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318-595 Statistics & Reliability
Statistics and Electronic Reliability
318-595 Statistics & Reliability
318-595 Statistics & Reliability
318-595 Statistics & Reliability
Printed Circuit Board Assemblies
Review of Printed Circuit Board Technology
– 3 Basic Types of PCB-Component Assembly Technology
• Thru Hole (TH) using prepackaged devices
• Surface Mount (SMT) using prepackaged devices
• Micro-electronic using bare die and prepackaged devices
– 3 Basic Types of PCB Substrates (fabs)
• Rigid copper-epoxy laminate PCB (single, dual up to ~40 layers)
• Alumina, Alum Nitride or other ceramic materials (up to ~20 layers)
• Flexible Substrate (Polyimide-Copper, up to 8 layers)
– Surface Metalization Finishes
• HASL – Hot Air Solder Leveling (Eutectic SnPb Surfaces, lowest cost)
• ENIG – Electroless Ni – Immersion Au (flatter for wirebonding, BGA, ACF)
• IAg – Immersion Silver (co-deposited with organics to reduce reactivity,
replacement for ENIG)
• Electroplated Finishes – NiAu over Cu, not always possible depending on circuit
318-595 Statistics & Reliability
Reliability of Electronic Circuits
Causes of Electronic Systems Failure
• Failures can generally be divided between intrinsic or extrinsic failures
•Intrinsic failures- Inherent in the component technology
• Electromigration (semiconductors, substrates)
• Contact wear (relays, connectors, etc)
• Contamination effects- e.g. channeling, corrosion, leakage
• CTE mismatch and other Interconnection joint fatigue
•Extrinsic failures- External stress to the components
• ESD or Electrostatic discharge energy
• Electrical overstress (over voltage, overload, overheat)
• Shock (Sudden Mechanical Impact)
• Vibration (Periodic Mechanical G force)
• Humidity or condensable water
• Package Mishandling, Bending, Shear, Tensile
Many “random” and infantile failures of components are due to extrinsic failures
Wearout failures are usually due to intrinsic failures
318-595 Statistics & Reliability
PCB Assembly Failure Mechanisms
Stresses & Major Factors
I.
Thermal Excursion and Cycling
•
Coef of Thermal Expansion (CTE) mismatches
•
Package and Substrate Dimensions (Larger is worse)
•
# of Interconnects on Package (More failure opportunities)
•
Solder joint geometry including cracks, voids and skew
II.
Mechanical Shock and Vibration
•
Mass of Components and Overall Assembly
•
Height of Component Center of Mass (COG)
•
Thickness, Rigidity and Support Pts of PCB
•
Solder joint geometry including cracks, voids and skew
318-595 Statistics & Reliability
Printed Circuit Board Assemblies
CTE Mismatches in PCB Assemblies
Si Die CTE = 2.8e-6/C
Thin Epoxy Solder Mask
Copper
Gold CTE = 14.2e-6/C
5 – 15 μ in.
NiAu Pad
Nickel CTE = 13.4e-6/C
> ~100 μ in.
FR4 Laminate
CTE = ~20e-6/C
Copper CTE = 16.5e-6/C
> ~1.2 mil
SnPb Eutectic Solder Joint CTE = ~25e-6/C
318-595 Statistics & Reliability
PCB Assembly Failure Mechanisms
Stresses & Major Factors - continued
III.
Electrochemical
•
Usage environment incl ambient temp & humidity
•
Usage environment incl corrosive materials, salts, etc
•
Maximum electrical field (induced by spacing, voltage on
PCB)
•
Ionic Cleanliness of PCB over/under solder mask and other
coatings
•
Cations: Including Lithium, Sodium, Ammonium, Potassium, Magnesium and Calcium. Many companies limit each individual cation
contribution to be less than 0.2ug/cm2 and the combined total of all cations to be less than 0.50ug/cm2.
•
Anions: Most Destructive Includes Fluoride, Chloride, Nitride, Bromide, Sulfate, and Phosphates. Many companies limit each individual
anion contribution to be less than 0.1ug/cm2 and the combined total of all anions to be less than 0.25ug/cm2.
