**RSICC CODE PACKAGE PSR-475**

**1. NAME AND TITLE**

SIGPI: Fault Tree Cut Set System Performance.

**2. CONTRIBUTORS**

Lawrence Livermore National Laboratory, Livermore, California, through the Energy Science and Technology Software Center, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN 77; DEC VAX11/750 (P00475D078500).

**4. NATURE OF PROBLEM SOLVED**

SIGPI computes the probabilistic performance of complex systems by combining cut set or other binary product data with probability information on each basic event. SIGPI is designed to work with either coherent systems, where the system fails when certain combinations of components fail, or noncoherent systems, where at least one cut set occurs only if at least one component of the system is operating properly. The program can handle conditionally independent components, dependent components, or a combination of component types and has been used to evaluate responses to environmental threats and seismic events. The three data types that can be input are cut set data in disjoint normal form, basic component probabilities for independent basic components, and mean and covariance data for statistically dependent basic components.

**5. METHOD OF SOLUTION**

SIGPI uses two fast complementary methods to compute the probabilistic performance of complex systems: the pi method and the sigma method. The pi method exploits the fact that defined system components are often statistically independent conditional to the environment in which they are embedded. The sigma method computes the probability of combinations of components produced by the pi method by disjointing and partitioning the components, thereby allowing the exact computation of performance. The computational complexity of the overall process is a polynomial function of the number of components. When statistical independence is not possible, dependent data can be used in the calculation, although both speed and accuracy may suffer.

**6. RESTRICTIONS OR LIMITATIONS**

None noted.

**7. TYPICAL RUNNING TIME**

The running time depends on the complexity of the problem. The sample problems required from 3.8 seconds to 53 minutes on the DEC VAX11/785.

**8. COMPUTER HARDWARE REQUIREMENTS**

1.85 Mbytes of hard-disk space was required on a DEC VAX 11/750.

**9. COMPUTER SOFTWARE REQUIREMENTS**

VMS 4.0; VMS 4.5.

**10. REFERENCE**

C.J. Patenaude, "SIGPI: A User's Manual for Fast Computation of the Probabilistic Performance of Complex Systems," NUREG/CR-4800 (UCID-20679) (September 1986).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and the SIGPI source code plus data and test case input in a 32-bit PKZIP from PKWARE® self-extracting executable.

**12. DATE OF ABSTRACT**

February 2000.

** KEYWORDS: **RISK ASSESSMENT; PROBABILITY SAFETY ANALYSIS