__Example
6__:

Twenty items undergo a
replacement test. Testing continues until ten failures are observed. The tenth
failure occurs at 80 hours. Determine (1) the mean life of the items; and (2)
the one-sided and two- sided 95% confidence intervals for the MTBF.

(1) From Equation
(8.4)

"1">

(2) a = 1 - Confidence Level = 1
- 0.95 = 0.05

2r = 2(number of failures) = 2(10) = 20

That is, 101.88 hours is
the lower (one-sided) 95% confidence limit of q, the true mean life where
X^{2} _{(0.05,
20)} = 31.41 is from Table
8.3-11.

In other words, we are 95%
confident that the true MTBF exceeds 101.88 hours.

(3) From Equation
(8.13)

That is, 93.65 hours is
the lower (two-sided) 95% confidence limit for the mean life and 333.65
hours is the upper (two-sided) 95% confidence limit for that true mean. We
are 95% confident that the interval between 93.65 and 333.65 hours
contains the true MTBF.