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The application of availability analysis to nuclear power plants
Reliability Engineering 9 (1984) 127 131
The Application of Availability Analysis to Nuclear Power Plants A. C. Brooks NUS Corporation, 910 Clopper Road, Gaithersburg, Maryland 20878, USA (Received: 10 November, 1983)
ABSTRACT The use oJ probabilistic risk analysis (PRA) to assess the risks Jrom nuclear power plants is now well established. Considerably less attention has been given so Jar to the use oj availability analysis techniques. The economics of power generation are non, such that with nuclear power currently supplying a suhstantial J?action ~/'power in many countries, increasing attentiori is being paid to improving plant availability. This paper presents a technique Jor systematically identifying the areas in which measures to improve plant availability will be most effective.
1.
INTRODUCTION
The emphasis, so far, in the application of reliability analysis to nuclear power plants has been on assessing core damage probability and public risk. As a result there has been a continuing improvement in the techniques used for nuclear probabilistic risk analysis (PRA). Considerably less attention has been given to the use of reliability techniques for nuclear power plant availability improvement. In non-nuclear reliability analysis, the use of reliability assessment for availability and maintainability improvement is widespread. The emphasis on core damage and public risk in nuclear power has arisen from concerns for public safety, and disquiet by plant utilities and reactor vendors that such concerns are having a negative impact on plant licensing and operability. However, there is increasing attention being 127 Reliability Engineering 0143-8174/84/$03.00 ~) Elsevier Applied Science Publishers Ltd, England, 1984. Printed in Great Britain
128
,4. C. Brooks
paid to plant availability now that a number of nuclear power plants have been in operation for several years. In several countries, nuclear power is supplying a substantial percentage of electrical power and therefore low plant availability has a significant impact.
2.
NEAT T E C H N I Q U E
This paper presents a technique known as NEAT (Nuclear Equipment Availability Trees) which provides a logical means of assessing which changes to plant equipment, procedures, and spare parts stocks would be most effective in improving plant availability. The NEAT technique utilizes a variant of the event tree methodology which has been used so successfully in PRA work. 2.1. Functional event trees
The first step in the NEAT technique consists of constructing functional event trees in order to determine the importance of plant restored states (PRS). A PRS is defined as the return of a nuclear plant to normal operational mode following some event which has taken the plant down. The functional event trees were specifically designed to deal with situations in which corrective actions designed to mitigate the cause of plant shutdown are successful. In other words, the work done to date has been focused on events which do not lead to core damage. Events which do lead to core damage are dealt with more appropriately by conventional PRA techniques. Figure 1 shows the layout of a functional event tree. The tree is divided into five functional headings: (1) The initiating event which is the cause of the nuclear plant shutdown. (2) Diagnosis of the reason for the plant shutdown. (3) The taking of appropriate corrective action to clear or repair the cause of plant shutdown. (4) The restoration of the plant to a normal operating mode. (5) The final column is used for determining the probability of, and time taken to reach, a plant restored state (PRS).
Application oJavailability analysis to nuclear plants DIAGNOSE REASON FOR PLANT OUTAGE
PLANT DOWN FROM CAUSE X
~1
\
r,
c,
~t',, P(I', ))
TAKE APPROPRIATE CORRECTIUEACTION
C
~',
q
PLANT RESTORED STATES, S ~ OF PROB.,P3 ,TIME T3
RESTORATIONOF PLANTTO OPERATION
q
t;
q
q ----I~ S, (p,, T, -----I S~(P~ ~ T~
-
(t'~, P ( t ; ) )
129
I I I I I
(t ~, , P(t~ ) ) 0--
_
----
(t',,p(tl >)
@
s (P..., T ?
(t[ ,p(~;))
I I I I
t :MEAN TIME FOR TIME P(t~):PROBABJLITY OF S :;th PLANT RESTORED P :PROBABILITY OF ;th T :MEAN TIME TO REACH
ZONE K ON EUENT j TIME ZONE K ON EUENT J STATE PLANT RESTORED STATE [th PLANT RESTORED STATE
Fig. i.
Layout of a functional event tree.
Each column from (2) to (4) inclusive is further divided into time zones. The number of time zones depends upon the state of knowledge about the time taken to perform the function in question and the level of complexity desired in the tree. Where knowledge of a function is sufficient to define a probability distribution then, in principle, any number of time zones can be defined. In practice, the author has found that the definition of more than four zones per functional event is usually not warranted. One result of increasing the number of time zone divisions per event is a rapidly increasing complexity of the event tree in terms of end points. Also, a high level of detail (i.e. many time zones) for one functional event is often inconsistent with the detail in other events. For functional events with an adequately defined distribution, the author usually constructs a histogram with four time zones. For events with less detailed information, the author normally defines two or three time zones. Each time zone class, k, of functional event, j, has defined a class mid point, t~, and probability p(t~), t~ represents a specified time taken to perform an event such as 'diagnose reason for plant outage', and p(t~) represents the probability of that event taking time t~.
