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Atomic Energy, Vol. 79. No I2. 1996
O P T I M I Z A T I O N O F N U C L E A R P O W E R S A F E T Y B A S E D O N
S O C I O E C O N O M I C I N D I C A T O R S
T. V. Amosova, V. F. Kozlov,
I. I. Kuz 'min, V. N. Lystsov,
and V. F. Men'shikov
UDC 621.039.533
In 1990 the International Commission on Radiation Protection (MCRP) adopted new recommendations on radiation
safety: ICRP publications Nos. 60 and 61 [1. 2]. They provide only for estimation of the radiation risk, though it is noted
that such estimates should be compared with other types of nontraditional risk. Experience has shown that it is impossible to
optimize a solution on liquidation of the consequences of an accident by estimating only the radiation risk from the accident
[3]. In order that the solutions be optimal it is also necessary to take into account nontraditional factors resulting in an effect
on the population (ecological, psychological, social, and others). To take this circumstance into account, we employed the
principles of estimating risk for human health and the state of the socioeconomic and natural environment and controlling the
risk in the socioeconomic system, as proposed in [4].
The risk associated with a specific source of danger must be controlled by taking into account the entire risk to an
individual, the population, and the environment resulting from the economic activity in the socioeconomic system and its
socioeconomic development. According to this principle, one or another form of practical activity directed toward a stable
development of the socioeconomic system must be implemented in a manner so that an individual person and society as a
whole would obtain a maximum benefit: the equality of life should increase and safety should increase.
The radiation safety system recommended by the MCRP for intervention after an accident for purposes of protecting
the public is based on the following two principles:
the proposed intervention should produce more good than harm, i.e., a decrease in harm as a result of a decrease in
the irradiation dose should be sufficient to justify the harm done by intervention and the cost of doing so, including social
costs;
the forms, scales, and work of intervention must be optimized so that the pure gain obtained by lowering the dose,
i.e., the gain obtained by decreasing the harm from radiation minus the harm associated with the intervention, is maximized.
Unfortunately, practical implementation of these principles encounters serious difficulties - there is no generally
accepted method for determining the optimal balance between the danger and the advantage of intervention or one or another
activity, making it possible to express quantitatively in some units both the danger and gain of one or another action taking
into account social and economic consequences to individuals and society as a whole.
The proposed principle of estimating and controlling the aggregate risk in the socioeconomic system makes it possible
to implement most effectively the ICRP recommendations in practice. The circumstance that the proposed principle employs
as the units of measurement of individual safety the average expected remaining lifetime is of fundamental importance. Since
this is a quantitative indicator, the risk-control process can be placed on a scientific basis [1, 4-6].
In accordance with this principle, the risk to the public from intervention or incorporating in practice the type of
activity under consideration is expressed as a decrease in the average expected remaining life (we denote it as ~-) and the
gain from it in the form of an increase in the remaining life as ~§ By comparing these indicators (Fig. 1) it is possible to
obtain a quantitative estimate of the magnitude and character of the change in the safety level from the activity or intervention
contemplated.
Russian Science Center "Kurchatov Institute." A. A. Blagonravov Institute of Machine Science, Russian Academy of
Sciences. Safety Council of the Russian Federation. Translated from Atomnaya l~nergiya, Vol. 79, No. 6, pp. 443-448,
December. 1995. Original article submitted August 17. 1995.
1063-4258/95/7906-0845512.50 ~ 1996 Plenum Publishing Corporation 845
L_
DIRECT Risk to the public:
accident situations. normal conditions
Risk for protes~ion:[t! workers:
accident situations, normal conditions
Total risk, Increase in the total mortality
ACTIVITY: modernization of the traditional technology: adoption of alternative technology; adoption of economic decisions and/or measures of an organizational character.
HAZARD J
INDIRECT
Harm to the environment:
natural: social:
�9 compensation: pretenses
GOOD
I; DIRECT olume o[ p_ure pr-oduction ure contribution to the
gross national products IPure good per person
Fraction in the internal 'national product
INDIRECT Moral aspects:
internal national product, employment
L , ESTIMATE OF PURE GOOD
PURE HARM
decrease in the avera_ge expected lifetime A'P ).
r
I PURE GOOD
length of the average expected lifetime AT ~ +).
Fig. 1. Estimate of the resulting useful activity: if T (T) - - T( - ) > 0, then the activity is
justified.
The goal of safety optimization is to ensure a pure gain which can be expressed as follows:
B= T(+)--T(-), (1)
where B is the pure gain; 7 -(+) and T(') are, respectively, the increase and decrease in the average expected remaining life,
which are determined by the "good" and "harm", respectively, characterizing the contemplated activity or intervention (see
Fig. 1).