•
Weak Organic Acids: May include Acetate, Formate, Succinate, Glutamate, Malate, Methane Sulfonate (MSA), Phthalate, Phosphate,
Citrate and Adipic Acids. Many companies limit the combined total of all weak organic acids to be less than or equal to ~0.75ug/cm2
•
Ion cleanliness is tested per IPC TM-650 2.3.28 using Ion Chromatography for high reli assemblies. IPC-6012/15 mandate a total ionic
cleanliness of less than 1.56ug/cm2 = 10ug/in2.
318-595 Statistics & Reliability
Ionic Test Methods for PCBs
Resistivity of Solvent Extract (ROSE) Test Method IPC-TM-650 2.3.25
The 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 IPC-TM-650 2.3.28
This 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.
318-595 Statistics & Reliability
Specifying Warranty: Must Understand Reliability of Product
•
Life of Product should be less than wear out failure mode period
•
Bathtub Reli Curve:
(Failure Rate vs Time) Area
Infantile
Period
~ Constant Failure Rate
Minimize or
Precipitate using
ESS in factory
Warranty Period Using ESS
Warranty Period
(1, 5 yrs, etc)
under curve = total failures
318-595 Statistics & Reliability
Basic Statistics and Reliability Statistics
25
22
20
18
15
12
10
8
5
2
0
1.238
1.240
1.242
1.244
318-595 Statistics & Reliability
Basic Statistics Review
Example: The following data represents the amount of time it takes 7 people to do a 355 exam problem.
X i= 2, 6, 5, 2 ,10, 8, 7 in min.
n = 7
where Xi = index notation for each individual.
where n = 7 people
n
Calculate the mean(average):
n = 7 people
S Xi
m= X =
Step 1
(Xi - X)
2-5.7= -3.7
6-5.7= .3
5-5.7 = -.7
2-5.7 = -3.7
10-5.7 = 4.3
8-5.7 = 2.3
2
7-5.7 = 1.3
S (Xi - X) =
Xi = Sum of the individual times
where X and m = Average or Mean
n
Equation
Mean:X = (2+6+5+2+10+8+7)/7 = 5.7 minutes
n
Calculate the standard deviation:
where S
i=1
s = s=
Step 22
Step 4
(Xi - X)
53.43
13.69 Square each one
s=s=
7-1
.09
.49 Then Add All
13.69
Standard Deviation:
18.49
s = s = 2.98 minutes
5.29
1.69
53.43 Step 3
S ( Xi - X )
i =1
n-1
2
where s = s = Standard Deviation
Sum or Variance
Equation
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
Std Deviation is a measure of the inherent spread in the data
318-595 Statistics & Reliability
Bar Chart or Histogram
25
22
20
18
15
12
10
8
5
2
0
1.238
1.240
1.242
1.244
Provides a visual display of data distribution
Shape of Distribution May be Key to Issues
1.
2.
3.
4.
5.
Normal (Bell Shaped)
Uniform (Flat)
Bimodal (Mix of 2 Normal Distributions)
Skewed left or right
Total number of bins is flexible but usually no more than 10
By using an infinite number of bins, resultant curve is a distribution
Use T-Test to Compare Means, F-Test to Compare Variances
318-595 Statistics & Reliability
• Normal (Gaussian) Distributions
318-595 Statistics & Reliability
Target
Specification Limit
3s
Histogram vs
Spec Limits
Area under curve
Is probability of
failure
1s
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
m
Z = 3s
PPM = Part per Million Defects
Much Less
Chance of
Failure
1s