130
A. C, Brooks
In some cases the author has found it necessary to make subjective judgements on the time for system diagnosis or repair. In these cases no more than two time zones have been defined for the event with a best estimate made of 'optimistic' and 'pessimistic' times for corrective actions and their respective probabilities. 2.2. The NEAT tree When all the time zones and probabilities have been assigned for each functional event, it is then a straightforward matter to construct the N E A T tree. The tree branches into two paths at each time zone; thus if there are z zones for each event./then the total number of end points n, is j = nl
~
1
Thus if three time zones are defined for four functional events, then 81 tree end points are defined. The importance of limiting the number of time zones per event can be seen since the use of five time zones per event would result in 625 end points. The n end points of the event tree are called plant restored states (PRS) since each one represents the restoration of the plant to normal operation. There are two parameters associated with each restored state, Si; its probability, pi, and its total time, t u The probability, P i , for a restored state is obtained by multiplying together the point estimates of probability for each event tree branch on the tree path leading to the state S u The time, t~, is obtained by adding together the time for each event tree branch on the path leading to the state S u The significance of each event PRS is defined in a way analogous to the definition of risk in conventional PRAs. PRS Significance = State probability x State time = p,. x S i
This definition of plant restored state significance enables one to rank all the states in order of contribution to plant downtime and assess which states should receive priority investigation. The author has found it useful to express each restored state as a percentage of the total sum of all the
Application of arailability analysis to nuclear plants
131
restored states and use this as the definition of state importance: 100 x Piti Importance of state S i - - -
Z Piti i=1
Once the significance of each state is defined, it is possible to rank the states in order of importance. The ranking of plant restored states is an important asset in determining the most effective means of improving plant availability since the highest ranked sequences can be examined in detail in order to determine which actions can reduce their importance. The importance of a plant restored state can be reduced either by taking measures to reduce the frequency of the initial cause of plant downtime or by reducing the time to diagnose, repair, and restore the plant to operating condition. The measures which can be taken are sequence dependent. However, diagnoses ol~the most important sequences will often demonstrate that relatively modest costs incurred in improved procedures, test equipment, plant monitoring, or spares stocking will effect a reduction in the importance of the sequences and therefore an increase in plant availability.
BIBLIOGRAPHY 1. Shooman, M. L. Probabilistic Reliability, McGraw-Hill, New York, 1968. 2. Barlow, R. E. and Proschan, F. Mathematical Theory of Reliability, John Wiley & Sons, New York, 1967. 3. Olson, E. A. J. Nuclear Unit Operating Experience--1978 and 1979 Update, NP-2092, Research Project 771-4, Electric Power Research Institute, Palo Alto, 1981.
The Application of Availability Analysis to Nuclear Power Plants A. C. Brooks NUS Corporation, 910 Clopper Road, Gaithersburg, Maryland 20878, USA (Received: 10 November, 1983)
ABSTRACT The use oJ probabilistic risk analysis (PRA) to assess the risks Jrom nuclear power plants is now well established. Considerably less attention has been given so Jar to the use oj availability analysis techniques. The economics of power generation are non, such that with nuclear power currently supplying a suhstantial J?action ~/'power in many countries, increasing attentiori is being paid to improving plant availability. This paper presents a technique Jor systematically identifying the areas in which measures to improve plant availability will be most effective.
1.
INTRODUCTION
The emphasis, so far, in the application of reliability analysis to nuclear power plants has been on assessing core damage probability and public risk. As a result there has been a continuing improvement in the techniques used for nuclear probabilistic risk analysis (PRA). Considerably less attention has been given to the use of reliability techniques for nuclear power plant availability improvement. In non-nuclear reliability analysis, the use of reliability assessment for availability and maintainability improvement is widespread. The emphasis on core damage and public risk in nuclear power has arisen from concerns for public safety, and disquiet by plant utilities and reactor vendors that such concerns are having a negative impact on plant licensing and operability. However, there is increasing attention being 127 Reliability Engineering 0143-8174/84/$03.00 ~) Elsevier Applied Science Publishers Ltd, England, 1984. Printed in Great Britain
128
,4. C. Brooks
paid to plant availability now that a number of nuclear power plants have been in operation for several years. In several countries, nuclear power is supplying a substantial percentage of electrical power and therefore low plant availability has a significant impact.
2.
NEAT T E C H N I Q U E
This paper presents a technique known as NEAT (Nuclear Equipment Availability Trees) which provides a logical means of assessing which changes to plant equipment, procedures, and spare parts stocks would be most effective in improving plant availability. The NEAT technique utilizes a variant of the event tree methodology which has been used so successfully in PRA work. 2.1. Functional event trees
The first step in the NEAT technique consists of constructing functional event trees in order to determine the importance of plant restored states (PRS). A PRS is defined as the return of a nuclear plant to normal operational mode following some event which has taken the plant down. The functional event trees were specifically designed to deal with situations in which corrective actions designed to mitigate the cause of plant shutdown are successful. In other words, the work done to date has been focused on events which do not lead to core damage. Events which do lead to core damage are dealt with more appropriately by conventional PRA techniques. Figure 1 shows the layout of a functional event tree. The tree is divided into five functional headings: (1) The initiating event which is the cause of the nuclear plant shutdown. (2) Diagnosis of the reason for the plant shutdown. (3) The taking of appropriate corrective action to clear or repair the cause of plant shutdown. (4) The restoration of the plant to a normal operating mode. (5) The final column is used for determining the probability of, and time taken to reach, a plant restored state (PRS).
