AN1231 Motorola / Freescale Semiconductor, AN1231 Datasheet - Page 13

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

MOTOROLA FAST SRAM
Table 4. Sample Failure Data for a 225 Pin, 27 mm Body
PBGA Cycled from 0 to 100 C at Two Cycles per Hour
Failure Number
(Starting Sample Size, n = 28).
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
1
2
3
4
5
6
7
8
9
95
90
80
70
60
50
40
30
20
10
5
2
1
1000
W/rr/c = fm–95
DISTRIBUTION
WEIBULL
Cycles to Failure
Figure 12. Weibull Failure Distribution of the Data in Table 4
6253
6438
6536
6869
7105
7148
7195
7246
7291
7361
7405
7430
7521
7698
7720
7807
7819
7886
7887
7945
7991
8163
8197
8272
8497
8772
8874
9143
(t)
7958
13.0
NUMBER OF THERMAL CYCLES
N 50%
7737
(Gaussian) error function. The Log Normal scale and shape
parameters, N 50% and , may be calculated as mentioned
previously using a best fit procedure or preferably with a
statistical software package. N 50% is simply the mean time to
failure or the time at which 50% of the sample has failed.
Since 100% of the samples have failed, the Log Normal
parameters can be calculated directly as follows from the
cycles to failure data, with n being the sample size (Log
Normal standard deviation is actually calculated on the log of
the cycles to failure data):
and
and fitting it to the Log Normal distribution reliability function
gives an N 50% of 7628 cycles and a
cummulative failure 95% plot is represented in Figure 13 with
the lower confidence interval shown once again. Note that for
this data set the correlation coefficient (R 2 ) was 0.985 in the
Log Normal distribution, which is better than was achieved
with the Weibull distribution. Which failure distribution is used
ultimately depends on how it fits the majority of the collected
data as well as the availability of statistical software and
familiarity with a particular distribution.
Once again, t is expressed in cycles and erf refers to the
Taking the same 225 pin PBGA failure data from Table 4
R 2
0.965
=
N 50% =
t i – N 50% ) 2
n – 1
n
t i
10000
of 0.042. The
AN1231
(4)
(3)
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