Calculation of the Risk

The magnitude of the risk to people is normally taken as the Fatal Accident Rate (FAR). This is calculated by multiplying the size of the hazard (measured in fatalities per hazardous event) by the frequency of the hazardous event (measured in events per year). The FAR has units of fatalities per year. 

For the purpose of the example, let us further suppose that someone is in the close vicinity of the vessel for 10% of the time, and that overpressurisation of the autoclave could lead to vessel rupture and a potential fatality to that person. 

What is the magnitude of the risk (FAR) this arrangement presents  

The first step is to quantify the severity of the potential hazard. From the information we are given, we know that there is a 10% chance of a single fatality if vessel rupture occurs. In other words, there are 0.1 fatalities per hazardous event. 

Using the frequencies suggested in Table 3, we can see that we might expect the temperature controller to fail about 0.5 times per year. The 

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Remember that animal data are the basis for the calculation of the risks created by exposure. Thus, any risk analysis exercise might be of questionable value. 

The risk index for any hazardous substance in Equation 1.1 or 1.2 (see Section 1.5.1) is calculated based on assumed exposure scenarios for hypothetical inadvertent intruders at near-surface waste disposal sites and a specified negligible risk or dose in the case of exempt waste or acceptable (barely tolerable) risk or dose in the case of low-hazard waste. Calculation of the risk index also requires consideration of the appropriate measure of risk (health-effect endpoint), especially for carcinogens, and the appropriate approaches to estimating the probability of a stochastic response per unit dose for carcinogens and the thresholds for deterministic responses for noncarcinogens. Given a calculated risk index for each hazardous substance in a particular waste, the waste then would be classified using Equation 1.3. 

In general, calculation of the risk or dose from waste disposal in the numerator of the risk index in Equation 6.2 or 6.3 involves the risk assessment process discussed in Section 3.1.5.1. As summarized in Section 6.1.3, NCRP recommends that generic scenarios for exposure of hypothetical inadvertent intruders at waste disposal sites should be used in calculating risk or dose for purposes of waste classification. Implementation of models describing exposure scenarios for inadvertent intruders at waste disposal sites and their associated exposure pathways generally results in estimates of risk or dose per unit concentration of hazardous substances in waste. These results then are combined with the assumptions about allowable risk discussed in the previous section to obtain limits on concentrations of hazardous substances in exempt or low-hazard waste. 

Stochastic Risk Index for Hazardous Chemical Constituents. Calculation of the risk index for all hazardous chemicals in the waste that cause stochastic effects is performed in the same manner as in the previous examples for radioactive wastes. The calculated risk for each such substance, based on the assumed exposure scenario, is summed and then divided by the acceptable lifetime risk of 10 3 for classification as low-hazard waste (see Table 7.1). The risk for each chemical is calculated by multiplying the arithmetic mean of the concentration in the waste given in Table 7.5 by the intake rate from ingestion, inhalation, or dermal absorption per unit concentration discussed in Section 7.1.7.3 and 10 percent of the appropriate slope factor in Table 7.7 (see Section 7.1.7.1) adjusted for the exposure time. Since the slope factors assume chronic lifetime exposure, they must be reduced by a factor of 70 based on the assumption that the exposure scenario at the hazardous waste site occurs only once over an individual s lifetime. In addition, a simplifying assumption is made that whenever more than one slope factor is given for a hazardous substance in Table 7.7, the higher value was applied to the total intake rate by all routes of exposure of about 4 X 10 8 mg (kg d) 1 per ppm. This assumption should be conservative. 

Skates SJ, Menon U, MacDonald N, et al. Calculation of the risk of ovarian cancer from serial CA-125 values for preclinical detection in postmenopausal women. J Clin Oncol 2003 21 206-10. 

Taking the logarithm of both sides, this yields a number that can be directly inserted into the calculation of the risk index ... 

Risk Analysis (RA) is a fundamental process to prevent accidents and other unwanted events possibly occurring during industrial process activities handling of hazardous materials. It is defined as the process of systematic use of available information in order to identify hazards and to estimate the risk (lEC 60300 1995). Depending on the accuracy required to the analysis, it can be qualitatively or quantitatively carried out. In qualitative methods no explicit quantification of the risk is obtained, whereas in the quantitative ones a numerical calculation of the risk level is addressed. 

This performs studies that are more relevant, coherent and comprehensive than what is described in these standards and, in particular, to replace the Lego analysis with real systemic analysis and to conduct rigorous and conservative calculations using available powerful algorithms in place of simplistic formulations that might induce the uninitiated to believe that the indiscriminate application of certain magical formulas is enough to understand calculation problems. The problem is particularly evident in the calculations of the risk reduction factors that may be vastly overvalued. 

A method for graphically displaying individual risk results is use of the risk contour, or risk isopleth. If individual risk is defined as the likelihood of someone suffering a specified injury or loss, then individual risk can be calculated at particular geographic locations around the vicinity of a facility or operation. If the individual risk is calculated at many points surrounding the facility, then points of equal risk can be connected to... 