Normal
Distribution
66807ppm
Z = 6s
3.4ppm*
* Assumes Z is 4.5 long term
318-595 Statistics & Reliability
Area under Distribution Curve Yields Probabilities
34%
34%
2%
2%
14%
-3s
-2s
-1s
14%
m
+1s
+2s
Characterized by Two Parameters
m and s2
Normal Distribution = N( m,s2 )
+3s
318-595 Statistics & Reliability
Life Cycle of a Component
Standard Normal Distribution
Apply
Original Distribution
m-s m m+s
Transformation
x-m
Z=
s
X
Standard Normal
Distribution
Area under
Curve =1
-1
0
1
Examples:
Z = +1.0 is one Standard Deviations above the mean
Z= -0.5 is 0.5 Standard Deviations below the mean
Z
318-595 Statistics & Reliability
1 Sided Normal Distribution, Probability Table
Z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
5.00e-001
4.60e-001
4.21e-001
3.82e-001
3.45e-001
3.09e-001
2.74e-001
2.42e-001
2.12e-001
1.84e-001
4.96e-001
4.56e-001
4.17e-001
3.78e-001
3.41e-001
3.05e-001
2.71e-001
2.39e-001
2.09e-001
1.81e-001
4.92e-001
4.52e-001
4.13e-001
3.74e-001
3.37e-001
3.02e-001
2.68e-001
2.36e-001
2.06e-001
1.79e-001
4.88e-001
4.48e-001
4.09e-001
3.71e-001
3.34e-001
2.98e-001
2.64e-001
2.33e-001
2.03e-001
1.76e-001
4.84e-001
4.44e-001
4.05e-001
3.67e-001
3.30e-001
2.95e-001
2.61e-001
2.30e-001
2.00e-001
1.74e-001
4.80e-001
4.40e-001
4.01e-001
3.63e-001
3.26e-001
2.91e-001
2.58e-001
2.27e-001
1.98e-001
1.71e-001
4.76e-001
4.36e-001
3.97e-001
3.59e-001
3.23e-001
2.88e-001
2.55e-001
2.24e-001
1.95e-001
1.69e-001
4.72e-001
4.33e-001
3.94e-001
3.56e-001
3.19e-001
2.84e-001
2.51e-001
2.21e-001
1.92e-001
1.66e-001
4.68e-001
4.29e-001
3.90e-001
3.52e-001
3.16e-001
2.81e-001
2.48e-001
2.18e-001
1.89e-001
1.64e-001
4.64e-001
4.25e-001
3.86e-001
3.48e-001
3.12e-001
2.78e-001
2.45e-001
2.15e-001
1.87e-001
1.61e-001
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
1.59e-001
1.36e-001
1.15e-001
9.68e-002
8.08e-002
6.68e-002
5.48e-002
4.46e-002
3.59e-002
2.87e-002
1.56e-001
1.33e-001
1.13e-001
9.51e-002
7.93e-002
6.55e-002
5.37e-002
4.36e-002
3.51e-002
2.81e-002
1.54e-001
1.31e-001
1.11e-001
9.34e-002
7.78e-002
6.43e-002
5.26e-002
4.27e-002
3.44e-002
2.74e-002
1.52e-001
1.29e-001
1.09e-001
9.18e-002
7.64e-002
6.30e-002
5.16e-002
4.18e-002
3.36e-002
2.68e-002
1.49e-001
1.27e-001
1.07e-001
9.01e-002
7.49e-002
6.18e-002
5.05e-002
4.09e-002
3.29e-002
2.62e-002
1.47e-001
1.25e-001
1.06e-001
8.85e-002
7.35e-002
6.06e-002
4.95e-002
4.01e-002
3.22e-002
2.56e-002
1.45e-001
1.23e-001
1.04e-001
8.69e-002
7.21e-002
5.94e-002
4.85e-002
3.92e-002
3.14e-002
2.50e-002
1.42e-001
1.21e-001
1.02e-001
8.53e-002
7.08e-002
5.82e-002
4.75e-002
3.84e-002
3.07e-002
2.44e-002
1.40e-001
1.19e-001
1.00e-001
8.38e-002
6.94e-002
5.71e-002
4.65e-002
3.75e-002
3.01e-002
2.39e-002
1.38e-001
1.17e-001
9.85e-002
8.23e-002
6.81e-002
5.59e-002
4.55e-002
3.67e-002
2.94e-002
2.33e-002
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
2.28e-002
1.79e-002
1.39e-002
1.07e-002
8.20e-003
6.21e-003
4.66e-003
3.47e-003
2.56e-003
1.87e-003
2.22e-002
1.74e-002
1.36e-002
1.04e-002
7.98e-003
6.04e-003
4.53e-003
