MANUAL No - Forest and Wood Products Australia

Manual No. 8: Termite Attack 44
4.2.5 The Apparent Risk in the Future
The apparent risk in the future will be defined as the apparent probability that a house will be
attacked between the time t1 and t2, where t1 and t2 denote the time taken since construction of
the house. This probability will be denoted by Papp,future (t1 t2). To take into account the fact
P
that some of the houses under consideration may already true have risk of attack been attacked in the past, the
assumption will be made that
1.0
Papp,future (t1 t2) = Papp (t2 – t1) (4.13)
where Papp,future (t2 – t1) will be evaluated according to equations tmem (4.11) tmax and (4.12) but t using a
age of house (yrs)
value of mean (t) chosen as discussed in Section 4.2.1. To account for the fact that the suburb
(a) for positive a
is effectively t1 years older than when the house was first built.
Probability of attack Probability that attack has occurred
P
1.0
P
1.0
0
0
true risk of attack
tmem
tmax
true risk of attack
P(house, attack, true, t)
age of house (yrs)
(a) for positive a
apparent risk of attack
t
P = A + Bt
Probability that attack has occurred
ta ta + tM tmax
define the probability distribution function. t It was therefore an obvious choice to use mean(t)
age of house (yrs)
(ii) for negative a
4.3 and 4.4. The relationship between the mean value and their risk of attack within 50 years
Probability that attack has occurred
P
1.0
0
0
true risk of attack
ta
ta + tmem
tmax
age of house (yrs)
(b) for negative a
apparent risk of attack
apparent risk of attack
Figure 4.2. Schematic illustration of the cumulative distribution functions of the attack time.
4.2.6 The Distribution Parameters
apparent risk of attack
It should be noted that two parameters, P(house, attack, obsv, a t) and b, are required to define the probability
distribution function. However, after examining the data from the Termite Tally, it was
decided to take b to be a fixed value b = 0.0002. Hence only one parameter is required to
as the defining parameter. The relationship between a, mean(t) and V(t) are shown in Figures
is shown in Figure 4.
The equation relating mean(t) and the probability of attack within 50 years, denoted by
risk50 can be closely approximated by the equation
risk50 = 0.000138 mean(t) × mean(t) – 0.029749 mean(t) + 1.618 (4.14)
For risk50 = 0.2, a typical value of risk that occurs in Australia, the corresponding mean attack
time is mean(t) = 44 years. Equation (4.14) is shown plotted in Fog. 4.5.
t
44