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Specifying Warranty: Must Understand Reliability of Product Bathtub Reli Curve : (Failure Rate vs Time) Area under curve = total failures Warranty Period << Useful Life Try to minimize total failures in warranty period reduce field failures. Infantile Period. ~ Constant Failure Rate.
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Specifying Warranty: Must Understand Reliability of Product
Infantile
Period
~ Constant Failure Rate
Minimize or Precipitate using ESS in factory
Warranty Period Using ESS (Environmental Stress Screening)
Warranty Period
X
S
i
i
=
1
m
=
=
X
n
n
2
S
(
X

X
)
i
s
i
=
1
=
s
=
n

1
Basic Statistics Review
Example: The following data represents the amount of time it takes 7 people to do a 355 exam problem.
X = 2, 6, 5, 2 ,10, 8, 7 in min.
n = 7
where X = index notation for each individual.
where n = 7 people
i
i
whereS X = Sum of the individual times
where X and m = Average or Mean
Calculate the mean(average):
Equation
i
n = 7 people Mean:X = (2+6+5+2+10+8+7)/7 = 5.7 minutes
where s = s = Standard Deviation
Sum or Variance
Calculate the standard deviation:
Equation
Step 1 Step 2
(Xi  X) (Xi  X)
25.7= 3.7 13.69
65.7= .3 .09
55.7 = .7 .49
25.7 = 3.7 13.69
105.7 = 4.3 18.49
85.7 = 2.3 5.29
75.7 = 1.3 1.69
S(Xi  X) = 53.43
Step 4
Definition:
Range = Max  Min
Median = Middle number when arranged low to high
Mode = Most common number
This Example:
Range = 10  2 = 8 minutes
Median = 6 minutes
Mode = 2 minutes
2
53.43
Square each one
Then Add All
s
=
s
=
7

1
Standard Deviation:
= 2.98 minutes
s
=
s
2
Step 3
Std Deviation is a measure of the inherent spread in the data
22
20
18
15
12
10
8
5
2
0
1.238
1.240
1.242
1.244
Bar Chart or Histogram
Provides a visual display of data distribution
Shape of Distribution May be Key to Issues
Specification Limit
3s
Std Deviation vs
Spec Limits
Area under curve
Is probability of
failure
1s
66807ppm
PPM = Part per Million Defects
Z is the number of Std Devs between the Mean and the spec limit. The higher the value of Z, the lower the chance of producing a defect
Z = 3s
Much Less
Chance of
Failure
1s
3.4ppm*
* Assumes Z is 4.5 long term
Normal Distribution
Z = 6s
34%
34%
2%
2%
14%
14%
2s
3s
+2s
+3s
1s
m
+1s
Characterized by Two Parameters
m and s2
Normal Distribution = N( m,s2 )
Standard Normal Distribution
Apply
Transformation
Standard Normal Distribution
Original Distribution
xm
Z=
Area under Curve =1
s
ms m m+s
1 0 1 Z
X
Examples:
Z = +1.0 is one Standard Deviations above the mean
Z= 0.5 is 0.5 Standard Deviations below the mean
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.005.00e001 4.96e001 4.92e001 4.88e001 4.84e001 4.80e001 4.76e001 4.72e001 4.68e001 4.64e001
0.10 4.60e001 4.56e001 4.52e001 4.48e001 4.44e001 4.40e001 4.36e001 4.33e001 4.29e001 4.25e001
0.20 4.21e001 4.17e001 4.13e001 4.09e001 4.05e001 4.01e001 3.97e001 3.94e001 3.90e001 3.86e001
0.30 3.82e001 3.78e001 3.74e001 3.71e001 3.67e001 3.63e001 3.59e001 3.56e001 3.52e001 3.48e001
0.40 3.45e001 3.41e001 3.37e001 3.34e001 3.30e001 3.26e001 3.23e001 3.19e001 3.16e001 3.12e001
0.50 3.09e001 3.05e001 3.02e001 2.98e001 2.95e001 2.91e001 2.88e001 2.84e001 2.81e001 2.78e001
0.60 2.74e001 2.71e001 2.68e001 2.64e001 2.61e001 2.58e001 2.55e001 2.51e001 2.48e001 2.45e001
0.70 2.42e001 2.39e001 2.36e001 2.33e001 2.30e001 2.27e001 2.24e001 2.21e001 2.18e001 2.15e001
0.80 2.12e001 2.09e001 2.06e001 2.03e001 2.00e001 1.98e001 1.95e001 1.92e001 1.89e001 1.87e001
0.90 1.84e001 1.81e001 1.79e001 1.76e001 1.74e001 1.71e001 1.69e001 1.66e001 1.64e001 1.61e001
1.00 1.59e001 1.56e001 1.54e001 1.52e001 1.49e001 1.47e001 1.45e001 1.42e001 1.40e001 1.38e001