Another way to evaluate risks is to calculate the sensitivity of the total risk estimates to changes in assumptions, frequencies, or consequences. Risk analysts tend to be conservative in their assumptions and calculations, and the cumulative effect of this conservatism may be a substantial overestimation of risk. For example, always assuming that short-term exposure to chemical concentrations above some threshold limit value will cause serious injury may severely skew the calculated risks of health effects. If you do not understand the sensitivity of the risk results to this conservative assumption, you may misallocate your loss prevention resources or misinform your company or the public about the actual risk. 

In the Verband Deutscher Elektrotechniker (VDE) regulations [1,4], no demands are made on the accuracy of the measured or calculated voltage drops in a rail network. An inaccuracy of 10% and, in difficult cases, up to 20%, should be permitted. A calculation of the annual mean values is required. If the necessary equipment is not available, a calculation is permitted over a shorter period (e.g., an average day). Voltage drops in the rail network only indicate the trend of the interference of buried installations. Assessment of the risk of corrosion of an installation can only be made by measuring the object/soil potential. A change in potential of 0.1 V can be taken as an indication of an inadmissible corrosion risk [5]. 

The next level of presentation is a technical summary that gives details of the risks including the system s importance measures systems, effects of data changes, and assumptions that are critical to the conclusions. It details the conduct of the analysis - especially the treatment of controversial points. The last level of presentation includes all of the details including a roadmap to the analysis so a peer can trace the calculations and repeat them for verification. 

At this point, following the chapters, the objectives have been defined, the effect of government regulations and standards are known, accidents have been identified and analyzed by various methods to determine the probability of an accident, and the accident consequences have been calculated. These parts must be assembled to present the risk and the analysis of the risk according to its various contributors. 

If workers are exposed simultaneously or successively to more than one chemical agent, the risk shall be assessed on the basis of the risk presented by all such chemical agents in combination. Usually, additive effects are assumed for the mixture of chemical agents, so the cumulative exposure is calculated as follows ... 

Toxicity alucs for carcinogenic effects also can be c.xprcsscd in terms of risk per unit concentration of the substance in the medium where human contact occurs. These measures, called unit risks, are calculated by dividing the slope factor by 70 kg and multiplying by the inhalation rate (20 m /day) or the water consumption rate (2 L/day), respecti ely, for risk associated with unit concentration in air or water. Where an absorption fraction less than 1.0 has been applied in deriving the slope factor, an additional conversion factor is necessary in the calculation of unit risk so that the unit risk will be on an administered dose basis. The standardized duration assumption for unit risks is understood to be continuous lifetime c.xposure. Hence, when there is no absorption conversion required ... 

In contrast, the calculation of human risk for genotoxic carcinogens from... 

When determining the dose of bicarbonate replacement, the goal for therapy is to achieve a normal serum bicarbonate level of 24 mEq/L (24 mmol/L). The dose is usually determined by calculating the base deficit [0.5 L/kg X (body weight)] x [(normal C02) - (measured C02)]. Because of the risk of volume overload resulting from the sodium load administered with bicarbonate replacement, the total base deficit should be administered over several days. Once the goal serum bicarbonate level is attained, a maintenance dose of bicarbonate is necessary and should be titrated to maintain serum bicarbonate levels. 

One approach is to compare the risks, calculated from a hazard analysis, with risks that are generally considered acceptable such as, the average risks in the particular industry, and the kind of risks that people accept voluntarily. One measure of the risk to life is the Fatal Accident Frequency Rate (FAFR), defined as the number of deaths per 108 working hours. This is equivalent to the number of deaths in a group of 1000 men over their working lives. The FAFR can be calculated from statistical data for various industries and activities some of the published values are shown in Tables 9.8 and 9.9. Table 9.8 shows the relative position of the chemical industry compared with other industries Table 9.9 gives values for some of the risks that people accept voluntarily. 

Because the whole idea of a tiered approach of the kind outlined above is in its initial stages, it will have to be validated and discussed further and will in all probability need to be refined afterwards. The aim here is to introduce the idea of a stepwise approach to the assessment of the risk to re-entry workers. The outlined procedure should be used to calculate the dermal re-entry exposure for real examples of rather dermally toxic compounds in order to gain experience with the recommended procedure. 

Risk Estimation. As mentioned above, chronic risk is expressed as a probability of occurrence per year or per lifetime of some adverse consequence caused by exposure to the pollutant. Statutory mandates have focused on human health effects as the primary expression of chronic risks. The basis of the risk calculation is the dose/response curve that relates the adverse effect to the amount or rate of a chemical taken in to the subject. Because of regulatory emphasis of cancer, most of the work devoted to the deviation of dose/response curves has been concerned with the probability of appearance of a tumor as the adverse effect. 

The hazards identification procedures presented in chapter 10 include some aspects of risk assessment. The Dow F EI includes a calculation of the maximum probable property damage (MPPD) and the maximum probable days outage (MPDO). This is a form of consequences analysis. However, these numbers are obtained by some rather simple calculations involving published correlations. Hazard and operability (HAZOP) studies provide information on how a particular accident occurs. This is a form of incident identification. No probabilities or numbers are used with the typical HAZOP study, although the experience of the review committee is used to decide on an appropriate course of action. 

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