3.36e-003
2.48e-003
1.81e-003
2.17e-002
1.70e-002
1.32e-002
1.02e-002
7.76e-003
5.87e-003
4.40e-003
3.26e-003
2.40e-003
1.75e-003
2.12e-002
1.66e-002
1.29e-002
9.90e-003
7.55e-003
5.70e-003
4.27e-003
3.17e-003
2.33e-003
1.69e-003
2.07e-002
1.62e-002
1.25e-002
9.64e-003
7.34e-003
5.54e-003
4.15e-003
3.07e-003
2.26e-003
1.64e-003
2.02e-002
1.58e-002
1.22e-002
9.39e-003
7.14e-003
5.39e-003
4.02e-003
2.98e-003
2.19e-003
1.59e-003
1.97e-002
1.54e-002
1.19e-002
9.14e-003
6.95e-003
5.23e-003
3.91e-003
2.89e-003
2.12e-003
1.54e-003
1.92e-002
1.50e-002
1.16e-002
8.89e-003
6.76e-003
5.08e-003
3.79e-003
2.80e-003
2.05e-003
1.49e-003
1.88e-002
1.46e-002
1.13e-002
8.66e-003
6.57e-003
4.94e-003
3.68e-003
2.72e-003
1.99e-003
1.44e-003
1.83e-002
1.43e-002
1.10e-002
8.42e-003
6.39e-003
4.80e-003
3.57e-003
2.64e-003
1.93e-003
1.39e-003
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80
3.90
1.35e-003
9.68e-004
6.87e-004
4.83e-004
3.37e-004
2.33e-004
1.59e-004
1.08e-004
7.23e-005
4.81e-005
1.31e-003
9.35e-004
6.64e-004
4.66e-004
3.25e-004
2.24e-004
1.53e-004
1.04e-004
6.95e-005
4.61e-005
1.26e-003
9.04e-004
6.41e-004
4.50e-004
3.13e-004
2.16e-004
1.47e-004
9.96e-005
6.67e-005
4.43e-005
1.22e-003
8.74e-004
6.19e-004
4.34e-004
3.02e-004
2.08e-004
1.42e-004
9.57e-005
6.41e-005
4.25e-005
1.18e-003
8.45e-004
5.98e-004
4.19e-004
2.91e-004
2.00e-004
1.36e-004
9.20e-005
6.15e-005
4.07e-005
1.14e-003
8.16e-004
5.77e-004
4.04e-004
2.80e-004
1.93e-004
1.31e-004
8.84e-005
5.91e-005
3.91e-005
1.11e-003
7.89e-004
5.57e-004
3.90e-004
2.70e-004
1.85e-004
1.26e-004
8.50e-005
5.67e-005
3.75e-005
1.07e-003
7.62e-004
5.38e-004
3.76e-004
2.60e-004
1.78e-004
1.21e-004
8.16e-005
5.44e-005
3.59e-005
1.04e-003
7.36e-004
5.19e-004
3.62e-004
2.51e-004
1.72e-004
1.17e-004
7.84e-005
5.22e-005
3.45e-005
1.00e-003
7.11e-004
5.01e-004
3.49e-004
2.42e-004
1.65e-004
1.12e-004
7.53e-005
5.01e-005
3.30e-005
4.00
4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
3.17e-005
2.07e-005
1.33e-005
8.54e-006
5.41e-006
3.40e-006
2.11e-006
1.30e-006
7.93e-007
4.79e-007
3.04e-005
1.98e-005
1.28e-005
8.16e-006
5.17e-006
3.24e-006
2.01e-006
1.24e-006
7.55e-007
4.55e-007
2.91e-005
1.89e-005
1.22e-005
7.80e-006
4.94e-006
3.09e-006
1.92e-006
1.18e-006
7.18e-007
4.33e-007
2.79e-005
1.81e-005
1.17e-005
7.46e-006
4.71e-006
2.95e-006
1.83e-006
1.12e-006
6.83e-007
4.11e-007
2.67e-005
1.74e-005
1.12e-005
7.12e-006
4.50e-006
2.81e-006
1.74e-006
1.07e-006
6.49e-007
3.91e-007
2.56e-005
1.66e-005
1.07e-005
6.81e-006
4.29e-006
2.68e-006
1.66e-006
1.02e-006
6.17e-007
3.71e-007
2.45e-005
1.59e-005
1.02e-005
6.50e-006
4.10e-006
2.56e-006
1.58e-006
9.68e-007
5.87e-007
3.52e-007
2.35e-005
1.52e-005
9.77e-006
6.21e-006
3.91e-006
2.44e-006
1.51e-006
9.21e-007
5.58e-007
3.35e-007
2.25e-005
1.46e-005
9.34e-006
5.93e-006
3.73e-006
2.32e-006
1.43e-006
8.76e-007
5.30e-007
3.18e-007
2.16e-005
1.39e-005
8.93e-006
5.67e-006
3.56e-006
2.22e-006
1.37e-006
8.34e-007
5.04e-007
3.02e-007
Z
318-595 Statistics & Reliability
Normal Distribution (cont.)
