEQ assessment consisting of the definition of a performance index (PI) which represents the percentage of values of a given metric during occupied hours that falls within an acceptability range [60]. Following the method proposed by [PERSON] et al. [18], a time fraction matrix is calculated for every room of the building with the PI of every metric in each class. This matrix is multiplied by the relative weight vector to obtain the time fraction weighted mean vector:  
\[\left[ \begin{array}{cccc}sDA_{I}&sDGP_{I}&Em_{I}&UGR_{I}&CCT_{I}\\ sDA_{II}&sDGP_{II}&Em_{II}&UGR_{II}&CCT_{II}\\ sDA_{III}&sDGP_{III}&Em_{III}&UGR_{III}&CCT_{III}\\ sDA_{IV}&sDGP_{IV}&Em_{IV}&UGR_{IV}&CCT_{IV}\end{array} \right]\times\left[ \begin{array}{c}0.30\\ 0.20\\ 0.25\\ 0.15\\ 0.10\end{array} \right]=\left[ \begin{array}{c}f_{I}\\ f_{II}\\ f_{II}\\ f_{IV}\end{array} \right]. \tag{1}\]  
This vector allows for the calculation of the VQI of the room using the following equation:  
\[VQI=100\cdot f_{I}+70\cdot f_{II}+35\cdot f_{III}+0\cdot f_{IV}. \tag{2}\]  
The building visual quality index (BVQI) is the result of a weighted average of the VQIs of all the rooms of the building (with the exclusion of corridors and non-heated zones) with the addition of the qualitative score. The weight of each room (W) is given by the formula  
\[W_{room}=\frac{A_{room}}{A_{building}}, \tag{3}\]  
where A\({}_{room}\) is the net floor area of the room and A\({}_{building}\) is the net floor area of the whole building. According to this definition, the sum of the weights of all the rooms equals one. This weighting model is based on the consideration that the size of the room is directly correlated with its importance. For the sake of completeness, other types of weighting were tested, for instance those considering the estimated hours of utilization of each room, but the results were comparable, and the proposed approach seemed the most direct and easy to apply. The qualitative score (QS) consists of a 0-8 points score, calculated only once for the whole building and added to the quantitative part. This score was assigned considering the eight checks relative to view out, shading devices, and flexibility and control. Each check was evaluated room by room and was gained when the assertion was true for more than 50% of the floor area of the building. \[BVQI=\left[ \begin{array}{cccc}VQI_{living}\\ VQI_{kitchen}\\ VQI_{bathroom}\\ \cdots\end{array} \right]^{T}\times\left[ \begin{array}{cccc}&W_{living}\\ W_{kitchen}\\ W_{bathroom}\\ \cdots\end{array} \right]+QS. \tag{4}\] \begin{table}
\begin{tabular}{l l l} \hline \hline
**Metric** & **Relative Weight \(\omega\)** & \\ \hline sDA & 0.30 & 0.5—Daylight \\ \hline sDGP & 0.20 & \\ \hline E\({}_{m}\) & 0.25 & \\ \hline UGR & 0.15 & 0.5—Electric lighting \\ \hline CCT & 0.10 & \\ \hline \hline \end{tabular}
\end{table}