Application oJavailability analysis to nuclear plants DIAGNOSE REASON FOR PLANT OUTAGE
PLANT DOWN FROM CAUSE X
~1
\
r,
c,
~t',, P(I', ))
TAKE APPROPRIATE CORRECTIUEACTION
C
~',
q
PLANT RESTORED STATES, S ~ OF PROB.,P3 ,TIME T3
RESTORATIONOF PLANTTO OPERATION
q
t;
q
q ----I~ S, (p,, T, -----I S~(P~ ~ T~
-
(t'~, P ( t ; ) )
129
I I I I I
(t ~, , P(t~ ) ) 0--
_
----
(t',,p(tl >)
@
s (P..., T ?
(t[ ,p(~;))
I I I I
t :MEAN TIME FOR TIME P(t~):PROBABJLITY OF S :;th PLANT RESTORED P :PROBABILITY OF ;th T :MEAN TIME TO REACH
ZONE K ON EUENT j TIME ZONE K ON EUENT J STATE PLANT RESTORED STATE [th PLANT RESTORED STATE
Fig. i.
Layout of a functional event tree.
Each column from (2) to (4) inclusive is further divided into time zones. The number of time zones depends upon the state of knowledge about the time taken to perform the function in question and the level of complexity desired in the tree. Where knowledge of a function is sufficient to define a probability distribution then, in principle, any number of time zones can be defined. In practice, the author has found that the definition of more than four zones per functional event is usually not warranted. One result of increasing the number of time zone divisions per event is a rapidly increasing complexity of the event tree in terms of end points. Also, a high level of detail (i.e. many time zones) for one functional event is often inconsistent with the detail in other events. For functional events with an adequately defined distribution, the author usually constructs a histogram with four time zones. For events with less detailed information, the author normally defines two or three time zones. Each time zone class, k, of functional event, j, has defined a class mid point, t~, and probability p(t~), t~ represents a specified time taken to perform an event such as 'diagnose reason for plant outage', and p(t~) represents the probability of that event taking time t~.
130
A. C, Brooks
In some cases the author has found it necessary to make subjective judgements on the time for system diagnosis or repair. In these cases no more than two time zones have been defined for the event with a best estimate made of 'optimistic' and 'pessimistic' times for corrective actions and their respective probabilities. 2.2. The NEAT tree When all the time zones and probabilities have been assigned for each functional event, it is then a straightforward matter to construct the N E A T tree. The tree branches into two paths at each time zone; thus if there are z zones for each event./then the total number of end points n, is j = nl
~
1
Thus if three time zones are defined for four functional events, then 81 tree end points are defined. The importance of limiting the number of time zones per event can be seen since the use of five time zones per event would result in 625 end points. The n end points of the event tree are called plant restored states (PRS) since each one represents the restoration of the plant to normal operation. There are two parameters associated with each restored state, Si; its probability, pi, and its total time, t u The probability, P i , for a restored state is obtained by multiplying together the point estimates of probability for each event tree branch on the tree path leading to the state S u The time, t~, is obtained by adding together the time for each event tree branch on the path leading to the state S u The significance of each event PRS is defined in a way analogous to the definition of risk in conventional PRAs. PRS Significance = State probability x State time = p,. x S i
This definition of plant restored state significance enables one to rank all the states in order of contribution to plant downtime and assess which states should receive priority investigation. The author has found it useful to express each restored state as a percentage of the total sum of all the
Application of arailability analysis to nuclear plants
131
restored states and use this as the definition of state importance: 100 x Piti Importance of state S i - - -
Z Piti i=1
Once the significance of each state is defined, it is possible to rank the states in order of importance. The ranking of plant restored states is an important asset in determining the most effective means of improving plant availability since the highest ranked sequences can be examined in detail in order to determine which actions can reduce their importance. The importance of a plant restored state can be reduced either by taking measures to reduce the frequency of the initial cause of plant downtime or by reducing the time to diagnose, repair, and restore the plant to operating condition. The measures which can be taken are sequence dependent. However, diagnoses ol~the most important sequences will often demonstrate that relatively modest costs incurred in improved procedures, test equipment, plant monitoring, or spares stocking will effect a reduction in the importance of the sequences and therefore an increase in plant availability.
BIBLIOGRAPHY 1. Shooman, M. L. Probabilistic Reliability, McGraw-Hill, New York, 1968. 2. Barlow, R. E. and Proschan, F. Mathematical Theory of Reliability, John Wiley & Sons, New York, 1967. 3. Olson, E. A. J. Nuclear Unit Operating Experience--1978 and 1979 Update, NP-2092, Research Project 771-4, Electric Power Research Institute, Palo Alto, 1981.