NESC0623 SETS.

1. NAME OR DESIGNATION OF PROGRAM:  SETS.

3. DESCRIPTION OF PROBLEM OR FUNCTION

SETS is used for symbolic manipulation of set (or Boolean) equations, particularly the reduction of set equations by the application of set identities. It  is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The  equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system.

4. METHOD OF SOLUTION

The SETS program is  used to read, interpret,
and execute  the statements  of a  SETS user  program which  is an
algorithm  that  specifies  the  particular  manipulations  to  be
performed and the order in which they are to occur.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Any       properly
formed  set  equation  involving  the  set  operations  of  union,
intersection, and complement  is acceptable for processing  by the
SETS program.  Restrictions on the size of a set equation that can
be processed are not absolute but rather are related to the number
of  terms in  the disjunctive  normal  form of  the equation,  the
number  of  literals  in the  equation,  etc.   Nevertheless,  set
equations involving  thousands and even  hundreds of  thousands of
terms can be processed successfully.

6. TYPICAL RUNNING TIME

Running time varies with respect to the particular set equations being processed and the symbolic manipulations being performed. Although no general rule for predicting run time is known, the reduction (expansion, simplification, and factorization) of a set equation usually requires more run time than other manipulations, and this time tends to increase as the number of terms in the disjunctive normal form of the set equation increases. NESC executed the SETS and FTD sample problem in 20 CP seconds on a CDC CYBER175. The SEP and FTD sample problems required 4 CP seconds and 1 CP second, respectively. The FTD sample problem was executed without plotting.

NEA-DB executed the test cases for the different programs contained in this package on CDC CYBER 740. The following CPU times were required: SETS - 122 seconds; SEP - 24 seconds; FTD - 4 seconds.

7. UNUSUAL FEATURES OF THE PROGRAM

The   SETS    program   is    an
interpretive program used to execute the statements of a SETS user
program.  The SETS user program provides  the user with a flexible
capability  for   achieving  the  symbolic  manipulation   of  set
equations.

8. RELATED AND AUXILIARY PROGRAMS

Two auxiliary programs, SEP and FTD, are included. SEP performs the quantitative analysis of reduced Boolean equations (minimal cut sets) produced by SETS. The user can  manipulate and evaluate the equations to find the probability of occurrence of any desired event and to produce an importance ranking of the terms and events in an equation. FTD is a fault tree drawing  program which uses the proprietary ISSCO DISSPLA graphics software to produce an annotated drawing of a fault tree processed by SETS. The DISSPLA routines are not included.

10. REFERENCES

- D.W. Stack,
  A SETS User's Manual Accident Sequence Analysis,
  NUREG/CR-3547 (SAND83-2238), January 1984.
- R.B. Worrell,
  SETS Tape Reference Manual,
  (SAND83-2675), Draft to be published.
- G.B. Varnado, W.H. Horton, and P.R. Lobner,
  Modular Fault Tree Analysis Procedures Guide, Volume 1 - Main
  Report,
  NUREG/CR-3268/1 (SAND83-0963/1), August 1983.
- G.B. Varnado, W.H. Horton, and P.R. Lobner,
  Modular Fault  Tree Analysis Procedures Guide, Volume 2 -
  Appendices A, B,and C,
  NUREG/CR-3268/2 (SAND83-0963/2), August 1983.
- G.B. Varnado, W.H. Horton, and P.R. Lobner,
Modular Fault Tree Analysis Procedures Guide, Volume 3 - Appendice    D, E, F, G, and H,
  NUREG/CR-3268/3 (SAND83-0963/3), August 1983.
- G.B. Varnado, W.H. Horton, and P.R. Lobner,
  Modular Fault Tree Analysis Procedures Guide, Volume 4 - Appendix
  I,
  NUREG/CR-3268/4 (SAND83-0963/4), August 1983.

- M.D. Olman:
  Quantitative Fault Tree Analysis Using the Set Evaluation
  Program (SEP).
  NUREG/CR-1935 (SAND80-2712) (September 1982).
- R.B. Worrell:
  SETS Reference Manual.
  NUREG/CR-4213  (SAND83-2675)  (May 1985)
- D.A. Oliver:
  Fault Tree Drawing Program Users Instructions.
  SLA-73-0409 (April 1973).
- A.W. Shiver:
  Notes on Using the Fault Tree Drawing Program.
  (June 25, 1981).
- L. Eyberger:
  SETS Tape Description and Implementation Information.
  NESC Note 85-68 (May 7, 1985).
- L. Eyberger:
  Additional Material for SETS.
  NESC Note 85-84 (August 12, 1985).

11. MACHINE REQUIREMENTS

SETS requires 155,000 (octal) words of SCM and 12,000 (octal) words of LCM for execution. SEP requires 147,000  (octal) words of SCM and 230,000 (octal) words of LCM: FTD requires  70,000 (octal) words of SCM and 350,000 (octal) words of LCM.

Main storage requirements to run the test cases on CDC CYBER 740 are: SETS - 202,600 (octal) words; SEP - 216,200 (octal) words; FTD - 211,000 (octal) words.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

SCOPE 2.1 (CDC CYBER76) NOS 2.2 (CDC CYBER175), NOS 2.3(CDC CYBER180).

NOS 1.4+531.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

SETS
must be compiled with optimization level of 0 or 1. Full optimization (OPT=2) produces compiler table overflows.
A substantial reprogramming effort would be required to convert the SETS program to a machine that is not compatible with the CDC6600 due to the extensive use of masking instructions and the packing of data within the 60-bit word structure.

15. NAME AND ESTABLISHMENT OF AUTHOR

         R. B. Worrell*
         Reactor Systems Safety Analysis Division 6412
         Sandia National Laboratories
         P. O. Box 5800
         Albuquerque, New Mexico 87115
* Present-address-Logic Analysts
         1717 Louisiana, NE
         Albuquerque, New Mecixo 87110

File name	File description	Records
NESC0623_02.001	information file	91
NESC0623_02.002	job control cards	41
NESC0623_02.003	SETS source program	8087
NESC0623_02.004	SETS test case user program	7
NESC0623_02.005	SETS test case fault tree data	160
NESC0623_02.006	SEP source program	2290
NESC0623_02.007	SEP test case input data	18
NESC0623_02.008	FTD source program	2278
NESC0623_02.009	FTD test case input data	63
NESC0623_02.010	dummy graphics routine	42
NESC0623_02.011	SETS test case printed output	261
NESC0623_02.012	SEP test case printed output	167
NESC0623_02.013	FTD test case printed output	306