7.3.1 Societal risk
Based on the information in Appendix B, a standard QRA of the hospital ward can be performed. The analysis results in 100 subscenarios. The first 96 subscenarios represent the final
outcomes of the event trees in Figures B2 and B3; 48 for daytime conditions and 48 for night-time conditions. The last four
subscenarios can be found in the initial part of the event tree (Figure B1) but do not result in any unwanted consequences as the fire is either extinguished or will not continue to grow.
The Kaplan-Garrick triplets are derived and collected in two vectors, containing subscenario probabilities and consequences. The consequences are expressed in terms of the number of patients not being able to escape within the available time defined by the occurrence of untenable conditions. The consequences have been derived using values representing the credible worst conditions. No specific distribution fractile has been used in estimating these values, see Chapter 4. The triplets are sorted according to the procedure described in Chapter 6 and the resulting risk profile is shown in Figure 7.3 as the solid line.
The initial probability of fire, pinitial, has been chosen to be 0.07
fires per year per ward based on the reasons presented in Appendix B. The vertical axis in the diagram for societal risk will then express the probability of the occurrence per year per ward.
An alternative design strategy, with no sprinkler system, was also examined using this method. The dashed line shows this design risk profile. This risk profile indicates a higher risk, which is rational and understandable as sprinkler systems are assumed to decrease the hazard of fires.
The profiles in Figure 7.3 were derived using the critical conditions for untenable environment. The same information, using lethal conditions, can be found in Figure 7.4.
100 101 102 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1
X, Number of affected patients
P(X>x)
Figure 7.3. Risk profile for the standard quantitative risk analysis using critical untenable conditions. Dashed line = risk profile for design alternative without sprinkler system.
100 101 102 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 X, Number of fatalities P(X>x)
Figure 7.4. Risk profile for the standard quantitative risk analysis using lethal untenable conditions. Dashed line = risk profile without sprinkler system.
There is only a small difference between the corresponding curves in the two figures, indicating a small difference in available escape time between the two conditions critical and lethal. The risk profile for critical conditions is, of course, located slightly higher than that for lethal conditions. This difference should not be interpreted as a difference in risk level, but indicates the difference in the
definition of hazardous environment. Using the more severe lethal conditions result in a longer available escape time.
The result is that a higher number of patients can be evacuated within the available time. The maximum number of patients unable to be evacuated is also different: 17 patients versus 15.5 patients for the critical and lethal conditions, respectively. The conclusion that can be drawn from this is that there is only a small time
margin between the two levels of untenable conditions for growing fires. One should bear in mind that the fires are assumed to grow continuously as a function of time. Other kinds of fire development
might result in a different situation. It is, however, believed that the trend would be similar, i.e. a small difference in available time between critical conditions and lethal conditions.
Based on the results, the average societal risk can also be obtained. The products of the probability and the consequences for each subscenario are summed to give the average societal risk, according to Eq. [6.1]. For this scenario the average risk using critical conditions is 4.4+10-4 persons per year per ward. This means that in an average year 4.4+10-4 persons will become exposed to untenable conditions and prevented from further evacuation due to fire.
This can be expressed in another way. A fire resulting in at least one victim, i.e. a patient being exposed to the defined untenable conditions, can be expected to occur once every 227 years. The measure can be used to compare different design solutions and to make statements on relative safety.
The average societal risk of suffering multiple fatalities in the ward can also be calculated using the same procedure but different criteria for determining the available time. When the risk measure is derived assuming the lethal conditions, the value found is 2.7+10-4 persons per year per ward.
The two values of average societal risk given above were derived for a situation in which sprinklers are operating with a conditional probability of 0.96. The alternative design solution without the sprinkler system has also been analysed in terms of the average societal risk. The corresponding values for the average societal risk are 2.7+10-3 patients per year per ward, assuming critical
conditions and 2.2+10-3 patients per year per ward assuming lethal conditions. There is thus, a difference in risk of a factor of
approximately 6 - 10 between the scenarios with and without sprinklers.
This comparison between a ward with and without sprinklers was presented to illustrate the capability of the method. Similar results can be obtained by comparing situations with and without an automatic fire detection device, etc. The risk profiles and average risk measures will be different, but it is possible to illustrate the benefit of devices which increase safety in a quantitative manner. The question is whether the ward without the sprinkler system is acceptable or not. The sprinkler-equipped ward may result in an "oversafe" and too expensive situation. On the other hand, with a sprinkler system, a higher number of patients could be housed on the ward with the same risk level as the ward without the sprinkler system.
7.3.2 Individual risk
The individual risk has also been derived for the two levels of untenable conditions. The individual risk is defined here as the probability per year of the escape routes being blocked by the fire or patients being killed by the fire, depending on the choice of untenable conditions.
In the critical conditions case, the individual risk was equal to 1.8+10-4 per year and 1+10-4 per year in the lethal conditions case. The measure of risk is the sum of the subscenario outcome
probabilities leading to the unwanted event, i.e. that the escape routes are blocked or that a patient is killed, cf. Eq. [6.2]. These values can also be found from the risk profiles as the points at which the curves cross the vertical axis.