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For testing the concept of the Risk Number R(i), 12 objects have been selected, four statues of marble, four of sandstone and four sandstone tombstones from the Jewish Cemetery in Baiersdorf/Erlangen (see Figure 2).

Figure 2: The objects chosen for testing the Risk Number.

The Overall Risk Number R(total) in data sheet 11 of the Excel work sheet is automatically calculated. Although this data sheet lists both the arithmetic mean of the Risk Number and the quadratic mean, only the arithmetic is considered in the following because the overall statement remains the same even if the quadratic mean provides slightly different values.

The individual Risk Number calculations of the 12 examined objects yielded surprising results in an initial, unbiased assessment, which, however, have proved to be very useful.

The Overall Risk Numbers of the individual sculptures and tombstones are depicted in Figure 3.

The object with the lowest Risk Number is tombstone No. 1901, the one with the highest is Vestalin. In addition, at the upper and lower ends of the scale the realistic maximum and minimum limits for marble and sandstone are presented. These limits indicate possible maximum and minimum overall Risk Numbers for these rock types. The range extents from 0.24 to 0.88 for marble and from 0.18 to 0.79 for sandstone. The reason for these limits lies in the fact that certain data sheets or parameters cannot reach a value like zero or one.

For example, data sheet “Environment – Exogenous Risk Factors” could theoretically assume a value of 1 in the case of very extreme climate, but never a value of zero, because a “non-climate” does not exist. This also applies to data sheets “Natural Stone – Endogenous Risk Factors”. Even in a very favourable climate, thermal and hydric expansion and water absorption exert an influence on the weathering.

Figure 3: Overall Risk Numbers of the selected objects.

39The calculation system for the Overall Risk Number permits model calculations for open air exposure or location in a store. Relevant for this are the data sheets “Environment – Exogenous Risk Factors”, “Vandalism” and certain rock properties such as thermal and hygric expansion. These parameters vary according to the location of the sculpture. Comparisons have shown that the risk reduces by 0.22 to 0.25 for marble objects and 0.18 to 0.22 for sandstone objects when moving them from outdoors to a depot.

Whatever the value of an object’s Risk Number, the question arises as to how large the numerical change regarding the Overall Risk Number must be in order to be able to draw a valid conclusion as to a greater or lesser overall risk. As we could see, the values of some sculptures are very close to each other, for example Aeolus (R(total) = 0.60) and Flora (R(total) = 0.59). The question is whether 0.01 points is significant or not. Simple considerations demonstrate that even small differences are important. Because, for calculating the Overall Risk Number R(total) the sum of the individual Risk Numbers R(i) is divided by seven so that even a small difference of 0.01 can be significant in one of the data sheets.

More straightforward, three types of endangerments can be defined: “little endangered” – “endangered” – highly endangered”. These categories range approximately from 0.2 to 0.4, 0.4 to 0.6 and 0.6 and 0.8. Figure 4 shows that the marble sculptures Vestalin, Flora and Äolus are highly endangered.