Update documentation to represent new risk score calculation

solution_architecture.md

@@ -208,9 +208,19 @@ The information listed above is not visible to the user, but is used internally
 
 ![Figure 12: Risk calculation](images/solution_architecture/figure_12.svg "Figure 12: Risk calculation")
 
-*Figure 12* displays how the total risk score is calculated. The application is provided with a set of parameters, which are marked in blue in the figure. Each risk category (days since exposure, exposure duration, weighted signal attenuation, and the transmission risk factor) receives an input value from the event which is then mapped to a predefined value range. According to the [documentation of the framework](https://developer.apple.com/documentation/exposurenotification/enexposureconfiguration), "the attenuation is weighted by the duration at each risk level and averaged for the overall duration". 
-Each of those value ranges is assigned a risk score from 0-8, where 0 represents a very low risk and 8 represents a very high risk. This means that from each of the rows in the figure, one value is selected according to the input value for the corresponding category. The product of risk scores is the total risk score which is used to determine the defined risk levels that should be displayed to the user (e.g. “low risk” or “high risk”). For this decision, app-defined thresholds for the individual risk levels apply. 
-As all values are multiplied, a single category with a risk score of 0 means that also the overall risk score will be 0. Additionally, a central risk threshold specifies, when the user shall be explicitly notified about an exposure event.
+*Figure 12* displays how the total risk score is being calculated. The application is provided with a set of parameters, which are marked in blue within the figure. Each risk category (days since exposure, exposure duration, weighted signal attenuation and the transmission risk factor) receives an input value from the event, which is then mapped to a pre-defined value range. According to the [documentation of the framework](https://developer.apple.com/documentation/exposurenotification/enexposureconfiguration), "the attenuation is weighted by the duration at each risk level and averaged for the overall duration". 
+Each of those value ranges gets assigned a risk score from 0-8, where 0 represents a very low risk and 8 represents a very high risk. This means that from each of the rows in the figure, one value is selected according to the input value for the corresponding category. The product of the risk scores is used as the **total risk score** of the individual exposure.
+
+In order to incorporate the time spent within the ranges of attenuation buckets mentioned before, each of those three buckets is assigned a weight value, as shown in *Figure 13*.
+ The individual time values are multiplied with their according weight (*weight_1*, *weight_2* and *weight_3*). 
+ Their sum and a default bucket offset (called *weight_4* in *Figure 13*) forms the *Exposure Score*. 
+ The *total risk score*, provided by the Exposure Notification framework is then normalized and multiplied with the exposure score, resulting in the combined risk score.
+
+This combined risk score is used to determine, which defined risk level should be displayed to the user (e.g. “low risk” or “high risk”). For this decision, app-defined thresholds for the individual risk levels apply. 
+As the values above are multiplied with each other, a single category with a risk score of 0 means that also the overall risk score will be 0. 
+Additionally, a central threshold for the combined risk score specifies, whether an exposure event should be considered or not.
+
+![Figure 13: Calculation of the combined risk score](images/solution_architecture/figure_13.svg "Figure 13: Calculation of the combined risk score")
 
 Note that the transmission risk level plays a special role: It can be defined by the app and be associated with each individual diagnosis key (i.e. specific for each day of an infected person) that is being sent to the server. It contains a value from 1 to 8, which can be used to represent a calculated risk defined by the health authority.
 
@@ -252,10 +262,10 @@ Further details will be added as soon as they are available.
 
 ## LIMITATIONS
 
-Even though the system can support individuals in finding out whether they have been in proximity with a person that has been tested positively later on, the system also has limits (shown in *Figure 13*) that need to be considered. One of those limitations is that while the device constantly broadcasts its own Rolling Proximity Identifiers, it only listens for others in defined time slots. Those [listening windows are currently up to five minutes](https://covid19-static.cdn-apple.com/applications/covid19/current/static/contact-tracing/pdf/ExposureNotification-BluetoothSpecificationv1.2.pdf) apart and are defined as being only very short. In our considerations we expect the windows to have a length of two to four seconds. For the attenuation, the two buckets provided by the framework are being considered. A lower attenuation means that the other device is closer; we assume that an attenuation <50dB translates to a distance below two meters. A higher attenuation might either mean that the other device is farther away (i.e. a distance of more than two meters) or that there is something between the devices blocking the signal. This could be objects such as a wall, but also humans or animals.
+Even though the system can support individuals in finding out whether they have been in proximity with a person that has been tested positively later on, the system also has limits (shown in *Figure 14*) that need to be considered. One of those limitations is that while the device constantly broadcasts its own Rolling Proximity Identifiers, it only listens for others in defined time slots. Those [listening windows are currently up to five minutes](https://covid19-static.cdn-apple.com/applications/covid19/current/static/contact-tracing/pdf/ExposureNotification-BluetoothSpecificationv1.2.pdf) apart and are defined as being only very short. In our considerations we expect the windows to have a length of two to four seconds. For the attenuation, the two buckets provided by the framework are being considered. A lower attenuation means that the other device is closer; we assume that an attenuation <50dB translates to a distance below two meters. A higher attenuation might either mean that the other device is farther away (i.e. a distance of more than two meters) or that there is something between the devices blocking the signal. This could be objects such as a wall, but also humans or animals.
 
-![Figure 13: Limitations of the Bluetooth Low Energy approach](images/solution_architecture/figure_13.svg "Figure 13: Limitations of the Bluetooth Low Energy approach")
+![Figure 14: Limitations of the Bluetooth Low Energy approach](images/solution_architecture/figure_14.svg "Figure 14: Limitations of the Bluetooth Low Energy approach")
 
-In *Figure 13*, this is visualized while focusing on the captured Rolling Proximity Identifiers by only a single device. We assume that devices broadcast their own RPI every 250ms and use listening windows with a length of two seconds, five minutes apart. There are five other active devices – each representing a different kind of possible exposure. In the example, devices 3 and 4 go completely unnoticed, while a close proximity with the user of device 2 cannot be detected. In contrast to that very brief, but close connection with the user of device 5 (e.g. only brushing the other person in the supermarket) is noticed and logged accordingly. The duration and interval of scanning needs to be balanced by Apple and Google against battery life, as more frequent scanning consumes more energy.
+In *Figure 14*, this is visualized, while focusing on the captured Rolling Proximity Identifiers by only a single device. We are assuming that devices broadcast their own RPI every 250ms and use listening windows with a length of two seconds, five minutes apart. There are five other active devices – each representing a different kind of possible exposure. In the example, devices 3 and 4 go completely unnoticed, while a close proximity with the user of device 2 cannot be detected. In contrast to that very brief, but close connection with the user of device 5 (e.g. only brushing the other person in the supermarket) is noticed and logged accordingly. The duration and interval of scanning needs to be balanced by Apple and Google against battery life, as more frequent scanning consumes more energy.
 
 It must be noted that some of the encounters described above are corner cases. While especially the cases with a very short proximity time cannot be detected due to technical limitations, the framework will be able to detect longer exposures. As only exposures of longer duration within a certain proximity range are considered relevant for the intended purpose of this app, most of them will be covered.