1.10 1.36e001 1.33e001 1.31e001 1.29e001 1.27e001 1.25e001 1.23e001 1.21e001 1.19e001 1.17e001
1.20 1.15e001 1.13e001 1.11e001 1.09e001 1.07e001 1.06e001 1.04e001 1.02e001 1.00e001 9.85e002
1.30 9.68e002 9.51e002 9.34e002 9.18e002 9.01e002 8.85e002 8.69e002 8.53e002 8.38e002 8.23e002
1.40 8.08e002 7.93e002 7.78e002 7.64e002 7.49e002 7.35e002 7.21e002 7.08e002 6.94e002 6.81e002
1.50 6.68e002 6.55e002 6.43e002 6.30e002 6.18e002 6.06e002 5.94e002 5.82e002 5.71e002 5.59e002
1.60 5.48e002 5.37e002 5.26e002 5.16e002 5.05e002 4.95e002 4.85e002 4.75e002 4.65e002 4.55e002
1.70 4.46e002 4.36e002 4.27e002 4.18e002 4.09e002 4.01e002 3.92e002 3.84e002 3.75e002 3.67e002
1.80 3.59e002 3.51e002 3.44e002 3.36e002 3.29e002 3.22e002 3.14e002 3.07e002 3.01e002 2.94e002
1.90 2.87e002 2.81e002 2.74e002 2.68e002 2.62e002 2.56e002 2.50e002 2.44e002 2.39e002 2.33e002
2.00 2.28e002 2.22e002 2.17e002 2.12e002 2.07e002 2.02e002 1.97e002 1.92e002 1.88e002 1.83e002
2.10 1.79e002 1.74e002 1.70e002 1.66e002 1.62e002 1.58e002 1.54e002 1.50e002 1.46e002 1.43e002
2.20 1.39e002 1.36e002 1.32e002 1.29e002 1.25e002 1.22e002 1.19e002 1.16e002 1.13e002 1.10e002
2.30 1.07e002 1.04e002 1.02e002 9.90e003 9.64e003 9.39e003 9.14e003 8.89e003 8.66e003 8.42e003
2.40 8.20e003 7.98e003 7.76e003 7.55e003 7.34e003 7.14e003 6.95e003 6.76e003 6.57e003 6.39e003
2.50 6.21e003 6.04e003 5.87e003 5.70e003 5.54e003 5.39e003 5.23e003 5.08e003 4.94e003 4.80e003
2.60 4.66e003 4.53e003 4.40e003 4.27e003 4.15e003 4.02e003 3.91e003 3.79e003 3.68e003 3.57e003
2.70 3.47e003 3.36e003 3.26e003 3.17e003 3.07e003 2.98e003 2.89e003 2.80e003 2.72e003 2.64e003
2.80 2.56e003 2.48e003 2.40e003 2.33e003 2.26e003 2.19e003 2.12e003 2.05e003 1.99e003 1.93e003
2.90 1.87e003 1.81e003 1.75e003 1.69e003 1.64e003 1.59e003 1.54e003 1.49e003 1.44e003 1.39e003
3.00 1.35e003 1.31e003 1.26e003 1.22e003 1.18e003 1.14e003 1.11e003 1.07e003 1.04e003 1.00e003
3.10 9.68e004 9.35e004 9.04e004 8.74e004 8.45e004 8.16e004 7.89e004 7.62e004 7.36e004 7.11e004
3.20 6.87e004 6.64e004 6.41e004 6.19e004 5.98e004 5.77e004 5.57e004 5.38e004 5.19e004 5.01e004
3.30 4.83e004 4.66e004 4.50e004 4.34e004 4.19e004 4.04e004 3.90e004 3.76e004 3.62e004 3.49e004
3.40 3.37e004 3.25e004 3.13e004 3.02e004 2.91e004 2.80e004 2.70e004 2.60e004 2.51e004 2.42e004
3.50 2.33e004 2.24e004 2.16e004 2.08e004 2.00e004 1.93e004 1.85e004 1.78e004 1.72e004 1.65e004
3.60 1.59e004 1.53e004 1.47e004 1.42e004 1.36e004 1.31e004 1.26e004 1.21e004 1.17e004 1.12e004
3.70 1.08e004 1.04e004 9.96e005 9.57e005 9.20e005 8.84e005 8.50e005 8.16e005 7.84e005 7.53e005
3.80 7.23e005 6.95e005 6.67e005 6.41e005 6.15e005 5.91e005 5.67e005 5.44e005 5.22e005 5.01e005
3.90 4.81e005 4.61e005 4.43e005 4.25e005 4.07e005 3.91e005 3.75e005 3.59e005 3.45e005 3.30e005
4.00 3.17e005 3.04e005 2.91e005 2.79e005 2.67e005 2.56e005 2.45e005 2.35e005 2.25e005 2.16e005
4.10 2.07e005 1.98e005 1.89e005 1.81e005 1.74e005 1.66e005 1.59e005 1.52e005 1.46e005 1.39e005
4.20 1.33e005 1.28e005 1.22e005 1.17e005 1.12e005 1.07e005 1.02e005 9.77e006 9.34e006 8.93e006
4.30 8.54e006 8.16e006 7.80e006 7.46e006 7.12e006 6.81e006 6.50e006 6.21e006 5.93e006 5.67e006
4.40 5.41e006 5.17e006 4.94e006 4.71e006 4.50e006 4.29e006 4.10e006 3.91e006 3.73e006 3.56e006
4.50 3.40e006 3.24e006 3.09e006 2.95e006 2.81e006 2.68e006 2.56e006 2.44e006 2.32e006 2.22e006
4.60 2.11e006 2.01e006 1.92e006 1.83e006 1.74e006 1.66e006 1.58e006 1.51e006 1.43e006 1.37e006
4.70 1.30e006 1.24e006 1.18e006 1.12e006 1.07e006 1.02e006 9.68e007 9.21e007 8.76e007 8.34e007
4.80 7.93e007 7.55e007 7.18e007 6.83e007 6.49e007 6.17e007 5.87e007 5.58e007 5.30e007 5.04e007
