3.2.1 Safety Demand

An essential concept in economic theory is that of “demand.” Demand is the quantity of goods and services that consumers may want to purchase at a specific price. Due to the usefulness of a certain good or service, some people are interested in purchasing it; it has a value for these consumers, and thus a certain price follows. The demand will then change depending on the price. In the case of operational safety economics, one might reason that the good or service represents safety or, more specific, safety measures: the demand curve of a safety good or service (e.g., a safety measure or a portfolio of safety measures) depends on the price of the safety good or service. Even if all goods and services (in this case, operational safety) were free to the consumer, there would be a limit on how much consumers could use. Therefore, there would be a demand figure even at this price. In case of safety, this restriction would, for example, be imposed by production and physical limitations of implementing the safety measures. The reason is simple: every production, no matter how small, goes hand in hand with risks, even if operational safety were free of costs.

In general, in economics, the demand curve defines the purchase characteristics of consumers at all conceivable prices, whereas the quantity demanded defines the purchase characteristics of consumers at a particular price. Demand depends on a number of parameters. In case of safety as a good or service, it first depends on the preferences of safety managers and their safety utility curves (see Section 3.5.1). Second, it depends on the available safety budget of an organization. In general, the higher the budget, the higher the demand. Third, it depends on the number of organizations needing this specific kind of safety good or service. The more companies that need it, the higher the demand. Fourth, the demand will be influenced by the industrial sector where the safety good or service is used. The demand of safety can differ drastically from sector to sector, due to the industrial activities and agreements with unions, legislation, profit, and income specificities within the sectors. Fifth, in case of some safety goods or services, a substitution effect may be observed, for example, if the price rises. In this case, the price relative to the prices of other safety goods or services is important, not the absolute price of the good or service.

To investigate the influence of each of the parameters on the safety demand, every parameter can be changed or fluctuated while the other factors are kept constant (according to the well-known “ceteris paribus” – other things being equal – principle).

Thus far, safety was looked upon from the perspective of “safety measures,” and the price of safety measures influenced by the possible market demand. This reasoning assumes that safety is a regular good comparable with all other goods and/or services. However, this is not the case and a regular demand curve for safety such as for other goods and services is not applicable. Some safety measures, almost no matter how expensive, will be purchased anyway, and others might only be purchased for the happy few who have a company culture strongly tending toward high reliability organization (HRO) safety and who are also able to afford them. In other words, the purchase of safety measures within an organization strongly depends on a lot of other factors besides the market mechanism. The classic microeconomic demand function therefore does not fully apply to safety.

Safety is thus not a regular good or service, such as a book or a football match . Safety is actually, as already mentioned in this book, a “dynamic non-event.” As such, in economic terms, companies purchase a certain level of non-events over a certain period of time. The higher the price of non-events, the harder it is to obtain a lot of them and the lower the number of non-events that are purchased. In other words, if safety per unit costs more, there will be less safety demand per unit. This is illustrated in Figure 3.1. Notice that this figure only holds for one type of risk at a time. Hence, the figure should be seen in terms of either type I risks and avoiding type I accident scenarios, or type II risks and avoiding type II accident scenarios.

In standard works on microeconomy, the next step is to elaborate and show a supply curve, in order to finally explain the equilibrium mechanism and the market equilibrium, based on demand and supply curves. In the case of safety, however, it makes no sense to develop a supply curve. As “supply” can be defined as the quantity of goods and services that producers may want to sell at a specified price, in safety terms this would mean the number of non-events that a company would want to sell at a certain price. Of course, the company does not want to sell safety, or non-events, it just needs a certain level of safety itself. Therefore, although a demand curve of safety exists within a single company and on a microeconomic level, it is useless in this context to talk about a supply curve.

Safety goods and services can also be viewed from the perspective of the profitability of a company, and thus in that regard be linked to micro-economic theory.