Z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
5.00
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
2.87e-007
1.70e-007
9.96e-008
5.79e-008
3.33e-008
1.90e-008
1.07e-008
5.99e-009
3.32e-009
1.82e-009
2.72e-007
1.61e-007
9.44e-008
5.48e-008
3.15e-008
1.79e-008
1.01e-008
5.65e-009
3.12e-009
1.71e-009
2.58e-007
1.53e-007
8.95e-008
5.19e-008
2.98e-008
1.69e-008
9.55e-009
5.33e-009
2.94e-009
1.61e-009
2.45e-007
1.45e-007
8.48e-008
4.91e-008
2.82e-008
1.60e-008
9.01e-009
5.02e-009
2.77e-009
1.51e-009
2.33e-007
1.37e-007
8.03e-008
4.65e-008
2.66e-008
1.51e-008
8.50e-009
4.73e-009
2.61e-009
1.43e-009
2.21e-007
1.30e-007
7.60e-008
4.40e-008
2.52e-008
1.43e-008
8.02e-009
4.46e-009
2.46e-009
1.34e-009
2.10e-007
1.23e-007
7.20e-008
4.16e-008
2.38e-008
1.35e-008
7.57e-009
4.21e-009
2.31e-009
1.26e-009
1.99e-007
1.17e-007
6.82e-008
3.94e-008
2.25e-008
1.27e-008
7.14e-009
3.96e-009
2.18e-009
1.19e-009
1.89e-007
1.11e-007
6.46e-008
3.72e-008
2.13e-008
1.20e-008
6.73e-009
3.74e-009
2.05e-009
1.12e-009
1.79e-007
1.05e-007
6.12e-008
3.52e-008
2.01e-008
1.14e-008
6.35e-009
3.52e-009
1.93e-009
1.05e-009
6.00
6.10
6.20
6.30
6.40
6.50
6.60
6.70
6.80
6.90
9.87e-010
5.30e-010
2.82e-010
1.49e-010
7.77e-011
4.02e-011
2.06e-011
1.04e-011
5.23e-012
2.60e-012
9.28e-010
4.98e-010
2.65e-010
1.40e-010
7.28e-011
3.76e-011
1.92e-011
9.73e-012
4.88e-012
2.42e-012
8.72e-010
4.68e-010
2.49e-010
1.31e-010
6.81e-011
3.52e-011
1.80e-011
9.09e-012
4.55e-012
2.26e-012
8.20e-010
4.39e-010
2.33e-010
1.23e-010
6.38e-011
3.29e-011
1.68e-011
8.48e-012
4.25e-012
2.10e-012
7.71e-010
4.13e-010
2.19e-010
1.15e-010
5.97e-011
3.08e-011
1.57e-011
7.92e-012
3.96e-012
1.96e-012
7.24e-010
3.87e-010
2.05e-010
1.08e-010
5.59e-011
2.88e-011
1.47e-011
7.39e-012
3.69e-012
1.83e-012
6.81e-010
3.64e-010
1.92e-010
1.01e-010
5.24e-011
2.69e-011
1.37e-011
6.90e-012
3.44e-012
1.70e-012
6.40e-010
3.41e-010
1.81e-010
9.45e-011
4.90e-011
2.52e-011
1.28e-011
6.44e-012
3.21e-012
1.58e-012
6.01e-010
3.21e-010
1.69e-010
8.85e-011
4.59e-011
2.35e-011
1.19e-011
6.01e-012
2.99e-012
1.48e-012
5.65e-010
3.01e-010
1.59e-010
8.29e-011
4.29e-011
2.20e-011
1.12e-011
5.61e-012
2.79e-012
1.37e-012
7.00
7.10
7.20
7.30
7.40
7.50
7.60
7.70
7.80
7.90
1.28e-012
6.24e-013
3.01e-013
1.44e-013
6.81e-014
3.19e-014
1.48e-014
6.80e-015
3.10e-015
1.39e-015
1.19e-012
5.80e-013
2.80e-013
1.34e-013
6.31e-014
2.96e-014
1.37e-014
6.29e-015
2.86e-015
1.29e-015
1.11e-012
5.40e-013
2.60e-013
1.24e-013
5.86e-014
2.74e-014
1.27e-014
5.82e-015
2.64e-015
1.19e-015
1.03e-012
5.02e-013
2.41e-013
1.15e-013
5.43e-014
2.54e-014
1.17e-014
5.38e-015
2.44e-015
1.10e-015
9.61e-013
4.67e-013
2.24e-013
1.07e-013
5.03e-014
2.35e-014
1.09e-014
4.97e-015
2.25e-015
1.01e-015
8.95e-013
4.34e-013
2.08e-013
9.91e-014
4.67e-014
2.18e-014
1.00e-014
4.59e-015
2.08e-015
9.33e-016
8.33e-013
4.03e-013
1.94e-013
9.20e-014
4.33e-014
2.02e-014
9.30e-015
4.25e-015
1.92e-015
8.60e-016
7.75e-013
3.75e-013
1.80e-013
8.53e-014
4.01e-014
1.87e-014
8.60e-015
3.92e-015
1.77e-015
7.93e-016
7.21e-013
3.49e-013
1.67e-013
7.91e-014
3.72e-014
1.73e-014
7.95e-015
3.63e-015
1.64e-015
7.32e-016
6.71e-013
