Risk distribution.   The general KINNEY formula: { Sev * Poc * Exp < C} gives the impression that there is a constant level of acceptable risk. This is not entirely true, as the values used to define the components Sev, Poc and Exp are defined on a non-linear scale. The general public expects that the risk level would be more or less uniform for similar risk situations, but real accidents prove from time to time the contrary. Code requirements are normally NOT retro-active, which means that very often older buildings are less fire safe that new ones, and that a uniform legally accepted risk level does not exist.   A fire risk assessment method cannot link fire safety to a construction date; on the contrary it should be a tool to upgrade existing situations to present standards by supporting the equivalency concept. But even in comparable risk situations, the expression for the risk level should be modulated to reflect individual differences. This is the basis for fire insurance premium rates. It is basically the price for transferring risk to the insurance company. Basically, there is a standard rate per business category, reflecting the statistical observed fire damage/ property value ratio, based on the average fire severity for that business category. The basic fire insurance rate is then modified for the presence of well know risk varying circumstances, such as heating systems, use of flammable liquids, welding operations, etc. In such situations, the possibility of ignition is increased and in order to obtain the same premium rate (relevant for the risk level) additional safety precautions are required. It means that instead of a constant acceptable limit of risk, there should be a modulated limit, linked to identifiable ignition sources. In FRAME, this condition is met by the { 1.6 - a } common part of the acceptable risk A - formulas. This part of the formula transforms the risk value in a way similar to insurance tariffs. The value for that part of A means actually that a higher number of ignition sources in the compartment will increase the overall fire risk. It also emphasises the need for fire prevention, where the most elementary rule is to reduce as much as possible the combination of fire load and ignition sources in one place. Risk aversion   People do not like high severity risks even with low probabilities. This risk aversion is the basis for the whole insurance industry. By buying an insurance policy, the owner a a building transforms a high severity / low probability loss ( my house being destroyed by a fire) into a high probability / low severity loss : I have to spent every year a bit of my money on insurance premiums. This aspect of risk aversion must be reflected in the results of any risk assessment method. Kinney solved this by defining the values of the contributing factors on a non-linear scale. In FRAME, risk aversion is incorporated in the formulas used for P, A and D. A pure logarithmic risk calculation formula would be a sum of log values: "log Sev + log Poc £ Log C - log Exp " and not a division as in the FRAME formula R = P/D.A.  However, by choosing for FRAME probability parameters values in the range around 1 , combined with an expression of the type "log Severity(Q) + Correction" x Probability Modulation, a risk value scale is built where minor risks are slightly underestimated and higher risks overestimated, which corresponds with the risk aversion phenomenon. This difference between a pure log based risk scale and the  (1 + log) scale is given in the following table, which illustrates the value changes by both formulas:   basic value for "log S" 0.8 1 1.2 1.4 1.6 risk *2 =+ log (2) 1.1 1.3 1.5 1.7 1.9 risk * 2 = x {1 +log (2)} 1.04 1.3 1.56 1.82 2.08 risk * 5 = + log (5) 1.5 1.7 1.9 2.1 2.3 risk * 5 = x {1 +log (5)} 1.36 1.7 2.04 2.38 2.72 risk * 10 = + log (10) 1.8 2 2.2 2.4 2.6 risk * 10 = x {1 +log (10)} 1.6 2 2.4 2.8 3.2 risk / 5 = - log (5) 0.1 0.3 0.5 0.7 0.9 risk / 5 =/ {1 + log (5)} 0.47 0.59 0.71 0.82 0.94 risk / 10 = - log (10) -0.2? 0? 0.2? 0.4? 0.6 risk / 10 = / {1 +log (10)} 0.4 0.5 0.6 0.7 0.8 This modified formula avoids negative values for R, which would hurt the users’ need to express the risk on a positive growing scale. Furthermore preventive actions, such as avoiding ignition sources, have a greater risk reducing effect than adding a high level of protection. taken fully into account, which is an additional precaution. As preventive measures are in most cases more economical than protection systems, this feature of "FRAME" pushes the user to the more profitable design alternatives . Risk value expression.   The expression of the fire risk on a numerical scale is very much a convention, in the same way as using metric or American units for the characteristics of a building. In the KINNEY method risk values vary between 0.05 and theoretically 10.000 (a continuous threat of catastrophe). Why does FRAME (and its predecessor Gretener) use a scale that locates the value of the risk in a range around 1? The most elementary reason is that Gretener originally wanted to develop a technical system for insurance premium rates, and these happen to be around 1 ‰ of the insured value. To obtain this it was more convenient to work with logarithmic based expressions. A lot of work has been done by trial and error to find suitable coefficients to transform measurable and identifiable data such as building dimensions, system characteristics, reliability data into working formulas. The output of a risk assessment has to be communicated to the stakeholders in a way they can reach informed decisions. Ranking systems with a benchmark, like NFPA 101A FSES, are therefore much appreciated by the inexperienced observer. Probability and severity combinations, like 5.10 -6 deaths / million hours are understandable by scientists but mean very little for decision makers, unless compared with some benchmark, e.g. national averages. A loss potential calculation in thousands of Euros or dollars will not ring a bell for an insurance broker, but a correspondingly high fire insurance premium rate will do. The cost estimate becomes even more complicated when the costs are unevenly distributed among the interested parties. A particular complex situation is e.g. a large warehouse where the owner of the building, the owner(s) of the content and the user of the building are different companies, with competing interests. Decision makers are more interested to know what level of fire safety they can get for the budget foreseen to be spent on fire protection. A loss potential calculation is therefore more useful. FRAME results can be transformed into a) a fire loss estimate as % of the compartment; b) an insurance premium rate; and c) a relative probability of victims, compared to a residential fire risk. Most managers are happy with this kind of information that is easily understandable and still gives them the freedom of decision making. Conclusion.  The purpose of this note was to explain how the formulas of FRAME are based as far as possible on scientific knowledge, where available, but necessarily also on reasoning and experienced guesswork and equilibration by trial and error. The aim was to have a fire risk assessment tool that reflects the state of knowledge in fire safety with sufficient detail and built-in precautions to obtain reliable conclusions.  Numerous test calculations support the conclusion that FRAME risk assessment calculations comply with the available scientific knowledge and the experience of experts. The application of FRAME to real fire cases (see at : Examples) shows eventually that reality unfortunately validates the calculations. PRINT  THIS SECTION  (pdf)