3.2.2 Long-term Average Cost of Production and Safety

Looking at how safety influences the profitability of a company can be done via the so-called long-term average cost of production (LAC). Before explaining more microeconomic theories and models in depth, it is interesting to consider why safety economics and investing in safety – or not – may indeed make the difference to an organization in terms of its long-term profitability. The profitability of any organization depends on its profitability in the long term, and this in turn depends on the LAC of the firm. The average cost of production can be defined as the total cost of production divided by the total output in goods and services. In other words, the average cost of production can be seen as a proxy for the accumulated operational negative uncertainties divided by the accumulated operational positive uncertainties within an organization. Further, assume that the type of organization considered in this book is aimed at long-term existence and making profits in a sustainable way. In this case, to ensure the long-term viability of a company, the average cost of production should be less than the price at which the goods and services can be traded.

Inputs to production comprise any goods or services that are used to produce the output product or service, including, for example, labor costs, raw materials, utilities, and equipment, but also safety and safety-related goods and services (such as risk assessments, maintenance operations, and training). The production function determines the maximum output that can be produced from a defined level of inputs. The efficiency with which an organization achieves a specific output will define its long-term average costs. The importance of safety within the average costs of production can be illustrated by a simple example.

The costs, in broad terms, will vary with production output. As the production output increases, the unit costs of production will go down due to fixed costs staying the same irrespective of the production output (economies of scale). However, at a certain point, costs will rise again due to more levels of management, more difficult organizational management, transport costs, marketing costs, geographical location costs, and so on (diseconomies of scale). Hence, an organization's long-term average cost curve is likely to follow more or less the shape of the curve depicted in Figure 3.2.

Figure 3.2 shows the LAC curves of companies A and B. Both companies can sell their goods or services in the market at €50 per unit. However, company A can sell at a profit if it sells quantities of the good or service between and , whereas company B may be able to sustain production at a loss in the short term. Company B will have to lower its production costs if it desires to keep operating for a longer period of time though. Company B can, for example, lower its production costs by improving its health and safety standards and thereby suffering lower accident costs.

3.4.1 Expected Value Theory

The expected value associated with a situation where uncertainty is involved is a weighted average of the payoffs or values associated with all possible outcomes, with the probabilities of each outcome used as weights. Hence, the expected value measures the average payoff. To illustrate this, assume the following possible consequences of a certain undesired event, “”:

1. Outcome 1: a cost of with probability
2. Outcome 2: a cost of with probability
3. Outcome 3: a cost of with probability .

Assume that no other outcomes are possible, i.e. that,

Then, the expected value of the undesired event is:

The decision to take preventive measures or not against this particular undesired event with three possible outcomes is in the hands of the safety manager.

The expected value also refers to the weighted average value of all costs or effectiveness outcomes in a decision analysis tree. In safety management, event trees are often used to visualize different outcomes and their consequences and/or probabilities. Such trees can thus also be used to carry out decision analyses by calculating expected values using the information in the tree. An illustrative example is provided in Figure 3.5.

3.4.2 Value at Risk

A term much used in financial risk management is the so-called value at risk (VaR). The question that a VaR tries to answer is simple: “What is the most that can be lost on a particular financial investment with a certain level of confidence (typically 95% or 99%)?” VaR indeed provides a predicted loss over a target time horizon within a given confidence interval. The loss is usually called “maximum loss” (or “worst-case loss”) in financial risk management, but there is actually a chance that an even greater loss may occur, albeit small. In brief, a VaR measure determines an amount of money, such that there is that probability of the portfolio of assets not losing that amount of money over that time horizon. Hence, in statistical terms, this is called a percentile. So a 1-year 95% euro VaR is just the 95 percentile of a portfolio's yearly loss expressed in euros (see also Section 7.2.1.1).

This VaR can also be explained in terms of operational risk management. For example, if the worst-case summed consequence of accident scenarios (“VaR” in financial risk management terminology) in an organization is calculated to be €100 million/year, with a 95% confidence level, then there is only a 5% chance that the summed consequences of accident scenarios will be higher than €100 million over any given year.

In operational risk management, a VaR could be used for decision-making for type I, and also for type II, risks, as probability distributions can be used for both types of risk, and this kind of input information is needed for VaR statistic calculations. A VaR statistic indeed needs, among other things, an estimated input of loss (either in currency or in percentage terms) as a probability density.

