Computer program determines by numerical integration the exact statistical two-sided tolerance limits, when the proportion between the limits is at least a specified number. The program is limited to situations in which the underlying probability distribution for the population sampled is the normal distribution with unknown mean and variance

Friedman, H. A.

Webb, S. R.

English

NASA Technical Reports Server

May 1968	 Brief 68-10158 
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. 
Computer Program Determines 
Exact Two-Sided Tolerance Limits for Normal Distributions 
To meet the need for obtaining the exact statistical 
tolerance limits for the two-sided case in which, with 
given probability, the proportion between the limits is 
at least a specified number, a computer program has 
been designed which makes this determination by 
numerical integration. 
The program is limited to situations in which the 
underlying probability distribution for the population 
sampled is the normal distribution with unknown 
mean and variance. 
Given the limits, L and U, the program evaluates 
the exact probability that they will include at least a 
proportion, p, of the population for a given value of 
the tolerance factor, k. Newton—Raphson iteration is 
used to converge on the value of k associated with the 
desired probability, y. 
For each desired probability, the program generates 
a'table of k's associated with the varying values of p 
and sample size. 
Notes: 
1. This program is written in Fortran H for use on the 
IBM 360 computer.
This program can be used by mathematicians and 
statisticians who are interested in generating exact 
two-sided tolerance limits for normal distributions. 
Accuracy for small sample sizes is greater than that 
attained through the approximate formulas of 
Wald and Wolfowitz. 
Inquiries concerning this program may be made to: 
COSMIC 
Computer Center 
University of Georgia 
Athens, Georgia 30601 
Reference: B68-10158 
Patent status: 
No patent action is contemplated by NASA. 
Source: S. R. Webb and H. A. Friedman 
of North American Rockwell Corporation 
under contract to 
Marshall Space Flight Center 
(M FS- 18045) 
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=19680000158 2020-03-12T05:27:20+00:00Z


Computer program determines exact two-sided tolerance limits for normal distributions

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