4.90 4.79e007 4.55e007 4.33e007 4.11e007 3.91e007 3.71e007 3.52e007 3.35e007 3.18e007 3.02e007
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
5.002.87e007 2.72e007 2.58e007 2.45e007 2.33e007 2.21e007 2.10e007 1.99e007 1.89e007 1.79e007
5.10 1.70e007 1.61e007 1.53e007 1.45e007 1.37e007 1.30e007 1.23e007 1.17e007 1.11e007 1.05e007
5.20 9.96e008 9.44e008 8.95e008 8.48e008 8.03e008 7.60e008 7.20e008 6.82e008 6.46e008 6.12e008
5.30 5.79e008 5.48e008 5.19e008 4.91e008 4.65e008 4.40e008 4.16e008 3.94e008 3.72e008 3.52e008
5.40 3.33e008 3.15e008 2.98e008 2.82e008 2.66e008 2.52e008 2.38e008 2.25e008 2.13e008 2.01e008
5.50 1.90e008 1.79e008 1.69e008 1.60e008 1.51e008 1.43e008 1.35e008 1.27e008 1.20e008 1.14e008
5.60 1.07e008 1.01e008 9.55e009 9.01e009 8.50e009 8.02e009 7.57e009 7.14e009 6.73e009 6.35e009
5.70 5.99e009 5.65e009 5.33e009 5.02e009 4.73e009 4.46e009 4.21e009 3.96e009 3.74e009 3.52e009
5.80 3.32e009 3.12e009 2.94e009 2.77e009 2.61e009 2.46e009 2.31e009 2.18e009 2.05e009 1.93e009
5.90 1.82e009 1.71e009 1.61e009 1.51e009 1.43e009 1.34e009 1.26e009 1.19e009 1.12e009 1.05e009
6.00 9.87e010 9.28e010 8.72e010 8.20e010 7.71e010 7.24e010 6.81e010 6.40e010 6.01e010 5.65e010
6.10 5.30e010 4.98e010 4.68e010 4.39e010 4.13e010 3.87e010 3.64e010 3.41e010 3.21e010 3.01e010
6.20 2.82e010 2.65e010 2.49e010 2.33e010 2.19e010 2.05e010 1.92e010 1.81e010 1.69e010 1.59e010
6.30 1.49e010 1.40e010 1.31e010 1.23e010 1.15e010 1.08e010 1.01e010 9.45e011 8.85e011 8.29e011
6.40 7.77e011 7.28e011 6.81e011 6.38e011 5.97e011 5.59e011 5.24e011 4.90e011 4.59e011 4.29e011
6.50 4.02e011 3.76e011 3.52e011 3.29e011 3.08e011 2.88e011 2.69e011 2.52e011 2.35e011 2.20e011
6.60 2.06e011 1.92e011 1.80e011 1.68e011 1.57e011 1.47e011 1.37e011 1.28e011 1.19e011 1.12e011
6.70 1.04e011 9.73e012 9.09e012 8.48e012 7.92e012 7.39e012 6.90e012 6.44e012 6.01e012 5.61e012
6.80 5.23e012 4.88e012 4.55e012 4.25e012 3.96e012 3.69e012 3.44e012 3.21e012 2.99e012 2.79e012
6.90 2.60e012 2.42e012 2.26e012 2.10e012 1.96e012 1.83e012 1.70e012 1.58e012 1.48e012 1.37e012
7.00 1.28e012 1.19e012 1.11e012 1.03e012 9.61e013 8.95e013 8.33e013 7.75e013 7.21e013 6.71e013
7.10 6.24e013 5.80e013 5.40e013 5.02e013 4.67e013 4.34e013 4.03e013 3.75e013 3.49e013 3.24e013
7.20 3.01e013 2.80e013 2.60e013 2.41e013 2.24e013 2.08e013 1.94e013 1.80e013 1.67e013 1.55e013
7.30 1.44e013 1.34e013 1.24e013 1.15e013 1.07e013 9.91e014 9.20e014 8.53e014 7.91e014 7.34e014
7.40 6.81e014 6.31e014 5.86e014 5.43e014 5.03e014 4.67e014 4.33e014 4.01e014 3.72e014 3.44e014
7.50 3.19e014 2.96e014 2.74e014 2.54e014 2.35e014 2.18e014 2.02e014 1.87e014 1.73e014 1.60e014
7.60 1.48e014 1.37e014 1.27e014 1.17e014 1.09e014 1.00e014 9.30e015 8.60e015 7.95e015 7.36e015
7.70 6.80e015 6.29e015 5.82e015 5.38e015 4.97e015 4.59e015 4.25e015 3.92e015 3.63e015 3.35e015
7.80 3.10e015 2.86e015 2.64e015 2.44e015 2.25e015 2.08e015 1.92e015 1.77e015 1.64e015 1.51e015
7.90 1.39e015 1.29e015 1.19e015 1.10e015 1.01e015 9.33e016 8.60e016 7.93e016 7.32e016 6.75e016
8.00 6.22e016 5.74e016 5.29e016 4.87e016 4.49e016 4.14e016 3.81e016 3.51e016 3.24e016 2.98e016
8.10 2.75e016 2.53e016 2.33e016 2.15e016 1.98e016 1.82e016 1.68e016 1.54e016 1.42e016 1.31e016
8.20 1.20e016 1.11e016 1.02e016 9.36e017 8.61e017 7.92e017 7.28e017 6.70e017 6.16e017 5.66e017
8.30 5.21e017 4.79e017 4.40e017 4.04e017 3.71e017 3.41e017 3.14e017 2.88e017 2.65e017 2.43e017
8.40 2.23e017 2.05e017 1.88e017 1.73e017 1.59e017 1.46e017 1.34e017 1.23e017 1.13e017 1.03e017
8.50 9.48e018 8.70e018 7.98e018 7.32e018 6.71e018 6.15e018 5.64e018 5.17e018 4.74e018 4.35e018
8.60 3.99e018 3.65e018 3.35e018 3.07e018 2.81e018 2.57e018 2.36e018 2.16e018 1.98e018 1.81e018