3.24e-013
1.55e-013
7.34e-014
3.44e-014
1.60e-014
7.36e-015
3.35e-015
1.51e-015
6.75e-016
8.00
8.10
8.20
8.30
8.40
8.50
8.60
8.70
8.80
8.90
6.22e-016
2.75e-016
1.20e-016
5.21e-017
2.23e-017
9.48e-018
3.99e-018
1.66e-018
6.84e-019
2.79e-019
5.74e-016
2.53e-016
1.11e-016
4.79e-017
2.05e-017
8.70e-018
3.65e-018
1.52e-018
6.26e-019
2.55e-019
5.29e-016
2.33e-016
1.02e-016
4.40e-017
1.88e-017
7.98e-018
3.35e-018
1.39e-018
5.72e-019
2.33e-019
4.87e-016
2.15e-016
9.36e-017
4.04e-017
1.73e-017
7.32e-018
3.07e-018
1.27e-018
5.23e-019
2.13e-019
4.49e-016
1.98e-016
8.61e-017
3.71e-017
1.59e-017
6.71e-018
2.81e-018
1.17e-018
4.79e-019
1.95e-019
4.14e-016
1.82e-016
7.92e-017
3.41e-017
1.46e-017
6.15e-018
2.57e-018
1.07e-018
4.38e-019
1.78e-019
3.81e-016
1.68e-016
7.28e-017
3.14e-017
1.34e-017
5.64e-018
2.36e-018
9.76e-019
4.00e-019
1.62e-019
3.51e-016
1.54e-016
6.70e-017
2.88e-017
1.23e-017
5.17e-018
2.16e-018
8.93e-019
3.66e-019
1.48e-019
3.24e-016
1.42e-016
6.16e-017
2.65e-017
1.13e-017
4.74e-018
1.98e-018
8.17e-019
3.34e-019
1.35e-019
2.98e-016
1.31e-016
5.66e-017
2.43e-017
1.03e-017
4.35e-018
1.81e-018
7.48e-019
3.06e-019
1.24e-019
9.00
9.10
9.20
9.30
9.40
9.50
9.60
9.70
9.80
9.90
1.13e-019
4.52e-020
1.79e-020
7.02e-021
2.73e-021
1.05e-021
4.00e-022
1.51e-022
5.63e-023
2.08e-023
1.03e-019
4.12e-020
1.63e-020
6.39e-021
2.48e-021
9.53e-022
3.63e-022
1.37e-022
5.10e-023
1.88e-023
9.40e-020
3.76e-020
1.49e-020
5.82e-021
2.26e-021
8.66e-022
3.29e-022
1.24e-022
4.62e-023
1.70e-023
8.58e-020
3.42e-020
1.35e-020
5.29e-021
2.05e-021
7.86e-022
2.99e-022
1.12e-022
4.18e-023
1.54e-023
7.83e-020
3.12e-020
1.23e-020
4.82e-021
1.86e-021
7.14e-022
2.71e-022
1.02e-022
3.79e-023
1.39e-023
7.15e-020
2.85e-020
1.12e-020
4.38e-021
1.69e-021
6.48e-022
2.46e-022
9.22e-023
3.43e-023
1.26e-023
6.52e-020
2.59e-020
1.02e-020
3.99e-021
1.54e-021
5.89e-022
2.23e-022
8.36e-023
3.10e-023
1.14e-023
5.95e-020
2.37e-020
9.31e-021
3.63e-021
1.40e-021
5.35e-022
2.02e-022
7.57e-023
2.81e-023
1.03e-023
5.43e-020
2.16e-020
8.47e-021
3.30e-021
1.27e-021
4.85e-022
1.83e-022
6.86e-023
2.54e-023
9.32e-024
4.95e-020
1.96e-020
7.71e-021
3.00e-021
1.16e-021
4.40e-022
1.66e-022
6.21e-023
2.30e-023
8.43e-024
10.00
7.62e-024
6.89e-024
6.23e-024
5.63e-024
5.08e-024
4.59e-024
4.15e-024
3.75e-024
3.39e-024
3.06e-024
318-595 Statistics & Reliability
(with ± 1.5 s shift)
PPM Defects
1,000,000
Tax Advice
(phone-in)
(140,000 PPM)
100,000
Restaurant Bills
Doctor Prescription Writing
10,000
Average
Company
1,000
•
Restaurant Checks
Airline Baggage Handling
100
AircraftCarrier Landings
10
Best-in-Class
1
2
3
Z
4
5
6
7
Domestic Airline Flight
Fatality Rate
Examples of Fault/Failure Rates on
The Sigma Scale
(0.43 PPM)
318-595 Statistics & Reliability
Over time, a “typical” product process may
shift or drift by ~ 1.5s
Short Term Capability
Snapshots of the Product
. . . also called “short-term capability”
. . . reflects ‘within group’ variation
Shift and Drift
Time 1
Time 2
Time 3
Time 4
Actual Sustained Capability
of the Process
. . . also called “long-term capability”
. . . reflects ‘total process’ variation
LSL
T
Two Challenges:
USL
