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NEA-1058 POISSON.

POISSON, Analysis Solution of Poisson Problems in Probabilistic Risk Assessment

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1. NAME OR DESIGNATION OF PROGRAM:  POISSON.
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2. COMPUTERS
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Program name Package id Status Status date
POISSON NEA-1058/01 Tested 20-JAN-1986

Machines used:

Package ID Orig. computer Test computer
NEA-1058/01 IBM 3081 DEC VAX 11/780
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3. DESCRIPTION OF PROGRAM OR FUNCTION

Purpose of program:
Analytic treatment of two-stage Poisson problem in Probabilistic   Risk Assement.
Input: estimated a-priori mean failure rate and error factor of  system considered (for calculation of stage-1 prior),  number of failures and operating times for similar           systems (for calculation of stage-2 prior).
Output: a-posteriori probability distributions on linear and  logarithmic time scale (on specified time grid) and  expectation values of failure rate and error factors are           calculated for:
              - stage-1 a-priori distribution,
              - stage-1 a-posteriori distribution,
              - stage-2 a-priori distribution,
              - stage-2 a-posteriori distribution.
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4. METHOD OF SOLUTION

Bayesian approach with conjugate stage-1 prior, improved with experience from similar systems to yield stage-2 prior, and likelihood function from experience with system under study (documentation see below under 10.).
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Up to 100 similar systems (including the system considered), arbitrary number of problems (failure types) with same grid.
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6. TYPICAL RUNNING TIME

Test problem with 30 similar systems, 4 failures types, 72 grid points for the probability distributions needed 0.33 sec in go step, 0.74 sec total CPU time.
NEA-1058/01
NEA-DB executed the test case included in this package  on a VAX-11/780 computer in 16 seconds of CPU time.
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7. UNUSUAL FEATURES OF THE PROGRAM:  Analytic solution, no artificial discretisation.
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8. RELATED AND AUXILIARY PROGRAMS

none (the self-written subroutines  for the gamma-distribution and its first and second derivative may be less sophisticated than corresponding subroutines existing in program packages).
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9. STATUS
Package ID Status date Status
NEA-1058/01 20-JAN-1986 Tested at NEADB
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10. REFERENCES:
NEA-1058/01, included references:
- Input Description for POISSON
  User's Guide  (November 1985)
- F.H. Froehner:
  Analytic Bayesian Solution of the Two-Stage Poisson-Type
  Problem in Probabilistic Risk Analysis.
  Reprint from "Risk Analysis", Vol. 5, No. 3, 1985
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11. MACHINE REQUIREMENTS:  < 64 Kbytes, printer.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NEA-1058/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  OS, JES3.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHORS

        F.H. Froehner
        Kernforschungszentrum Karlsruhe, INR
        Postfach 3640
        D-75 Karlsruhe, West Germany
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16. MATERIAL AVAILABLE
NEA-1058/01
File name File description Records
NEA1058_01.001 information file 51
NEA1058_01.002 POISSON source program 243
NEA1058_01.003 GAMMA Function source program 1058
NEA1058_01.004 command procedure (VAX/VMS) to run test case 15
NEA1058_01.005 POISSON test case input data 148
NEA1058_01.006 POISSON test case printed output 615
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: risk assessment.