8.70 1.66e018 1.52e018 1.39e018 1.27e018 1.17e018 1.07e018 9.76e019 8.93e019 8.17e019 7.48e019
8.80 6.84e019 6.26e019 5.72e019 5.23e019 4.79e019 4.38e019 4.00e019 3.66e019 3.34e019 3.06e019
8.90 2.79e019 2.55e019 2.33e019 2.13e019 1.95e019 1.78e019 1.62e019 1.48e019 1.35e019 1.24e019
9.00 1.13e019 1.03e019 9.40e020 8.58e020 7.83e020 7.15e020 6.52e020 5.95e020 5.43e020 4.95e020
9.10 4.52e020 4.12e020 3.76e020 3.42e020 3.12e020 2.85e020 2.59e020 2.37e020 2.16e020 1.96e020
9.20 1.79e020 1.63e020 1.49e020 1.35e020 1.23e020 1.12e020 1.02e020 9.31e021 8.47e021 7.71e021
9.30 7.02e021 6.39e021 5.82e021 5.29e021 4.82e021 4.38e021 3.99e021 3.63e021 3.30e021 3.00e021
9.40 2.73e021 2.48e021 2.26e021 2.05e021 1.86e021 1.69e021 1.54e021 1.40e021 1.27e021 1.16e021
9.50 1.05e021 9.53e022 8.66e022 7.86e022 7.14e022 6.48e022 5.89e022 5.35e022 4.85e022 4.40e022
9.60 4.00e022 3.63e022 3.29e022 2.99e022 2.71e022 2.46e022 2.23e022 2.02e022 1.83e022 1.66e022
9.70 1.51e022 1.37e022 1.24e022 1.12e022 1.02e022 9.22e023 8.36e023 7.57e023 6.86e023 6.21e023
9.80 5.63e023 5.10e023 4.62e023 4.18e023 3.79e023 3.43e023 3.10e023 2.81e023 2.54e023 2.30e023
9.90 2.08e023 1.88e023 1.70e023 1.54e023 1.39e023 1.26e023 1.14e023 1.03e023 9.32e024 8.43e024
10.00 7.62e024 6.89e024 6.23e024 5.63e024 5.08e024 4.59e024 4.15e024 3.75e024 3.39e024 3.06e024
Z Value vs Probability of Failure or Defect
1 Sided Normal Distribution
PPM Defects
1,000,000
Tax Advice
(phonein)
(140,000 PPM)
Restaurant Bills
100,000
Doctor Prescription Writing
Restaurant Checks
10,000
•
Average
Company
Airline Baggage Handling
1,000
100
AircraftCarrier Landings
10
BestinClass
1
6
2
3
4
5
7
Z
Domestic Airline Flight
Fatality Rate
(0.43 PPM)
Examples of Fault/Failure Rates on
The Sigma Scale
Short Term Capability Snapshots of the Product
Over time, a “typical” product process may shift or drift by ~ 1.5
. . . also called “shortterm capability”
. . . reflects ‘within group’ variation
Time 1
Time 2
Time 3
Time 4
Actual Sustained Capability of the Process
. . . also called “longterm capability”
. . . reflects ‘total process’ variation
LSL
T
USL
Two Challenges:
Center the Process and Eliminate Variation!
Z Value vs Probability of Failure or Defect
1 Sided Normal Distribution
Industry Accepted 6 sigma quality level
Recall the Bathtub Curve Failure Rate (l) vs. Time behavior
lFIT = FITs = Failures per 109 hours
MTBF (years) = 1x109 / (lFIT * 8766 hours /year )
lMTBF = 1/MTBF = 1/Mean time between failure in time units
R(t) = elt, Note: lMTBF in hr1 and t in hr
l General Failure Rate Variable:
For CONSTANT FAILURE RATES – Exponential Distribution Applies and R(t) = (Reliability at Time t) = Probability that a system will not fail for a time period “t,” assuming constant failure rate;
R(t) = elt, Note: lis in failures/time, and t is time
Note: At T=0, R(0)=1.0 (100%)
F(t) = (UnReliability at Time t or Failures at Time t) = Fraction of population that has failed at Time t, probability that a given system will fail for a time period “t,” assuming constant failure rate;
F(t) = 1elt, Note: lis in failures/time, and t is time
Note: At T=0, F(0)=0.0 (0%)
For VARYING FAILURE RATES – Weibull Distribution Applies and R(t) = (Reliability at Time t) = Probability that a system will not fail for a time period “t,”;
F(t) = (1 – R(t))100%
Time to Failure(s)
At some time, t, 100% of the population will fail
Time to failure plot using Weibull tool
Decreasing
Failure Rates
<1
Increasing
Failure Rates
>1
The Bathtub Curve
Constant
Failure Rates
=1
Exponential Distribution
Failure Rate,
Weibull slope indicates where the product may be on the bathtub curve.
