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One Shot Reliability (UPF)

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:

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."


Trials are independent Bernoulli events. 


Subpages (1): Failure-Free Testing
Clifford Long,
Mar 12, 2010, 7:37 AM
Clifford Long,
Aug 29, 2011, 8:30 AM