Center the Process and Eliminate Variation!
318-595 Statistics & Reliability
Statistics Example: IPC Workmanship Classes: Solder Volume, Shape, Placement Control
3.
High Reliability Electronic Products: Includes the equipment for commercial and military products where
continued performance or performance on demand is critical. Equipment downtime cannot be tolerated, and
functionality is required for such applications as life support or missile systems. Printed board assemblies in
this class are suitable for applications where high levels of assurance are required and service is essential.
•
2.
Dedicated Service Electronic Products: Includes communications equipment, sophisticated business
machines, instruments and military equipment where high performance and extended life is required, and for
which uninterrupted service is desired but is not critical. Typically the end-use environment would NOT cause
failures.
•
1.
Requirement for Aero-Space, Certain Military, Certain Medical
Requirement for High Eng Telecom, COTS Military, Medical
General Electronic Products: Includes consumer products, some computer and peripherals, as well as
general military hardware suitable for applications where cosmetic imperfections are not important and the
major requirement is function of the completed printed board assembly.
100 %
100 %
75 %
75 %
50 %
50 %
25 %
25 %
0%
0%
Min PTH Vertical Fill: Class 2 = 75%
Ref: IPC-A-610, IPC-JSTD-001
IPC-7095
BGA Std
Class 1
Class 2
Class 3
Max Void Size
60% Dia
36% Area
45% Dia
20.3% Area
30% Dia
9% Area
Max Void
Size at
Interfaces
50% Dia
25% Area
35% Dia
12.3% Area
20% Dia
4% Area
Class 3 = 100%
318-595 Statistics & Reliability
BGA Void Size and Locations, Uniform Void Position Distribution, Varying Diameter
Sampling_Grid
Position
Model
Solder_Joint_Radius
Void_Distance
Void_Radius
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)
S
318-595 Statistics & Reliability
CLASS 1 - GOOD
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 %
318-595 Statistics & Reliability
Class vs Shell Size Relative Probabilities
~ 2x more likely to exceed D/10 threshold with Class 2 vs Class 3
S = Shell
Depth
318-595 Statistics & Reliability
• Exponential Distributions
= Reliability
= Time
318-595 Statistics & Reliability
Definitions
l General Failure Rate Variable:
Recall the Bathtub Curve- Failure Rate (l) vs. Time behavior
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) = e-lt, Note: l is in failures/time, and t is time
Note: At T=0, R(0)=1.0 (100%)
l FIT = FITs = Failures per 109 hours
MTBF (years) = 1x109 / (l FIT * 8766 hours /year )
l MTBF = 1/MTBF = 1/Mean time between failure in hours
R(t) = e-lt, Note: lMTBF in hr-1 and t in hr
318-595 Statistics & Reliability
Definitions
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) = e-lt, Note: l is 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) = 1-e-lt, Note: l is in failures/time, and t is time
Note: At T=0, F(0)=0.0 (0%)
318-595 Statistics & Reliability
Weibull or 2 Parameter Distributions
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,”;
b
R(t) = e-(t/ h) , Note: h is the dimensionless scale parameter (stretches)