A Monte Carlo simulation, randomly generating outcomes for a number of hypothetical trials, can be used to calculate the VaR.

The downside of using a VaR for operational risk management is that: (i) there is still a lot of epistemic uncertainty about type II risks (and thus the accuracy and probability distribution depend on the assumptions made and the scenarios considered); (ii) there is still a certain probability that a greater loss may occur; and (iii) due to (i) and (ii), avoiding a true disaster is not fully taken into account while using this VaR method for making safety investments.

3.4.3 Safety Attitude

One approach to characterizing a person's risk attitude is via the concept of the so-called “certainty equivalent.” A certainty equivalent is a value , such that the safety manager is indifferent between the consequences of the undesired event and the value that he obtains for certain.

Hence, depending on the certainty equivalent, safety managers can be categorized as being safety-seeking, safety-neutral, or safety-averse:

1. Safety-seeking: Certainty equivalent of investment > expected value of undesired event
2. Safety-neutral: Certainty equivalent of investment = expected value of undesired event
3. Safety-averse: Certainty equivalent of investment < expected value of undesired event.

Looking at it from the “hypothetical benefit” point of view, safety-seeking, safety-neutral, and safety-averse can be compared to risk-seeking, risk-neutral, and risk-averse. In case of “risk,” there is a possibility to win and to have a positive financial payoff, i.e., in this case, a hypothetical benefit of being safe. In the case of “safety,” the gains are equal to “not losing” or “not having accidents,” and hence they can be interpreted as necessary prevention investments to avoid human, social, and legal, losses. They thus represent the costs that go hand in hand with safety. Hence, in the case of safety there is no possibility of achieving a real positive financial payoff – the payoff is a hypothetical one. In this way, safety managers can be categorized into being risk-averse, risk-neutral, or risk-seeking:

1. Risk averse: Certainty equivalent of positive outcome < expected value of positive outcome
2. Risk neutral: Certainty equivalent of positive outcome = expected value of positive outcome
3. Risk seeking: Certainty equivalent of positive outcome > expected value of positive outcome.

A risk-averse person, for instance, is willing to accept, with certainty, an amount of money (i.e., a positive outcome) less than the expected amount that might be received if a decision were made to participate in a gamble. Risk-neutral and risk-seeking behavior can be understood in a similar manner.

3.5.1 Safety Utility Functions

A safety utility can be seen as a measure of safety management's satisfaction from a certain level of operational safety within an organization. Safety utilities can thus be employed to explain the economic behavior of a company's management in terms of attempts to increase operational safety. The “utility” concept is usually applied in economics by using indifference curves (see Section 3.7), which in operational economics represent the combination of measures that a safety management team would accept to maintain a given level of satisfaction.

A class of mathematical functions exhibits behaviors with respect to risk-seeking, risk-neutral, and risk-averse attitudes. These can be regarded as “safety utility” (S_u) functions. Figure 3.6 illustrates these functions.

A safety utility is a measure of preference that a certain safety situation or state has for a safety manager. Mathematically, it is a dimensionless number. A safety utility function is a real-value mathematical function comparable to the safety value function, the difference being that the safety value is, in this case, an abstract dimensionless “safety utility” related to a safety situation or state, and not, as in the safety value functions, a concrete safety value attached to a certain option of an operational safety measure or bundle. The approach to determine the functions is also different.

The vertical axis of a utility function can be any real number, but usually the axis is scaled between 0 and 100 or 0 and 1. If the latter range is chosen, the utility of the least preferred outcome is assigned “0” and the utility of the most preferred outcome is assigned “1.”

3.5.2 Expected Utility and Certainty Equivalent

The expected utility of an uncertain undesired event “” with utilities , , …, of possible outcomes , , …, , with respective probabilities , , …, is:

Furthermore, it is possible to illustrate the relationship between the expected value of an undesired event and the expected utility of this undesired event. Figure 3.7 displays this relationship for a monotonically increasing risk-averse utility function.

