Arboriculture & Urban Forestry 39(4): July 2013 Similarly, the expected (average) number of fail- ures in four and a half years is determined here [3] E = N × Pr × T where Pr is the QTRA probability of tree fail- ure per tree per year. QTRA results therefore indi- cate the following: 14 × 1/7.5 × 4.5 = 8.4 tree failures. The formula for determining the probabil- ity that no tree should fail in four and a half years is Pr(no tree failures) = [1 – Pr(tree failure)]N × time which results in the following: (1 – 1/7.5)14 × 4.5 [4] = 0.012%, or 1/8,000. The probability that at least one tree will fail in four and a half years is [5] which results in the following: 1 – (1 – 1/7.5)14 × 4.5 Pr(at least one tree failure) = 1 – [1 – Pr(tree failure)]N × time = 99.99%. Such probabilistic analyses were not included in the con- sultant reports prepared for NCC. Likewise, these statistics appear not to have been considered and/or appropriately weighed by NCC in making the decision to remove the trees. This type of analysis enables a kind of reality check when extrapolating rates of failure and harm for a single tree to a group of trees. These analyses indicate that the ROH provided to NCC by the QTRA assessors were excessively high. Moreover, all 14 trees remained upright, despite a predicted 99.99% prob- ability that at least one tree would fail in a 4.5-year period. A risk of death (or harm) per tree per year of 1 in 19.8 is the high- est estimate observed by the lead author for any activity. A single fig tree in Laman Street is ten times more dangerous than smok- ing 10 cigarettes a day (BMA 1990), ten times more dangerous than World War Two (Mueller and Stewart 2011), 75 times more dangerous than mountain climbing (BMA 1990), and 500,000 times more dangerous than trees in public places in the UK. A QTRA of the 14 trees was undertaken by Mike Ellison in January 2012. He estimated the ROH to be 1 in 170,000 for the worst tree, and a ROH of 1 in 2,000,000 for the best tree (Table 1). The largest discrepancy occurred in the estimation of prob- ability of failure. The fact that two licensed QTRA practitioners can calculate a ROH that is more than 8,000 times higher than that derived by the developer of QTRA is a cause for concern. QUANTIFIED RISK ASSESSMENT AND DECISION MAKING There is a long history dating from the 1960s on QRA and its application to decision making. Applications of QRA range from assessing the safety of nuclear power plants and aircraft to road safety and flood protection. These applications arise because there 2. 167 is uncertainty and variability of the hazard and risks, the costs of failure are high or catastrophic, the costs of protection are also high, and public safety needs to be safeguarded. The decisions also affect many interested parties, so there is a need for a decision process that has scientific rigor, is transparent, and is acceptable to society. An understanding of the principles and practices that underpin QRA provide context for future developments to QTRA. The QTRA system should develop longer and more intensive training that includes the principles of QRA as a starting point. The basic definition of risk has been standardized by inter- national agreement (ISO 31000-2009). The process has been summarized as follows (Stewart and Melchers 1997) (Figure 3): 1. Define context. The system being examined, and the internal and external influences, must be known and defined. Analyze hazard scenarios. Identification of what might go wrong, when and where. 3. Analyze risk. [6] Risk = (probability of failure) × (consequences) Risk (or expected loss) may be given in terms of dollars, the number of human fatalities, or other quantifiable means for a specific time period (often annually). Typically, the probabilities are estimated from a combination of relevant data and statistics, predictive models of system reliability, and subjective judgments as a last resort. 4. Evaluate risks. Analyzed risk must be compared with criteria of risk acceptability. 5. Treat the risk. If the estimated risk exceeds the risk acceptance criteria, risk treatment is required. This may involve risk avoidance, risk reduction, or risk transfer. 6. Monitor and review. Usually a risk analysis presents only a snapshot of the risk at a particular point in time. Therefore, there is a need to monitor the system and to repeat the risk analysis at regular intervals. While risks are seldom acceptable, they are often tolerable (or accepted reluctantly) if the benefits are seen to outweigh the costs [for a review, see Stewart and Melchers (1997) and Mueller and Stewart (2011)]. The benefit is the reduction in risk (damages or fatalities averted) associated with a decision, and the cost is the cost of the decision. The net benefit or net present value (NPV) is equal to benefit minus the cost equal to (e.g., Stewart 2010): [7] NPV = E(B) + ∆R(Pr × Consequences) – C∆R where E(B) is the expected benefit from the decision not directly related to mitigating the risk; Pr is the probability of failure, assuming no risk mitigating measures; and Con- Table 1. Results of QTRA for a single tree in Laman Street (Newcastle). Probability Newcastle City Council assessment (2009) Mike Ellison assessment (2012) Best tree Worst tree of failure 1/7.5 1/100,000 1/1,000 Target value 1/2.64 1/20 1/20 Impact potential 1/1 1/1 1/8.6 Risk of Harm (ROH) per tree per year 1/19.8 1/2,000,000 1/170,000 ©2013 International Society of Arboriculture
July 2013
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