Early
Life
Wear out
Useful Life
Time
Reliability Targets… Allocation & Flowdown
POF Approach
POF = Physics of Failure
Additional Keys to High Reliability
Key Strategies in Design for Reliability (DFR)
Some Typical Stresses – Most Can be Accelerated
Device
NiAu Pad
Thin Epoxy Solder Mask
SnPb or SAC Solder Joint
Copper
FR4 Laminate
Causes of Electronic Systems Failure
Reliability ofElectronic Circuits
PCB Assembly Failure Mechanisms
PCB Assembly Failure Mechanisms
CTE Mismatches in PCB Assemblies
Si Die CTE = 2.8e6/C
Gold CTE = 14.2e6/C5 – 15 μ in.
NiAu Pad
Thin Epoxy Solder Mask
Nickel CTE = 13.4e6/C> ~100 μ in.
Copper
FR4 Laminate
CTE = ~20e6/C
Copper CTE = 16.5e6/C> ~1.2 mil
SnPb Eutectic Solder Joint CTE = ~25e6/C
Resistivity of Solvent Extract (ROSE) Test Method IPCTM650 2.3.25The ROSE test method is used as a process control tool (rinse) to detect the presence of bulk ionics. The IPC upper limit is set at 10.0 mg/in2 .(1.56ug/cm2) This test method provides no evidence of a correlation value with modified ROSE testing or ion chromatography. This test is performed using an ionograph or similar style ionics testing unit that detects total ionic contamination, but does not identify specific ions present. Non destructive test.
Modified Resistivity of Solvent Extract (Modified ROSE)The modified ROSE test method involves a thermal extraction. The PCB is exposed in a solvent solution at a predetermined temperature for a specified time period. This process draws the ions present on the PCB into the solvent solution. The solution is tested using an ionographstyle test unit. The results are reported as bulk ions present on the PCB per square inch, similar to the standard ROSE method above. Can be destructive.
Ion Chromatography IPCTM650 2.3.28This test method involves a thermal extraction similar to the modified ROSE test. After thermal extraction, the solution is tested using various standards in an ion chromatographic test unit. The results indicate the individual ionic species present and the level of each ion species per unit area. This test is an excellent way to pinpoint likely process steps which are leaving residual contaminants that can lead to early reliability failures. Destructive test.
75 %
50 %
25 %
0 %
100 %
75 %
50 %
25 %
0 %
Statistics Example: IPC Workmanship Classes: Solder Volume, Shape, Placement ControlMin PTH Vertical Fill: Class 2 = 75% Class 3 = 100%
Ref: IPCA610, IPCJSTD001
Sampling_Grid
Position
Model
Solder_Joint_Radius
Void_Distance
Void_Radius
S
Void_Solder Interface Distance
S = Shell
Potential for Early Life Failure (ELFO) if S < D/10 = (solder_joint_radius)/10
S =Shell = solder_joint_radius – (void_distance + void_radius)
Solder Joint_Radius: 0.225 mm
Void_Radius: 0.135 mm
Void_Area: 36% of Joint Area
Failure criteria: D/10
P(D<10) = 81.11 %
CLASS 2  BETTER
Solder Joint_Radius: 0.225 mm
Void_Radius: 0.1013 mm
Void_Area: 20% of Joint Area
Failure criteria: D/10
P(D<10) = 52.21 %
CLASS 3  BEST
Solder Joint_Radius: 0.225 mm
Void_Radius: 0.0675 mm
Void_Area: 9% of Joint Area
Failure criteria: D/10
P(D<10) = 27.00 %
S = Shell
Depth
Component 1
l1
Component 2
l2
Component i
li
Component N
lN
Component 1
R1
Component 2
R2
Component i
Ri
Component N
RN
Reliability R Flowdown Example
Drive System,
needs R= 0.9 at 10 years
System Level
Power supply
R = 0.94
Subsystem Level
Motor
R = 0.97
Control Card
R = 0.99
Component Level
Part
R=0.9999
Part
R=0.9999
Part
R=0.9999
Part
R=0.9999
Part
R=0.9999
Part
R=0.999
Part
R=0.999
Reliability Requirements Flowdown Example
Recall Equations: R = e lt and MTBF = 1/l
Solve for MTBF: MTBF = 1/ l = 1/ {(1/t) * ln R }, R = 0.99, t = 8766 hrs
MTBF >= 872,000 hours (99.5 yrs) !
What is your product warranty cost goal expressed as an R(t)?:
Answer:What is the scrap or repair cost of a given % of failures during the warranty period? Need to know, annual production, and an assumed R(t). Good products have less than 1% annualized warranty cost as a percentage of the total contribution margin for that product.
