Method has been developed to improve the lower bound of the first excursion probability that can apply to the problem with either constant or time-dependent barriers. The method requires knowledge of the joint density function of the random process at two arbitrary instants

Yang, J. N.

English

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September 1969	 Brief 69-10334 
.
	
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. 
On the Bound of First Excursion Probability 
.
Bounding techniques of the first excursion proba-
bility in the area of random vibrations hav received 
considerable attention because of their direct applica-
tions in assessing the reliability performance of me-
chanical structures subjected to random external dis-
turbances. Previous studies have not presented solu-
tions to the governing equations associated with the 
initial and boundary conditions pertinent to the pres-
ent first passage time problem. Another limitation of 
previous work is due to the restriction that the input 
be "white" evens though the system is assumed to 
possess narrowband characteristics. As a result of 
these limitations this study was undertaken to pro-
vide alternative methods by which additional infor-
mation and practical results were obtained not only 
for the (stationary) white noise input, but also for 
more general cases involving nonstationary and non-
white inputs. A method has been developed to im-
prove the lower bound of the first excursion proba-
bility that can apply to the problem with either con-
stant or time-dependent barriers. The method re-
quires the knowledge of the joint density function of
the random process at two arbitrary instants. Other 
than this, the method can apply to stationary or non-
stationary, Gaussian or non-Gaussian processes. 
Numerical examples have indicated that the im-
provement is significant for the work involved and 
that the difference between the upper and lower 
bounds has been narrowed considerably, particularly 
for the example involving the nonstationary process. 
Note: 
Documentation is available from: 
Clearinghouse for Federal Scientific 
and Technical Information 
Springfield, Virginia 22151 
Price $3.00 
Reference: TSP69- 10334 
Patent status: 
No patent action is contemplated by NASA 
Source: Jann N. Yang of 
Caltech/J PL 
-	 under contract to 
NASA Pasadena Office 
(NPO-1 1158) 
Category 06 
This document was prepared under the sponsorship of the National	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States	 will be free from privately owned rights.
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On the bound of first excursion probability

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