SCOPE system computes an expression relating the probability of system success to the probabilities of success of its components. It is especially designed for complex system reliability studies

Ryan, K. E.

English

NASA Technical Reports Server

October 1969	 Brief 69-10566 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Ciearinghuse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
System for Computing Operational Probability Equations 
This program SCOPE, originally designed for relia-
bility studies of complex systems in the Saturn S- 11, 
has application to systems in general. 
The problem: 
To generate exact functional reliability relation-
ships between component and system, particularly 
for complex, highly redundant systems. 
The solution: 
To design a system (SCOPE) which computes an 
expression relating the probability of system success 
to the probabilities of success of its components. It 
is especially designed for complex system reliability 
studies. 
How it's done: 
A system is defined as a group of components 
designed to perform a specific function. Most space 
systems are designed with several success modes so 
that component failures need not cause system fail-
ure. A system having more than one success mode is 
said to possess redundancy, and the success modes 
are called success paths. Those success paths which 
contain only components essential to the successful 
operation of the path are called "minimal success 
paths" and they are used by SCOPE to compute the 
reliability equation. A reliability equation is simply the 
probability that any of its minimal success paths will 
work, thus the fundamental law for the addition of 
probabilities can be applied to the task of equation 
generation. 
Previous research described a method for apply-
ing this law to the equation generation task. A recur-
sion expression equivalent to this law is used to reduce 
computer time. Every system with n components 
contains less than 2." minimal success modes. SCOPE
generates all of a system's minimal success paths, 
and from these paths it computes the reliability equa-
tion by use of the recursion formula. In order to 
compute probabilities the APRDCT program 
(Apportionment-Prediction) must be employed since 
SCOPE only generates an equation and a set of 
minimal success paths. It should be noted that SCOPE 
will generate a reliability equation if minimal suc-
cess paths are used, and an unreliability equation if 
minimal failure paths are used. This property is often 
useful when computing an equation for a system with 
more failure paths than success paths, since failure 
paths can be used then and the result subtracted from 
one to give the required reliability result. 
Notes: 
1. The program is written in FORTRAN IV language 
for use on the IBM-7094 computer. 
2. Inquiries should be made to: 
COSMIC 
Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: B69-10566 
Patent status: 
Inquiries about obtaining rights for the commercial 
use of this invention may be made to NASA, Code GP, 
Washington, D.C. 20546.
Source: Kenneth E. Ryan of

North American Rockwell

Space and Information Systems Division

under contract to

Marshall Space Flight Center
(MFS- 16410)
Category 06 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19690000530 2020-03-16T18:08:05+00:00Z


System for computing operational probability equations

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