General Notes
This method accommodates Attributes, Go/No-Go, or Zero-One processes. This material and the method is based on Reliability Maintainability Availability (Locks).
The calculation provides an estimate of the lower confidence interval on (one-shot) reliability. Alternatively, it provides an estimate of the upper probability of failure (UPF) at a specific confidence level.
UPF0.95 = 1 - R0.95
Page 52 of Locks:
"Beta distributions are used in reliability analysis as distributions on the reliability, p, as an r.v. (random variable) with a continuous distribution over the range zero to one."
Locks also discusses the relationships between the binomial, beta, and negative binomial distributions.
Appendix Table 1 "provides percentage points of the beta distribution which can be used for reliability-confidence assessment of highly reliable components or systems."
The attached R script file provides code that duplicates the entries in the Table.
MO Locks Beta Table.R.txt (Contributed by Cliff Long)
upf_betadist.R.txt (Contributed by George Skountrianos) (Has code to emulate both results from Locks text and Navy tables.)
See also: Relationship Between AQL and UPF
Interpretation of UPF:
See the attached file below "ExampleofUPFInterpretation.pdf"
Alternative explanation (thanks to George S.):
"If we were to randomly sample 1000 groups of n = 298 devices from a large population of these devices, we would expect that the reliability would be at least 99% in 950 of those groups.
Link to the interpretation: http://www.cee.vt.edu/ewr/environmental/teach/smprimer/intervals/interval.html
Also I looked into the formula for the lower confidence limit on reliability and it turns out it is based off the Navy's upf calculation. I ran the upf R code and upf_navy(n=30,x=0,level=.90) gives a lower confidence limit of 0.92612 and upf_locks(n=30,x=0,level=.90) gives a lower confidence limit of 0.92841."
Assumptions
Trials are independent Bernoulli events.
References
Reliability Maintainability Availability (Locks)