Computer Programs
NESC0779 IMPORTANCE
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# NESC0779 IMPORTANCE

#### IMPORTANCE, Minimal Cut Sets and System Availability from Fault Tree Analysis

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1. NAME OR DESIGNATION OF PROGRAM:  IMPORTANCE
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2. COMPUTERS
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Program name Package id Status Status date
IMPORTANCE NESC0779/01 Tested 01-AUG-1979

Machines used:

Package ID Orig. computer Test computer
NESC0779/01 IBM 370 series IBM 370 series
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3. DESCRIPTION OF PROBLEM OR FUNCTION

IMPORTANCE  computes  various
measures of probabilistic  importance of basic events  and minimal
cut sets  to a  fault tree  or reliability  network diagram.   The
minimal cut sets,  the failure rates and the  fault duration times
(i.e., the  repair times)  of all  basic events  contained in  the
minimal cut  sets are  supplied as  input data.   The failure  and
repair distributions are assumed to be exponential.  IMPORTANCE, a
quantitative evaluation  code, then determines the  probability of
the top event and computes the  importance of minimal cut sets and
basic events by  a numerical ranking.  Two  measures are computed.
The first  describes system  behavior at  one point  in time;  the
second describes  sequences of failures  that cause the  system to
fail  in time.   All measures  are  computed assuming  statistical
independence of basic events.   In addition, system unavailability
and expected number of system failures are computed by the code.
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4. METHOD OF SOLUTION

Seven measures of basic  event importance and
two measures  of cut set  importance can be  computed.  Birnbaum's
measure  of importance  (i.e.,  the  partial derivative)  and  the
probability of the top event are  computed using the min cut upper
bound.  If there are no replicated events in the minimal cut sets,
then  the min  cut  upper bound  is exact.   If  basic events  are
replicated in the  minimal cut sets, then based  on experience the
min cut  upper bound  is accurate  if the  probability of  the top
event is less than 0.1.
Simpson's  rule  is  used   in  computing  the  time-integrated
measures  of importance.   Newton's method  for approximating  the
roots  of  an  equation  is employed  in  the  options  where  the
importance measures are computed as  a function of the probability
of the top event,  and a shell sort puts the  output in descending
order of importance.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:
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6. TYPICAL RUNNING TIME

The test  cases executed in about  1 second
on the IBM370/195.
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7. UNUSUAL FEATURES OF THE PROGRAM

For systems where  repair is not
allowed, the code accepts proportional  hazards as input data.  In
another option, where  repair is permitted, failure  rate data can
also be  expressed in relative  terms by representing  the failure
rate and  repair rate  data for  the basic  events in  terms of  a
reference time unit.
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8. RELATED AND AUXILIARY PROGRAMS

Other   qualitative    evaluation
programs  for system  safety and  reliability  analysis are  MOCUS
(NESC  Abstract  653),  PREP (NESC  Abstract  528),  COMCAN  (NESC
Abstract 704), SETS (NESC Abstract  623), FTA (NESC Abstract 666),
and  FTAP,   Department  of  Operations  Research,   Berkeley.   A
discussion of these and others is contained in reference 2.
The IMPORTANCE program was originally  developed on the CDC7600
by Howard  E. Lambert  at Lawrence  Livermore Laboratory,  and was
later converted to  the IBM370 by T.  Chawla and G. Hauser  of the
Reactor  Analysis   and  Safety   Division  at   Argonne  National
Laboratory.
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9. STATUS
Package ID Status date Status
NESC0779/01 01-AUG-1979 Tested at NEADB
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10. REFERENCES

- Howard E. Lambert and Frank M. Gilman,
The IMPORTANCE Computer Code,
UCRL-79269 (Preprint), March 14, 1977.
NESC0779/01, included references:
- H.E. Lambert:
Fault Trees for Decision Making in Systems Analysis,
UCRL-51829  (October 9, 1975)  (Ph.D. thesis)
- H.E. Lambert and B.J. Davis:
The Use of the Computer Code IMPORTANCE with SETS Input,
NUREG/CR-1965 (SAND81-7068)  (March 1981)
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11. MACHINE REQUIREMENTS

Execution  of the  sample problem  required
140K bytes of storage.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0779/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  OS/370.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:    The
program uses logical unit 8 as a storage device.
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15. NAME AND ESTABLISHMENT OF AUTHOR

H. W. Lambert
Lawrence Livermore Laboratory
P. O. Box 808
Livermore, California  94550
*Present address-3728 Brunnelle Drive
Oakland, California  94602
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16. MATERIAL AVAILABLE
NESC0779/01
File name File description Records
NESC0779_01.001 SOURCE PROGRAM (F4,EBCDIC) 1586
NESC0779_01.002 SAMPLE INPUT DATA 123
NESC0779_01.003 SAMPLE OUTPUT 147
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17. CATEGORIES
• G. Radiological Safety, Hazard and Accident Analysis
• P. General Mathematical and Computing System Routines

Keywords: fault tree analysis, probability, reliability, system failure analysis.