effects of the deck non-uniformity on those ships. The difficult task of deck non-uniformity correction is thus avoided for the risk assessment.
Because the deck wet bulb temperature rise is a function of both PAT and the stocking rate, the effective deck wet bulb probability is calculated for each stocking entry in the software. A
stocking entry is one line of animal on a particular deck.
6.2 Statistical Combination of Weather and Animal
Parameters
With the wet bulb temperature probability distribution calculated as above for each line of animal on each deck, the mortality statistics are estimated and presented in two ways:
i expected mortality rate, and ii probability of reaching a given mortality level.
6.2.1 Expected Mortality Rate
This is the standard way in which statistical conclusions are expressed. If a random experiment the weather is ‘random’ were repeated exactly, many times over, the average
outcome of all repetitions is termed the ‘expected’ outcome. Along with the clear mathematical meaning is a clear mathematical evaluation. Any narrow band of wet bulb
temperatures has a certain probability of occurrence. The mortality for that event is the cumulative mortality up to the wet bulb temperature in question. By multiplying the
probability of the wet bulb falling in that narrow range by the mortality for that wet bulb, we get a contribution to the estimate of expected mortality for that small fraction of possible
weather. By repeating the calculation for successive small ranges of wet bulb temperature to cover all possible wet bulbs, and adding all the results, the total is the expected mortality
for that stocking entry. When the wet bulb bands considered become vanishingly small, the summation to get
expected mortality becomes an integral. The mathematics is then as follows. The cumulative mortality probability at a given wet bulb temperature MTwb, is the integral
of the mortality probability density function, mTwb, up to that wet bulb:
∫
∞
=
Twb -
dt t
m Twb
M
The expected mortality rate is the integral over all wet bulbs of the product of the wet bulb probability density function, pTwb, and the cumulative mortality probability MTwb:
Expected Mortality =
∫
∞ ∞
−
dt t
M t
p
The above calculation is implemented in the risk estimation software for the weather, pTwb being Normally distributed and the animal response function, mTwb, being a beta
distribution as described earlier.
6.2.2 Probability of 5 Mortality
Project: LIVE.116 – Development of a Heat Stress Risk Management Model Revision F
Maunsell Australia Pty Ltd Page 49 of 129
Final Report December 2003
The ‘expected mortality’, while statistically valid, is not necessarily the preferred measure for those seeking to judge acceptability of risk. The emphasis is normally on the likelihood of
mortality exceeding a limiting level. The current reporting limits are 1 mortality for cattle and 2 for sheep. At these levels, it is difficult to verify from voyage reports, the importance
of heat stress relative to other causes. It is preferable for assessing past events and future outcomes, to look at a higher mortality level with an appropriately lower likelihood reduced
probability. We have chosen 5 mortality. At this level and above, if heat stress is not a
major cause, the alternative explanation will be obvious fire, sinking, etc.. We also note that adopting a probability measure at a higher mortality level does not imply acceptance of
greater risk. A single voyage will have different probability of 1 and 5 mortalities, but both will be a snapshot of the same risk profile. We note that the adoption of risk standards
is not the role of this report, neither do we comment on the variation of risk standard with mortality level.
The calculation of probability for a given mortality level in one stocking entry is more straightforward than that for expected mortality. The drawback is that combined results, to
give a voyage average across different lines, are not necessarily meaningful. Consequently, these figures are given only for each closed deck stocking entry and not for the voyage as a
whole. To find the probability of exceeding 5 mortality, the cumulative distribution of animal
response is first used to find the wet bulb temperature corresponding to 5 mortality. This wet bulb temperature is then compared to the cumulative probability curve for wet bulb
temperature on the particular deck to find the probability of wet bulb temperature exceeding the 5 mortality value. As before, the wet bulb probability on the deck is taken as the
ambient wet bulb probability shifted along the wet bulb scale by the deck wet bulb temperature rise.
6.2.3 Duration of Exposure
