Probabilistic analysis - Fire risk assessment:

Probabilistic analysis relies on data and data comes from experience.  The broader the experience, the larger the data source and the more accurate the data becomes.  Data gained from experience might tell us that we can generally expect there to be, for example, between 2 and 6 flat fires in a given city every Friday night.  The large data source (i.e. all the flats in the city - those that have fires and those that do not) ensures that we can be reasonably confident that this number of flat fires (between 2 and 6) will occur almost every Friday night.  This is the sort of data that is used to calculate how many fire appliances are needed in a city and where they should be located.

But if we try to use this data to predict the probability of a fire in a single particular flat on a single particular Friday night then we will run into difficulties.   It is not that we cannot manipulate the figures to come up with a probability, this can be done fairly easily.  For example, in a city with 100,000 flats the probability of a fire in a particular flat on a particular Friday night could be calculated as being between 2/100,000 and

6/100,000 or 0.00002 to 0.00006 or 0.002% to 0.006% and to extend this, if  we considered the flat over a period of 1,000 Friday nights (approximately 20 years) then the probability of a fire could be calculated as between 2% and 6%.   But all these figures would be wrong.

The data of between 2 and 6 flats every Friday night covers all flats in the city and those flats have a broad range of conditions and of type of people who live in them and of how well the flats are maintained.  The single particular flat that we are interested in might be very well maintained, in a luxury block occupied by very safety conscious people and the true probability of it having a fire on a Friday night might be virtually zero.     

Alternatively,  it  might  be  very  poorly  maintained,  in  a  semi-derelict  block occupied by people who have no sense of safety, in which case the probability of having a fire on a Friday night might be very high indeed.  If it was 1%, for example, we would expect there to be, on average one fire in the flat every two years.=

NFPA 551 does give guidance on assessing uncertainties and on 'What if?' analysis where foreseeable errors are built  into the assessment  process  but great caution should be used when attempting probabilistic fire risk analysis and generally such analysis would be best left to statisticians.