Systems Analysis Programs for Hands-On Integrated Reliability Evaluations (SAPHIRE) Technical Reference Manual

The Systems Analysis Programs for Hands-on Integrated Reliability Evaluations (SAPHIRE) is a software application developed for performing a complete probabilistic risk assessment (PRA) using a personal computer (PC) running the Microsoft Windows? operating system. Herein information is provided on the principles used in the construction and operation of Version 6.0 and 7.0 of the SAPHIRE system. This report summarizes the fundamental mathematical concepts of sets and logic, fault trees, and probability. This volume then describes the algorithms used to construct a fault tree and to obtain the minimal cut sets. It gives the formulas used to obtain the probability of the top event from the minimal cut sets, and the formulas for probabilities that apply for various assumptions concerning reparability and mission time. It defines the measures of basic event importance that SAPHIRE can calculate. This volume gives an overview of uncertainty analysis using simple Monte Carlo sampling or Latin Hypercube sampling, and states the algorithms used by this program to generate random basic event probabilities from various distributions. Also covered are enhance capabilities such as seismic analysis, cut set "recovery," end state manipulation, and use of "compound events."

[1]  W. Quine On Cores and Prime Implicants of Truth Functions , 1959 .

[2]  G. S. Fishman,et al.  A Statistical Evaluation of Multiplicative Congruential Random Number Generators with Modulus 231 — 1 , 1982 .

[3]  J. D. Beasley,et al.  Algorithm AS 111: The Percentage Points of the Normal Distribution , 1977 .

[4]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[5]  N. Singpurwalla Foundational Issues in Reliability and Risk Analysis , 1988 .

[6]  R. Cheng,et al.  The Generation of Gamma Variables with Non‐Integral Shape Parameter , 1977 .

[7]  J. Venn,et al.  . On the diagrammatic and mechanical representation of propositions and reasonings , 2022 .

[8]  T. Fearn,et al.  Bayesian statistics : principles, models, and applications , 1990 .

[9]  U. Jensen Probabilistic Risk Analysis: Foundations and Methods , 2002 .

[10]  Ernest J. Henley,et al.  Reliability engineering and risk assessment , 1981 .

[11]  Hiromitsu Kumamoto,et al.  Designing for reliability and safety control , 1985 .

[12]  Edwin Thompson Jaynes,et al.  Probability theory , 2003 .

[13]  Ronald A. Thisted,et al.  Elements of statistical computing , 1986 .

[14]  John Andrews,et al.  Reliability and Risk Assessment , 1994 .

[15]  K. D. Russell,et al.  Systems analysis programs for hands-on integrated reliability evaluations (SAPHIRE), Version 5.0 , 1995 .

[16]  S. K. Park,et al.  Random number generators: good ones are hard to find , 1988, CACM.

[17]  J. B. Fussell,et al.  How to Hand-Calculate System Reliability and Safety Characteristics , 1975, IEEE Transactions on Reliability.

[18]  D. M. Rasmuson,et al.  Fault tree reduction and quantificationan overview of IRRAS algorithms , 1993 .

[19]  W E Vesely,et al.  Fault Tree Handbook , 1987 .

[20]  Curtis Smith,et al.  Calculating and addressing uncertainty for risk-based allowable outage times , 1999 .

[21]  Joachim H. Ahrens,et al.  Computer methods for sampling from gamma, beta, poisson and bionomial distributions , 1974, Computing.

[22]  G. Apostolakis,et al.  Pitfalls in risk calculations , 1981 .

[23]  R. P. Kennedy,et al.  Probabilistic seismic safety study of an existing nuclear power plant , 1980 .