Where lB = Base Failure Rate for Component
Component 1
l1
Component 2
l2
Component i
li
Component N
lN
Max Tr
Max Vr
pT
pV
pE
pQ
C1
105C
50V
2.082
0.186
2.5
1.25
C2
105C
50V
2.082
0.186
2.5
1.25
C3
85C
15V
3.773
0.223
2.5
1.25
C4
125C
50V
1.548
0.151
2.5
1.25
R1
120C
20V
1.643
0.232
2.5
1.25
R2
150C
6V
1.249
0.549
2.5
1.25
Zener Diode
100C
N/A
2.318
1.0
2.5
1.25
Op Amp
125C
36V
1.548
1.0
2.5
1.25
74HCT14
125C
7V
1.548
1.649
2.5
1.25
LED
85C
N/A
3.773
1.0
2.5
1.25
Example: Method A, 050C Ambient, Indoor Mobile, Distributor Components
+5VDC
C1 0.1uf 50V
Polyester
+12VDC
C4 0.1uf 50V
Ceramic
+5VDC
LED
Vf=1.5V
R1 2KW 1/4W
Brand A Metal Film
Vin
BPLR
OP AMP
R2 150W 1/4W
Brand B Metal Film
C2 0.1uf 50V
Polyester
74HCT14
5V 1W
Zener
C3 10uf 15V
Electrolytic
12VDC
lFITS
10.29
10.29
552.2
1.46
0.83
1.50
23.18
67.73
217.77
106.16
991.37 Fits 115.1 Yrs MTBF
MTBF Data Input Sheet for eReliability.com COST: $500 per report
System / Equipment Name:Assembly Name:Quantity of this assembly:Parts List Number:Environment:Select One Of : GB, GF, GM, NS, NU, AIC, AIF, AUC, AUF, ARW, SF, MF, ML, or CLParts Quality:Select Either: MilSpec or Commercial/BellcoreQuantity Description Bipolar Integrated Circuits IC / Bipolar, Digital 1100 Gates IC / Bipolar, Digital 1011000 Gates IC / Bipolar, Digital 10013000 Gates IC / Bipolar, Digital 300110000 Gates IC / Bipolar, Digital 1000130000 Gates IC / Bipolar, Digital 3000160000 Gates IC / Bipolar, Linear 1100 Transistors IC / Bipolar, Linear 101300 Transistors IC / Bipolar, Linear 3011K Transistors IC / Bipolar, Linear 100110K Transistors, etc.
EXAMPLE: Actual Reli Tool Input
List of components, their number,
Environment conditions, components quality
Example Reliability calculation using actual MILHDBK217F
Failure rate of a Metal Oxide Semiconductor (MOS) can be expressed as
Parameters are listed in MIL Data base.
Temperature factor is modeled using Arrhenius type Eqn
595 charts are greatly simplified from actual parts count Reli

     Failure Rate in 
     Parts Per Million Hours 
 Description/  Specification/  Quantity  Quality 
 Generic Part Type  Quality Level   Factor   
    (Pi Q)  Generic  Total 
      
================================================================================
 Integrated Circuit/  MilM38510/  16  1.00  0.07500  1.20000 
 Bipolar, Digital  B     
 3000160000 Gates      
      
 Integrated Circuit/  MilM38510/  8  1.00  0.01700  0.13600 
 Bipolar, Linear  B     
 101300 Transistors      
      
 Diode/  MilS19500/  2  2.40  0.00047  0.00226 
 Switching  JAN     
      
      
 Diode/  MilS19500/  4  2.40  0.00160  0.01536 
 Voltage Ref./Reg.  JAN     
 (Avalanche & Zener)      
      
 Transistor/  MilS19500/  4  2.40  0.00007  0.00067 
 NPN/PNP  JAN    
Reliability Growth Methods: HALT
Repeat
Time Compression or Time Acceleration
Basic usage cycle is reduced by eliminating idle time and or off time.
Example: Opening and Closing a car door 10,000 times in 1 day. ~10 year:1day Acceleration
Stress Acceleration or Amplitude Acceleration
Amplitude of Stress is increased above normal usage cycle levels
Example: Thermal cycling a circuit board from –40 to 125C knowing the board will see a maximum ambient range of only 10 to 35C in its application. ~163cyles:1cycle Acceleration
Example of Time Accelerated Life Test (595 Team Project):“Rotating Bicycle Apparatus Project”
Potential reliability stress is the periodic gload (startstop cycles). This causes fatigue
failure mode (cracks in ceramic material, creep of plastics, adhesives, solder electrical contacts failure).
Assuming the throughput 35 startstops/day for 365 days/year
the total number of rotation cycles for 1 year is 35*365=12775 cycles /year (=12775 startstops).
Assuming 20% overhead the total number of cycles is going to be 1.2*12775=15330 cycles/year.
Test time worth of 1 year of the number of cycles is going to be 15330*20/(3600*24)=3.5 days
Stress Accelerations* High Temperature* High Voltage* Thermal Cycling* Vibration
High Temperature Acceleration Factor
Modified Arrhenius Equation:
AT = Acceleration Factor
Ea = Activation Energy Depends on failure modes; incl electromigration, contamination, etc.
