Data Reduction
5
note that
(x - 7) = 61/~ =
(1.19)
when
pf = 1 - exp[-1] = 0.632
0.20)
then drawing a line at pf = 0.632 intersecting the best fit straight line the
horizontal axis is (x-v). Since y and fl are known the values for 6 and
O can be calculated. The operations are developed more thoroughly in
[ 1.1-1.3]. Abernathy [1.1,1.2] especially has published two books with many
plotted engineering examples.
Now an indication of what kind of distributions the fls may indicate
[1.16].
1.
2.
3.
4.
fl = 1 Exponential distribution with constant rate failure.
fl = 2 Rayleigh distribution.
fl = 3 Log-normal distribution with normal wear out.
fl~5 or more normal distribution or Gaussian.
B, Gaussian
The data is divided into cells using Sturges Rule and plotted on normal
probability paper and is plotted as a percent pf. The peak at 50% should
be the mean. The values of 6.3 and 93.3 are plus and minus three standard
deviations about the mean. These values may be calculated from the plotted
data.
The same fix) and g(x) curves described in Section 1.1 can be
calculated. If only estimates are required the plotted data may suffice
but often more information is requested.
IV. CONFIDENCE LEVELS
The values of 6, fl, ~ and ~ and p are calculated or derived from plots for a
given sample size N. The test sample size, N _< 30, is normally called a small
sample.
5
note that
(x - 7) = 61/~ =
(1.19)
when
pf = 1 - exp[-1] = 0.632
0.20)
then drawing a line at pf = 0.632 intersecting the best fit straight line the
horizontal axis is (x-v). Since y and fl are known the values for 6 and
O can be calculated. The operations are developed more thoroughly in
[ 1.1-1.3]. Abernathy [1.1,1.2] especially has published two books with many
plotted engineering examples.
Now an indication of what kind of distributions the fls may indicate
[1.16].
1.
2.
3.
4.
fl = 1 Exponential distribution with constant rate failure.
fl = 2 Rayleigh distribution.
fl = 3 Log-normal distribution with normal wear out.
fl~5 or more normal distribution or Gaussian.
B, Gaussian
The data is divided into cells using Sturges Rule and plotted on normal
probability paper and is plotted as a percent pf. The peak at 50% should
be the mean. The values of 6.3 and 93.3 are plus and minus three standard
deviations about the mean. These values may be calculated from the plotted
data.
The same fix) and g(x) curves described in Section 1.1 can be
calculated. If only estimates are required the plotted data may suffice
but often more information is requested.
IV. CONFIDENCE LEVELS
The values of 6, fl, ~ and ~ and p are calculated or derived from plots for a
given sample size N. The test sample size, N _< 30, is normally called a small
sample.