Cost is not the only criterion for deciding if a risk is acceptable, or for making a decision involving risk.

The risk of being late for an important early meeting may be unacceptable, thus we accept a higher cost for travelling and accommodation the previous night.

The chance of winning a major lottery prize is extremely small, so small that there is basically a certain chance of financial loss, but we buy a ticket anyway.

The potential gain outweighs the certain cost. Were we to strictly apply a simple model of risk, we would not buy a ticket. For example, the expected cost and benefit of buying a $10 ticket in a lottery with a one in a million chance of winning $5M is:

It appears that risk has an upside and a downside. On the downside, risk is usually thought of as the likelihood and potential impact of an adverse event. On the upside, there is the opportunity or chance of gain; typically, as the potential gain increases, so does the acceptability of higher levels of risk.

Risk is a complex notion. However, many decisions require selecting an option involving risk or uncertainty. Characterising or measuring the risks of the different options can help the decision-making. If not by cost, how might risk be represented and assessed?

This case study shows how risk was represented by a 'risk index' in order to assess the risk associated with each of a number of different decision options, and choose the option with least risk.

Data shown in this case study is for illustrative purposes only and is fictitious.

Setting

The setting for this case study is as follows. The case study organisation was required to transport a range of liquid and solid materials by truck for significant distances along urban road routes. A number of alternative routes were available for trans-shipment of the goods. The organisation wished to use the safest route.

More specifically, the organisation wished to quantify the level of risk associated with the transportation of materials along each route in terms of safety and chance of any accidental loss of load due to spillage or other release. This risk analysis would then compare the alternative routes in terms of their risk to assist a decision on the choice of the preferred, or least risk, route.

Method

In general, risk is defined in terms of likelihood and consequence. That is, say:

Risk = Likelihood x Consequence

In this case, this definition led to the following representation, or model, of risk:

Risk fo accidental material release = (Accident probability x Release probability) x Consequence

Each of the terms on the right-hand side of the above equation are further defined below.

Accident probability = Vehicle accident rate x Vehicle distance travelled

Where:

• Accident Probability = accidents per year
• Vehicle Accident Rate = truck accidents per 100 million vehicle kilometres
• Vehicle Distance Travelled = number of trips per year x route length (kilometres).

Probability of Material Release = Probability of release after vehicle accident + Probability of release due to other causes

Where:

• Probability of release after accident = 0.06 - 0.09 for sealed roads (Based on US research findings – see Harwood DW, Viner JG and Russell ER Procedure for developing truck accident and release rates for hazmat routing. J Transportation Engineering 1993 pp. 189-199).
• Probability of release due to other causes like loose valves or seals, open hatches etc is taken as 17.3 times the average vehicular accident rate (Based on US research findings – see Ashtakala B and Eno LA 3. Minimum risk route model for hazardous materials, J Transportation Engineering 1996 pp. 350-357).

Consequence = Magnitude of any material release x route exposure

The large majority of truck accidents have produced spills or material releases of small magnitude – for example, over 80 per cent of spills release less than 50 litres. Less than 3 per cent of accidents have produced spills of up to 4000 litres or loss of 450 kilograms of load. Less than 0.5 per cent of accidents have produced a fire or explosion. Consequently, the potential magnitude of release was categorized as either 'minor' or 'more significant' (Based on US research findings – see Ashtakala B and Eno LA 3. Minimum risk route model for hazardous materials, J Transportation Engineering 1996 pp. 350-357).

In addition, the exposure of the route and surrounds to any release as a result of an accident was accounted for by using a five-point scale to represent land usage. This rating scale categorized land usage from central suburban (with high population density and close proximity to the route) to open rural, for example.

This model of risk enabled a risk index to be calculated as follows:

Data for route through unpopulated, rural, open, flat land, no environmental significance:

• Accident rate = 7 accidents per 100 million vehicle kilometres
• Trips per year = 50
• Route length = 40km

Thus:

Accidents per year = (7 x 50 x 40)/100 million = 0.00014.

Probability of any material released = (0.00014 x 0.09) + (17.3 x 0.00014) per year
= 0.0000126 + 0.002422
= 0.0024
= 0.24%
= 1 chance in 420.

Exposure rating of route = 1

Thus risk index = probability x exposure rating = 0.0024 x 1 = 0.0024.

Probability of a minor spill per year = 0.8 x 0.0024 = 0.0019 = 0.2% = 1 chance in 520

Probability of a more significant spill per year = 0.2 x 0.0024 = 0.00048 = 0.05% = 1 chance in 2000

Validity of risk index

The risk index was calculated as above for different segments along each of the different routes. These segments were essentially defined using the mapping grid and references of a typical street directory. Thus, risk along a single route was described by a sequence of risk index values that progressed along that route.

A statistical test of correlation was made between the risk index values along each route and the accident history known for that route. The risk index values were found to be statistically related to the accident history. Thus, the risk index values provided a valid indication of the risk along the route in this case.

Choosing the route of least risk

Each series of risk index values for each route were compared using a statistical test of difference. This test showed if there was a statistically significant difference between the series – that is, it proved if one series of risk index values was lower overall than another series of values. Where this was the case, the series of lowest values showed the route of least risk overall.

There were statistically significant differences between several of the series. One series was shown to be lower overall than the others and this therefore represented the safest route.

Risk management guidelines from this case study

This case study shows that 'risk' may be represented, or modelled, in a number of ways. In this case, the general model of risk as comprising likelihood and consequence was used.

Each of these two characteristics of risk were defined in terms of the measures appropriate to the circumstances of the case to produce a 'risk index' – that is, a measure of risk.

A decision was made by comparing the risk index values calculated for each of the decision options. The option with the lowest risk index was chosen as the option of least relative risk.

This case study indicates:

• Risk can be represented by a suitable measure or index
• Using such measures, options may be compared on the basis of their relative risk

Back to case studies