Voltage Stress Acceleration Factor
Modified Arrhenius Equation:
E
316 Stainless Steel
1.5
4340 Steel
1.8
Solder (97Pb/03Sn) T > 30°C
1.9
Solder (37Pb/63Sn) T < 30°C
1.2
Solder (37Pb/63Sn) T > 30°C
2.7
Solder (37Pb/03Ag & 91Sn/09Zn)
2.4
Aluminum Wire Bond
3.5
Au
Al fracture in wire bonds
4.0
4
PQFP Delamination / Bond Failure
4.2
ASTM 2024 Aluminum Alloy
4.2
Copper
5.0
Au Wire Bond Heel Crack
5.1
ASTM 6061 Aluminum Alloy
6.7
Alumina Fracture
5.5
Interlayer Dielectric Cracking
4.86.2
Silicon Fracture
5.5
Silicon Fracture (cratering)
7.1
Thin Film Cracking
8.4
Thermal Cycle Stress Accelerations
Primarily used to stress CTE mismatch, accumulated fatigue damage failures
Basic CoffinManson Equation – Temperature Cycle
SnPb Eutectic (single melting point) Solder Joint Creep Failure Application
AF = (DTs/ DTa)E
Where;
DTs = Stress Test Thermal Excursion Range oK
DTa = Application Thermal Excursion Range oK
E = Material Dependent Exponent
E = 1.9 – 2.7 for 63/37 SnPb Eutectic Solders
AF = Per Cycle Stress Test Acceleration Factor
SnPb Eutectic Solder Joint Creep Failure Application, Conservative Acceleration
AF = (DTs/ DTa)1.9
Application, 1 Cycle/Day;
Tmin = 10 oC = 283 oK, Tmax = 50 oC = 323 oK
Stress Test Design;
Tmin = 40 oC = 233 oK, Tmax = 125 oC = 398 oK
DTs = 165 oK, DTa = 40 oK
AF = (165/ 40)1.9 = 14.8
1 Stress Cycle = 14.8 Applications Cycles
If 1 Stress Cycle takes ~60 minutes (average chamber ramp rate)
1 Stress Cycle Day = 24 x 14.8 = 355.2 Application Day Cycles
Modified CoffinManson Equation – Temp and Temp Gradient
SnPb Solder Joint Creep Failure
AF = (DTs/ DTa)E (Fa/Fs)1/3 e(DTsa/100)
Where;
DTs = Stress Test Thermal Excursion Range oK
DTa = Application Thermal Excursion Range oK
E = Material Dependent Exponent (1.9 – 2.7 SnPb Solders)
Ts(max) = Max Stress Temp oK
Ta(max) = Max Application Temp oK
DTsa = Ts(max) – Ta(max) oK
Fs = Thermal Cycle Frequency of Stress Test
Fa = Thermal Cycle Frequency of Application
AF = Per Cycle Stress Test Acceleration Factor
Alternate Form Modified CoffinManson Equation (Common)
NorrisLandsberg Equation for Solder Joint Creep Failure
AF = (DTs/ DTa)E (Fa/Fs)1/3 e1414(1/Tamax – 1/Tsmax)
Where;
DTs = Stress Test Thermal Excursion Range oK
DTa = Application Thermal Excursion Range oK
E = Material Dependent Exponent (1.9 – 2.7 SnPb Solders)
Tsmax = Max Stress Temp oK
Tamax = Max Application Temp oK
DTsa = Ts(max) – Ta(max) oK
Fs = Thermal Cycle Frequency of Stress Test
Fa = Thermal Cycle Frequency of Application
AF = Per Cycle Stress Test Acceleration Factor
Modified CoffinManson Equation
SnPb Solder Joint Creep Failure
Example
Application;
Tmin = 10 oC = 283 oK, Tmax = 50 oC = 323 oK, DTa = 40 oK
Fa = 1 cycle/day
Stress Test Design;
Tmin = 40 oC = 233 oK, Tmax = 125 oC = 398 oK, DTs = 165 oK
Ts(max) = 398 oK, Ta(max) = 323 oK, DTsa = 75 oK
Fs = 1 cycle/hr = 24 cycle/day
AF = (165/40)1.9 (1/24)1/3 e(75/100) = 10.8
1 Stress Test Cycle = 10.8 Application Cycles
1 Stress Test Day = Fs X AF = 259.2 Application Cycles
(Taking thermal gradient into account is more conservative)
Reliability Growth Methods: HAST
Repeat
Reliability Growth Methods: HASS
Repeat
infant mortality constant failure rate wearout
Time
Reliability Bathtub CurveLife Stress Models and Qualification
More on Component DeratingIntentional limiting of usage stress vs rated capabilityVoltagePower
Physics of Failure: Accumulated Fatigue Damage (AFD) is related to the number of stress cycles N, and mechanical stress, S, using Miner’s rule
Exponent Bcomes from the SN diagram. It is typically between 2 and 20
Example: Solder Joint
Shear
Force
voids
Effective crosssectional
Area: D/2
Effective crosssectional
Area: D
F
Applied stress:
Applied stress:
Let = 10, then
AFD with voids will “age” about
1000x faster than AFD with no voids
Voids in solder joints
=
N
cycles
D
b
T
Failure Mechanism/Material
b
316 Stainless Steel
1.5
4340 Steel
1.8
Solder (97Pb/03Sn) T > 30°C
1.9
Solder (37Pb/63Sn) T < 30°C
1.2
Solder (37Pb/63Sn) T > 30°C
2.7
General Failure Mechanism
b
Solder (37Pb/03Ag & 91Sn/09Zn)
2.4
Ductile Metal Fatigue
1 to 2
Aluminum Wire Bond
3.5
Commonly Used IC Metal Alloys and
Au
Al fracture in wire bonds
4.0
3 to 5
4
Intermetallics
PQFP Delamination / Bond Failure
4.2
Brittle Fracture
6 to 8
ASTM 2024 Aluminum Alloy
4.2
Copper
5.0
Au Wire Bond Heel Crack
5.1
ASTM 6061 Aluminum Alloy
6.7
Alumina Fracture
5.5
Interlayer Dielectric Cracking
4.86.2
Silicon Fracture
5.5
Silicon Fracture (cratering)
7.1
Thin Film Cracking
8.4
Physics of failure: Thermal Fatigue Models
Coefficients for Coffin

Manson Mechanical Fatigue Model
•
The Coffin

Manson model is most often used to model mechanical failures
caused by thermal cycling in mechanical parts or electronics.
