

MILHDBK338B: Electronic Reliability Design Handbook 
 

8.3.2.5.3 ConfidenceInterval Estimates for the Binomial Distribution
8.3.2.5.3 ConfidenceInterval
Estimates for the Binomial Distribution
For situations where reliability is measured as a ratio of the
number of successes to the total number of trials, e.g., oneshot items,
missiles, etc., the confidence interval is determined by consideration of the
binomial distribution. Table XI of Hald’s Statistical Tables and Formulas
(John Wiley and Sons, Inc., New York, 1952) and Ref. [10] gives 95%
and 99% confidence limits for a wide range of values. Figure 8.317 allows a
rough estimate to be made when the number of successes (S) and the number of
trials (N) are known.
FIGURE 8.317: CHART FOR
95% CONFIDENCE LIMITS ON THE PROBABILITY S/N^{1}
Example 9:
S = 8; N = 10. (a) What is the reliability estimate? (b) What
are the twosided upper and lower 95% confidence limits? Answers: (a) 0.80;
(b) 0.98 and 0.43.
More detailed analyses of confidence limits and intervals, with
many more examples under a variety of circumstances, and for a variety of
distributions, e.g., binomial, gamma, Weibull, etc., are given in Refs. [5], [8], [9] and
[10].
^{1}From Clopper, C.J., and
Pearson, E.S., “The Use of Confidence or Fiducial Limits Illustrated in the
Case of the Binomial,” BIOMETRIKA, Vol. 26 (1934), p. 410. Reprinted with
permission.




 
 