The expected pure gain from the contemplated activity in units of an increase in the lifetime will be estimated by
employing statistical data, which determine the dependence of the average expected remaining lifetime in some socioeconomic
system on the level of economic development (Fig. 2). Using these data, it is possible to calculate for one or another
socioeconomic system, which has reached a definite level of economic development (gross national product per capita), the
effectiveness of decreasing the inherent risk. The following relation was chosen as the indicator o f effectiveness S(Mi): .... . .
where S(Mi) = AMi/ATi, where AM i = Mi+ 1 -Mi ; AT i = Ti+ 1 - T i ; M i are the yearly material resources of an average
statistical person in the given society (the gross national income or the product per capita); and, T i is the average expected
lifetime in this society. This formula is used to determine the-yearly expenditures per capita which are necessary in a given
socioeconomic system, characterized by the indicators T i and M i, for the lifetime of the average statistical person per year.
Since the yearly expenditures (AM i = M i + 1 - - Mi) are required for the entire lifetime of a person, the total cost of lengthen-
ing the lifetime (by one additional year) of an average statistical person is
Tmlti S = Si(Mi) f exp(- r t ) at = Si(Mi) [1 - exp(-rTmax) ]It,
0
846
N,.years.
70
60
S0
itO
30
20
10
o
Y I I I I ! I Z 4~ 6 8 10 1Z
~/, thousands of dollars/(person.yr)
Fig. 2. Expected lifetime N as a function of economic
development Y: 1) USSR; o , ,5 - groups including 11-13
and 3-4 countries, respectively.
where exp(-rt) is the discount function (time waiting factor), which is well known in economics and makes it possible to
weight the costs as a function of time; r is the discount factor (standard for scaling the costs to unit time, yr-1); and, Tma x is
the increased average expected lifetime. We note that a quantity of the type S is called "the maximum costs" in economic
theory. Here they mean the cost of increasing the lifetime of the average statistical person by one year in the socioeconomic
system of interest by increasing the persons prosperity (per unit gross national product or income) and correspondingly
decreasing for that person the aggregate risk from numerous hazards existing in this system.
The costs, determined in this manner, of increasing the lifetime for some countries with different socioeconomic development levels are presented in Table 1.
The following conclusion can be drawn from the data presented in Table 1 and Fig. 2: the development of every
socioeconomic system (for example, government or one or another economically independent region in the country) must be
characterized by, besides the generally accepted indicators, such as the gross national product and income, determining the
economic development and consumption in society, one other indicator - the cost of increasing the expected lifetime, which
is an estimate of the effectiveness of the safety system in the given socioeconomic system. As the socioeconomic development
proceeds, the contribution of a unit of resources to the socioeconomic safety system becomes increasingly less effective from
the standpoint of increasing the average expected lifetime, i.e., the protection of the public from hazards in the given socio-
economic system. The nature of this law has a simple interpretation. In the highly developed countries the hazards that can be
eliminated with the aid of economically relatively inexpensive protection measures have actually been eliminated. As a result,
in these countries expensive programs are required in order to increase the public safety. In the weakly developed countries
the decrease in mortality and morbidity and correspondingly the increase in the lifetime is achievable by less expensive
programs (protection measures), such as providing the population with the simplest food products and the simplest medica- tions, increasing the hygiene, literacy, and so on.
It follows from the data in the table and Fig. 2 that the cost of increasing the average expected lifetime by one
additional year in a socioeconomic system is equal to the yearly squared yearly gross national product (P) or income (I) per capita: S = [P/(person.yr)] 2 = [I/(person.yr)] 2.
It should be noted that the concept "cost of increasing the lifetime" must be distinguished from the concept "cost of
a human life," which is ordinarily used in the standard risk-control methods. However, the concept "cost of a life" presented
as a money equivalent is inadmissable for moral and ethical considerations. No one, except the individual himself, can set the
monetary cost of a life. If the cost of increasing the life in some socioeconomic system has been determined, then the gain
7 ~+) from the work considered in units of increasing the life is T (+) = `5C/S, where `5C is the yearly increment of the gross
national product or income per capita as a result of the adoption of this work in practice.
The estimate of the hazard from the work considered in units of the decrease in the lifetime, i.e., 7 ('l), should be
made for each specific form of activity, taking into account its peculiarities. This estimate must include different types of action on the person and the environment which are due to this form of activity (see Fig. 1).