(Most electronic
failures are mechanical in nature)
N cycles = number of cycles to failure at reference condition
b = typical value for a given failure mechanism, a = prop constant
•
The values of the coefficient b for various failure mechanisms and materials
(derived or taken from empirical data)
Reference: “EIA Engineering Bulletin: Acceleration Factors”, SSB
1.003, Electronics

Industries Alliance, Government Electronics andInformation
Technology Association
Engineering Department, 1999.
=
N
cycles
D
b
T
Normal operating conditions cycling 15C to 60C (T=45C)
Plan for N Stress (Accelerated) cycles –40 to 125 C (T=165C)
Find Mean life at stress level MTTF=4570 hrs=0.5 yrs
Calculated acceleration factor and MTTF (and B10) @ normal stress:
AF = Nstress / Nuse = (DT/DT)b = (165/45)2.7 = 33.4
MTTF (use)=MTTF(stress)*AF = 4570*33.4 = 152638hrs = 17.4 yrs
 ( )
t / h
F(t) = 1  e
Reliability Distributions are nonNormal, require 2 parameters
beta, b  slope/shape parameter
Intro: Weibull Distribution
ln ln (1 / (1 – F(t))) = b ln(t) – b ln(h)
F(t) = Cumulative fraction of parts that have failed
at time t
Y = b X + a
eta, h – characteristic life or
scale parameter
when t = h
F(t) = 63.2%
Knowing the distribution Function allows to
address the following problem (anticipated future failure):
What is the probability, P , that the failure will occur for the
period of time T if it did not occur yet for the period of time t ? (T>t)
P={F(T)F(t)}/[1F(t)]=
Physical Significance of Weibull Parameters
When Weibull distribution parameters are defined, B10 and MTTF can be computed.
99
MTTF = mean time to failure (nonrepairable)
= h G ( 1 + 1/b )
When b = 1.0, MTTF = h
When b = 0.5, MTTF = 2h
Cumulative Failure (%)
F(t)
MTBF = mean time between failure (repairable)
(MTBSC)
b
Slope =
= total time on all systems / # of failures
10
When there is no suspension data, MTBF = MTTF
B10
100
1
10
Time to Failure (t)
The slope parameter, Beta (b), indicates failure type
b < 1 rate of failure is decreasing infantile (early) failure
b = 1 rate of failure is constant random failure
b > 1 rate of failure is increasing wear out failure
Estimating Reliability from Test Data
The calculations are based on the Binomial Distribution and the following formula:
where:
n
=
sample size
p
=
proportion defective
r
=
number defective
Confidence Level CL =
=
probability of k or fewer failures occurring in a test of n units
Pass/Fail Test Sample Sizes?
Example:
Suppose that 3 failed parts have been observed in the test equivalent to 1 year life, what minimum sample size is needed to be 95% confident that the product is no more than 10% defective?
Inputs in the formula are:
p =0.1(10%), r = 3, CL = 0.95(95%), P(r<k) = 0.05 and calculate n.
The minimum sample size will be 76.
Reliability test should start using just a few parts in order to get preliminary number of failed parts. Using this data a required sample size can then be estimated.
MTTF~=10 years (B10=1 year) results in failure rate 1F=1exp(1/10*10)=0.63,
i.e. 63% of units on average will fail for 10 years
MTTF= 47.5 years (B10=5 years) results in failure rate 1F=1exp(1/47.5*10)=0.19,
i.e. 19% of units on average will fail for 10 years.
System Reliability Target Must be Allocated
Linear Correlation of Input to Output
1.4
1.2
1
0.8
mArms
0.6
Vrms
0.4
Output
0.2
0
0
0.5
1
1.5
Input
Plot or Scatter Plot
Used to Illustrate Correlation or Relationships
Root Cause Failures Example
Used to Illustrate Contributions of Multiple Sources
Excellent when data is abundant
Ambient Temp
Load Res
Line Voltage
Effect:
Temp
Of Amp
For example
Line Frequency
Volume
Input Amplitude
Illustrates Cause & Effect Relationship
Replacement Parts Example