The equation of the chord from Figure 3.7 can be written as:

We also know that . If we set in the equation of the chord, then it can algebraically be shown that (see also Garvey [2]):

Furthermore, the certainty equivalent (CE) is the value on the horizontal axis at which a person is indifferent between a lottery and receiving the amount CE with certainty. Hence, the utility of CE must be equal to the expected utility of a lottery; thus,

3.1

The information in Figure 3.7 shows this reasoning. From Eq. (3.1), it follows that when a safety utility function of a safety management team has been drafted and is known, the certainty equivalent CE can be determined by taking the inverse of the safety utility function:

3.8.1 Questionnaire-based Type I Safety Indifference Curves

Investigating the preferences of an individual safety decision-maker or of a safety management team is possible through the development and use of questionnaires. Using human preferences derived from a well-constructed survey, an indifference curve can be drafted. In an organizational context, it is assumed that the individual decision-maker or the team represents the organization and makes decisions in its interest, and not in their own interest.

With respect to safety management, “revealed preference with discrete choice” (mentioned earlier in this book) is a very interesting and straightforward method (used within consumption theory) to obtain preferences. It is an approach to determine which bundle of goods and/or services is preferred over another bundle of goods and/or services. The method can be explained as follows. When a person (e.g., a safety manager) chooses a bundle A from a series of affordable alternatives, he thus reveals his preference for this bundle A over a series of other bundles he could have chosen. All other bundles within his budget that this person did not choose, represent a lower utility for him. Hence, if it were possible to determine all bundles having a higher utility and a lower utility than bundle A, it would also be possible to pinpoint all bundles having the same utility as bundle A (i.e., those bundles that were left over at the end of the exercise). Graphically, these leftover bundles together form the so-called indifference curve [5].

The purpose of the questionnaire is to determine such indifference curves. This can be achieved by letting a safety manager or a safety management team choose between two safety commodity bundles. If it is indicated that bundle 1 is preferred over bundle 2, the utility of bundle 2 will be increased, or the utility of bundle 1 will be decreased, until the situation occurs that the manager or management team displays an indifference between both safety commodity bundles. By repeating this procedure, it is possible to also determine other safety commodity bundles showing an equal utility. The more this procedure is repeated, the more accurate the resulting indifference curve will be.

In the following paragraphs, a concrete working procedure is described to reveal the preferences of safety management with respect to safety measure X in contrast to all other possible safety measures. It may be interesting to position the most important safety measure, according to the opinion of company safety management, in relation to all other safety measures, and in this way to determine the allocation of the safety budget.

The initial questions serve to obtain the required background information:

1. 1. What is the company's safety budget?
2. 2. What are all possible safety measures and what are their investment costs?
3. 3. What is, according to you, the most important safety measure for the company?

The most important measure is then displayed in a graph versus the aggregate of all other possible measures. To determine the indifference curve, the respondent needs to make a number of choices using a number of closed questions, whereby every choice is between two safety commodity bundles.

A possible closed question can be:

1. Bundle 1 contains four measures of type X and five other measures.
2. Bundle 2 contains two measures of type X and seven other measures.

Make your choice:

1. Bundle 1 is preferred over bundle 2.
2. Bundle 2 is preferred over bundle 1.
3. Indifference between bundle 1 and bundle 2.

It is then possible to develop an indifference curve in safety commodity space in the following manner. Figure 3.9 displays the initial choice between the two safety commodity bundles.

If safety commodity bundle 1 is chosen over safety commodity bundle 2, bundle 1 obviously represents a higher utility for the respondent than bundle 2. The next step is to lower the utility of bundle 1 by decreasing the number of measures of type X by one unit. Hence, bundle , positioned perpendicular beneath bundle 1, is used to formulate the following closed question:

1. Bundle contains three measures of type X and five other measures.
2. Bundle 2 contains two measures of type X and seven other measures.

Make your choice:

1. Bundle is preferred over bundle 2.
2. Bundle 2 is preferred over bundle .
3. Indifference between bundle and bundle 2.

