AN1231 Motorola / Freescale Semiconductor, AN1231 Datasheet - Page 12

• Manufacturer Part Number: AN1231
• Description: Plastic Ball Grid Array (PBGA)
• Manufacturer: Motorola / Freescale Semiconductor

AN1231
12
FAILURE DATA STATISTICAL ANALYSIS
ber of PBGA device failures (typically at least 50%, greater
than 75% is preferred), the data can be fit to a statistical fail-
ure distribution. The two most commonly used for fatigue are
the Weibull and the Log Normal distributions. The reliability
function that describes failure in the Weibull distribution is as
follows:
survived and
ters, respectively. The scale parameter,
the time at which 63.2% of all devices fail. Time, t, is usually
expressed in cycles.
data pairs that is equal to the number of devices that failed.
Each pair will contain the failure number and the cycles to
failure for that specific device. An example of some actual
data for a 225 pin PBGA that was subjected to 30 minute
thermal cycles from 0 to 100 C is presented in Table 4 on the
next page. In this example the sample size was 28 and cycl-
ing continued until all devices failed (100% device failure or
R = 0). Larger sample sizes such as these on the order of 30
or greater are recommended. The
After the thermal cycling has resulted in a substantial num-
In the above equation R is the fraction of devices that have
After testing is complete the data consists of a number of
and are called the scale and shape parame-
R(t) = e
Figure 11. Typical 0 to 100 C Thermal Cycling Profile Showing the Difference
Between Chamber Air Temperature and Temperature Seen by the Test Board
140
120
100
–20
80
60
40
20
0
–
0
t
and are determined by
, corresponds to
5
(1)
10
TIME (MINUTES)
doing a best fit curve of equation (1). Statistical software
packages with Weibull capability can automate the process
of determining
bullSmith
software that comes with the previously mentioned Anatech
event detectors. The Anatech software presents the data in
terms of cycles to 50% failure as opposed to 63.2% ( . For
the case of the data in Table 4, N 50% was determined to be
7737,
dimensionless, was 13.0.
ure 12. Note that also plotted on this graph is the 95% lower
confidence limit of the data. It is also important to note that
each set of data has a correlation coefficient or a measure of
its goodness of fit to the particular failure distribution. In this
case, the correlation coefficient (R 2 on the graph) was an ad-
equate 0.965.
tribution but it operates on the logarithm of the failure data. In
other words, if the distribution of the log of the cycles to fail-
ure data is normal, the data is Log Normally distributed. The
reliability function for the Log Normal distribution cannot be
written in closed form and is closely approximated by the
following:
The data can then be plotted on Weibull axes as it is in Fig-
The Log Normal distribution is similar to the Normal dis-
15
was determined to be 7958 cycles and , which is
R(t) =
(written by Fulton’s Findings) and another is the
CHAMBER AIR
BOARD
100 C
0 C
1
2
and . One powerful tool to do this is Wei-
1 – erf
20
ln(t) – ln(N 50% )
MOTOROLA FAST SRAM
2
25
(2)