NEA-1058 POISSON.

1. NAME OR DESIGNATION OF PROGRAM:  POISSON.

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.

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.).

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.

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-DB executed the test case included in this package  on a VAX-11/780 computer in 16 seconds of CPU time.

7. UNUSUAL FEATURES OF THE PROGRAM:  Analytic solution, no artificial discretisation.

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).

10. 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

11. MACHINE REQUIREMENTS:  < 64 Kbytes, printer.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  OS, JES3.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

15. NAME AND ESTABLISHMENT OF AUTHORS

        F.H. Froehner
        Kernforschungszentrum Karlsruhe, INR
        Postfach 3640
        D-75 Karlsruhe, West Germany

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