In an analogous way, the utility of commodity bundle 1 can also be decreased by lowering the number of other measures, and hence by choosing a commodity bundle situated to the left of bundle 1 (see Figure 3.10a). This procedure is repeated until the respondent is indifferent between the two bundles. At that point, the two bundles have an equal utility and they then belong to the same indifference curve. Another analogous procedure is to increase the utility of bundle 2, and in this way determine the indifference curve (see Figure 3.10b).

The procedure described allows us to identify two points belonging to one indifference curve. To further determine other points belonging to this curve, bundles need to be compared two-by-two with a bundle belonging to the curve. Theoretically, this procedure needs to be repeated infinitely. Evidently, applying a procedure infinitely is impossible, and therefore in practice a limited number of points will be satisfactory to establish a proxy for the indifference curve of an individual safety decision-maker or a safety management team.

3.8.2 Problems with Determining an Indifference Curve

In trying to determine the preferences of safety management by using the procedure described in the previous section and the closed questions, a number of problems may be encountered that can influence the quality of the result. The main problem stems from the fact that humans do not always take decisions rationally, i.e., in a way that maximizes their utility. Often, decisions depend on rather arbitrary parameters, such as mood, temper, or the weather, leading to not following the condition of transitivity of preferences. One possible approach to deal with such variations is to add an extra term to take stochastic influences into consideration. However, introducing such a term would probably make the procedure too complex to be usable by most companies.

3.8.3 Time Trade-off-based Safety Utilities for Type II Safety Indifference Curves

As type II risks are characterized with much lower probabilities and much more severe outcomes, the method described in Section 3.8.1 would not be suitable for determining an indifference curve for such risks. It may be possible, however, to use the time trade-off approach in this case.

The time trade-off method asks people to consider relative amounts of time (such as the number of years a certain safety situation exists) that they would be willing to give up in order to achieve another safety situation. Consider the following two alternatives of one investment where a safety team may choose from:

1. Safety situation A (e.g., 7% probability of an accident) during time period ;
2. Safety situation B (e.g., 0.1% probability of an accident) during time period .

Then, time period is varied until the safety team is indifferent between alternative A and alternative B. In this case, a point belonging to the indifference curve is obtained: .

The following illustrative table may, for example, be obtained.

Quality-adjusted accident probabilities can be used to make decisions concerning prevention investments for type II risks more objective. As an illustrative example, from Table 3.1, if an installation I decreases in accident probability, for example, from 10% to 5%, and hence there is an increase in QAAP from 0.2 to 0.35, over 2000 years, and also (via other safety investments) from 10% to 7%, hence from 0.2 to 0.25, in the next 2000 years, then the total equivalent safety benefit for installation I is

If installations and , by a similar approach of calculations, received 0.35 and 0.40 QAAPs respectively, the total safety benefit would be . Notice that this safety investment would be similar to (for example) the choice for a prevention investment leading to 0.95 QAAPs only for installation , and no safety changes/improvements/investments for installations and . In summary, this number (i.e., 0.95 QAAPs) represents a numerical estimate of a company's valuation of the safety investments for installations , , and , and this can be compared with other possible safety investments within the company. This approach can be employed for very low probability risks.

Using QAAPs, different safety investments leading to changing accident probabilities at an industrial site can be compared with one another. Any investment leading to a decrease in accident probability leads to an increase in safety utility (expressed in QAAPs). This utility measure can then be used for comparing various safety investments.

A QAAP can thus be interpreted as a utility number expressing the value that a safety team assigns to a specific time period in a particular safety (accident probability) situation relative to the value of a reference safety situation (e.g., the 0.1% accident probability situation in the example above).

In short, time trade-off is a technique for generating a safety management team's or a safety manager's preferences by offering a hypothetical decision between a shorter time period of a higher safety situation (lower accident probability), on the one hand, or a longer time period of a lower safety situation (higher accident probability) on the other. The time trade-off scores can then be used, in turn, to calculate QAAPs. QAAPs may be particularly useful in the case of prevention with respect to extremely low probability type accidents.