Algebraic Monte Carlo procedure statistically analyzes performance parameters in large, complex systems. The individual effects of input variables can be isolated and individual input statistics can be changed without having to repeat the entire analysis

Africano, R. C.

Logsdon, T. S.

English

NASA Technical Reports Server

November 1967
	
Brief 67-10434 
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 Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Algebraic Monte Carlo Procedure Reduces Statistical Analysis Time 
and Cost Factors 
The problem: 
In statistically analyzing performance parameters in 
large, complex systems, various approaches have been 
ekplored in an effort to control the error factor. Two 
of these, the Monte Carlo method, and the root-sum-
square method have been freely employed but exhibit 
certain deficiencies. Given an accurate simulation 
program and unlimited computer time, an output his-
togram can be constructed by the Monte Carlo 
method to any required accuracy. Because accuracy of 
the Monte Carlo procedure is proportional to the 
reciprocal of the square root of the sample size, those 
cases where the simulation program is expensive to 
operate would find a Monte Carlo study prohibitively 
costly. 
In root-sum-square studies, individual one sigma 
perturbations on the input variables are run through 
the simulation program one at a time. The resultant 
effects on the output variable are root-sum-squared to 
get its standard deviation. Although a fast method, the 
assumptions required for use of the root-sum-square 
method are rarely satisfied by the factual situation. 
The solution: 
An algebraic Monte Carlo procedure that requires 
fewer restrictive assumptions than the root-sum-
square method and that is significantly cheaper to 
operate than true Monte Carlo. Basically, the alge-
braic Monte Carlo procedure makes a series of pertur-
bations on the input variables at selected probability 
levels. The effect on the output variables is lit with a
series of polynomial curve fits. With the curve fits 
established the simulation program is no longer used, 
but instead, Monte Carlo samples are derived from the 
polynomials. This procedure drastically reduces the 
number of expensive simulations and, therefore, the 
analysis time. Additionally, the individual effects of 
input variables can be isolated and individual input 
statistics can be changed without having to repeat 
the entire analysis. 
Notes: 
1. By using the expectation operator, the input varia-
bles can be ranked in order of decreasing effect, 
allowing engineering effort to be focused on that 
reduction of statistics that will yield the greatest 
effectiveness. 
2. Inquiries concerning this innovation may be di-
rected to:
Technology Utilization Officer 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B67-10434 
Patent status: 
No patent action is contemplated by NASA. 
Source: R. C. Africano and T. S. Logsdon 
of North American Aviation, Inc. 
under contract to 
Marshall Space Flight Center 
(M FS-1 887) 
Category 01 
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=19670000434 2020-03-11T21:14:11+00:00Z


Algebraic Monte Carlo precedure reduces statistical analysis time and cost factors

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