847
TABLE
Lowering the Collective Irradiation Dose per Person-Zv (for 1985)
Country
China i~-SSR- Great Britain USA
i. Estimate of the Cost of Lengthening the Lifetime and the Optimal Costs for
Gross national product, interna- tional dollar per one person/yr .- _
2444 4996 8655 12532
Cost of increasing the lifetime by one year. thousands of international dollars
1--6 5--30
30--80 80--200
per capita con- sumption, inter- national dollar per one person/yr
1114 2198 5174 8542
P
Optimal costs of de- I creasing the dose by [ one person.Zv, thousands of international dollars 1~--6 ]
$7-30 30--80 $0--200
We point out that the transition from the risk indicators Rq) for the population living in regions of a nuclear power r
plant to lifetime indicators can be made with the aid of the relation AT(-) = [ R(t) t dt, where AT(-) is the decrease in the '0
average lifetime as a result of the individual risk of premature death at age t, equal to R(t). IfR(t) = R 0 = const, then T(-) = ROT2/2.
We note that, for example, for an average lifetime of 75 years, the additional individual risk of premature death,
equal to, for example, R 0 = 10 -5 per yr, leads to a decrease of the lifetime by Ai r'f-) = 24.6 h, i.e., by one day, i.e., it is
actually not important and according to international standards [8] it is considered to be negligibly small.
As the data in Fig. 2 show, the lifetime iv(+) can be increased up to any desired level by using increasingly improved
protection measures in the activity being considered. However, this entails an increase in the cost of such measures and,
correspondingly, a decrease in the contribution of the indicated activity to the increase in the gross national product and other
indicators determining its advantage. Ultimately, the increment to the lifetime 7"(+) on account of the adoption of a given
activity decreases.
Therefore, there arises the problem of optimizing the costs of decreasing the risk from the activity being studied. The
condition of cost optimality, i.e., maximization of the pure gain B, determined by the relation (1), is the necessary and
sufficient condition giving the maximum social utility of the activity. According to the theorem of equilibrium in the risk
control this condition can be represented in the form
S, = S, (2)
where the cost S T of increasing the lifetime determines the effectiveness of the costs of decreasing the risk from the activity
(for example, the development of nuclear power) on account of the improvement of safety measures (technical or organiza-
tional character), and the cost of increasing the lifetime S determines the effectiveness of the cost of decreasing the aggregate
of all other forms of risk characterizing the given socioeconomic system.
The condition of optimality of the costs of decreasing the risk (2), which follows from the theorem of equilibrium in
risk control, makes it possible to develop a relatively simple, for practical applications, method for optimizing the cost of
decreasing different forms of risk. For this, it is suggested that data on the cost of increasing the lifetime in the given socioeconomic system (see Table
1) be used as a standard (S s = S) for adopting a decision on admissable costs of the safety system in the technology, which
is operating or proposed in the given socioeconomic system.
According to the condition (2), safety systems in one or another technology can be put into practice if the cost S T of
increasing the lifetime with their aid does not exceed the computed standard S s for the given system: ST < S s.
We shall use this approach to determine the admissable cost of decreasing the risk from nuclear power. The risk level
depends on the collective effective irradiation dose to the public. In accordance with the current level of knowledge, the
collective dose of one person.Zv decreases the expected lifetime as a whole by 0.5-2 persons.yr on account of mortality from
cancer or oncological diseases [1, 2]. Therefore, according to the condition (2), the cost of decreasing the dose by one
person.Zv by adopting technical systems for shielding from irradiation or taking measures of an organizational character after
accidents, for example, evacuating the population, equal to (0 .5-2)S t will be optimal if ST = S n, where S n is the standard
cost of increasing the lifetime in a socioeconomic sphere in any region (see Table 1).
848
The optimal costs, calculated with the aid of this formula, for decreasing the irradiation dose due to nuclear power by
one person.Zv in countries with equal level of economic development are presented in the last column of Table 1.
In accordance with the ICRP recommendations It] it was assumed in the calculations that a dose of one person Zv decreases the expected lifetime by one person.yr. It follows from the data presented in Table I that the optimal costs for
decreasing the irradiation dose by one person.Zv is equal to the squared yearly gross national product or income per capita
in the given socioeconomic system.
In addition, it follows from the table that: if the cost of the technical safety systems at nuclear power plants in the region correspond to (equal to) the optimal
costs indicated in Table 1, then the total risk to the public of a given socioeconomic system corresponds to the minimum
achieved level in this region; it is assumed that the same optimization of the costs is realized for technical safety systems in
other industries and economic activity in the socioecological system; if the costs of the technical safety systems at nuclear power plants in the region are higher than the costs indicated in
Table 1, then the total risk to the population of a given region will be higher than the minimum achievable level for this
region as a result of the excess costs at the nuclear power plant and the deficiency of means in other industries. We note that
the Union of Independent States will fall into this situation if the Union employs in its nuclear power plants expensive safety
systems adopted, for example, at nuclear power plants in the USA.
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849