10
Table 1.1 Confidence levels
Confidence level
Z a/2
99%
2.576
95%
1.960
90%
1.645
Chapter 1
calculation. Then for the infinite sample size
/’-0.78 Z~/2"~
n /’0.78 Z~/2"~
Bexp~,. ~ -) _< fl_< ~exp~,- 7/~ .)
(1.37)
/’-1.05 Z~/2" ~
~
/’-+- 1.05 Z~/2"~
0 expt, -)
)
These are the ranges for ~ and ~. The values can be substituted into Eq.
(1.16) and plotted on Weibull paper with the test data. Also note Eq. (1.15)
where for infinite sample-size
~ =~
In terms of the test samples
0 ~ = A
(1.39)
For the infinite sample size
For Eq. (1.38) the 6 for infinite sample size is in terms of A from raw data
6l/~ex" [:~’05z~’]
~’/~ ( !’05z~/: )
~.40)
It should be noted the spread on fl, 0, 6 is smaller as N increases.
On Weibull paper, percent failures are plotted but Eq. (1.16) is
reliability and Eq. (1.18) is the probability of failure. Which has values when
O< (x-y)_ (1.41)
or from the lowest value data point ~ to the highest as partitioned using
Sturges Rule. When the failure is calculated it is multiplied by 100 to
get percent failure. Also note Eq. (1.18) with solutions for 7 fixed at the
lowest test value
(1.42)