Sampling distributions, constructed by Monte Carlo simulation are used in hardware development to establish a design reliability goal, to place a confidence coefficient on reliability estimates, and to determine whether sample stress/strength data demonstrate a specified reliability at a specified confidence level

Burrows, D. L.

Heathcock, R.

English

NASA Technical Reports Server

September 1966	 Brief 66-10405 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U. S. space 
program and to encourage their commercial application. Copies are available to the public from 
the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Design Reliability Goal Developed from Small Sample 
The problem: 
In space vehicle development programs as in other 
sophisticated and complex hardware design, where 
delivery deadlines must be rigidly adhered to, high 
reliability requirements are frequently coupled with 
a limited number of test articles. It is necessary to 
determine if a specified minimum reliability is demon-
strated at some fairly high confidence level. 
The solution: 
Sampling distributions, constructed by Monte Carlo 
simulation are used to aid in establishing a design 
reliability goal, place a confidence coefficient on re-
liability estimates, and determine whether sample 
stress/strength data demonstrate a specified reliability 
at a specified confidence level. 
How it's done: 
In reaching reliability goals, the designer has several 
possible approaches: safety margin, stress/strength 
relationships, and others of a statistical nature. The 
approach used here concerns the use of stress/strength 
statistics in design reliability, demonstration, and 
confidence limits. It is primarily concerned with the 
solution of statistical sampling problems for which 
no theoretical solution is readily available, and with 
the application of the data provided by these solu-
tions. Application of Monte Carlo simulation to con-
structing empirical sampling distribution of reliability 
estimates are obtained by sampling from the classical 
stress/strength (load and failure) distributions, that
are assumed gaussian. Typical stress/strength distribu-
tions, representing specific values of reliability, are 
stored in a computer. From these distributions various 
sample sizes are taken and the resulting estimate of 
reliability computed. Iteration of this procedure re-
sults in the construction of empirical sampling dis-
tributions for specific levels of reliability and specific 
sample sizes. Emphasis is placed on very high values 
of reliability (0.99 to 0.99999999) and on very small 
sample sizes (2 to 8). 
Notes: 
1. This approach will be useful to designers who have 
only a small sample of tested items to determine 
if a specified minimum reliability is demonstrated 
at an acceptable confidence level. 
2. Inquiries concerning this innovation may be di-
rected to: 
Technology Utilization Officer 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B66-10405 
Patent status: 
No patent action is contemplated by NASA. 
Source: Ray Heathcock 
and Dale L. Burrows 
(M-FS-403) 
Category 05 
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.
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Design reliability goal developed from small sample

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