b is the shape or slope parameter (exponent)
Note: At T=0, R(0)=1.0 (100%)
Relationship of Weibull parameters to Failure Rate
l = (b/h)(t/h)b-1
b
R(t) = e-(t/ h)
b
F(t) = 1-e-(t/ h)
318-595 Statistics & Reliability
Typical Reliability Plot using Weibull Dist
Generated by: ReliaSoft's W eibull++ 5.0 - www.W eibull.com - 888-886-0410
Probability Plot
l = (b/h)(t/h)b-1
F(t) =
99.00
b
1-e-(t/ h)
Weibull
Supplier 1
90.00
P=2, A=RRX-S
F=10 | S=0
Supplier 2
P=2, A=RRX-S
F=10 | S=0
CB/FM: 90.00%
2 Sided-B
C-Ty pe 2
Unreliability, F(t)
50.00
10.00
5.00
F(t) = (1 – R(t))100%
Douglas C. Kemp
GE Appliances
2/22/00
1:31:22 PM
1.00
1.00
10.00
Time to Failure(s)
100.00
1000.00
Time, (t)
10000.00 100000.00
b11, h113,  
b2, h2331,  3
At some time, t, 100% of the population will fail
318-595 Statistics & Reliability
Typical Reliability Plot assuming Weibull Dist
Generated by: ReliaSoft's W eibull++ 5.0 - www.W eibull.com - 888-886-0410
Probability Plot
l = (b/h)(t/h)b-1
99.00
P=2, A=RRX-S
F=10 | S=0
Supplier 2
b
R(t) = e-(t/ h)
b
F(t) = 1-e-(t/ h)
P=2, A=RRX-S
F=10 | S=0
CB/FM: 90.00%
2 Sided-B
C-Ty pe 2
Unreliability, F(t)
50.00
Time to failure plot
using Weibull tool
Decreasing
Failure Rates
b<1
Weibull
Supplier 1
90.00
Increasing
Failure Rates
b>1
10.00
5.00
Douglas C. Kemp
GE Appliances
2/22/00
1:31:22 PM
1.00
1.00
10.00
100.00
1000.00
Time, (t)
10000.00 100000.00
b11, h113,  
b2, h2331,  3
Failure Rate, l
The Bathtub Curve
Constant
Failure Rates
b=1
Weibull slope indicates where
the product may be on the
bathtub curve.
Exponential Distribution
Early
Life
Useful Life
Time
Wear out
318-595 Statistics & Reliability
Reliability Prediction: Assume Constant Failure Rate
b = 1.0
• Basic Series Reli Method of an Electronic System:
Component 1
Component 2
Component i
Component N
l1
l2
li
lN
• Each component has an associated reliability l
• The System Reli lss is the sum of all the component l
lss = S li
• Reli l is expressed in “FITs” failure units
x FIT = x Failures/109 hours
Note: 109 hours = 1 Billion Hours
318-595 Statistics & Reliability
Example: MTBF not so good to use for Reliability Specification
• An electronics assembly product has an MTBF of 20000 hours; constant failure rate
• What is the probability that a given unit will work continuously for one year?
• For this problem, we have the following facts;
• Reliability R(t) = e-lt
• l = 1/MTBF = 1/20000 hr
• l = 0.00005 hr-1 (Failure rate)
• t = 8766 hours (1 year)
318-595 Statistics & Reliability
Example: MTBF not so good to use for Reliability Specification
• An electronics assembly product has an MTBF of 20000 hours; constant failure rate
• What is the probability that a given unit will work continuously for one year?
• Reliability R(t) = e-lt
• l = 1/MTBF = 1/20000 hr
• l = 0.00005 hr-1 (Failure rate)
• t = 8766 hours (1 year)
• R(1yr) =e-(8766/20,000) = 0.65 = 65%  F(1yr) = 35% of population has failed !
In other words, the Mean Time Between failures is 20,000 hours or about 2.3 years
But … 35% of the units would likely fail in the first year of operation.
Remember, after 1 MTBF period R(t) = 1/e = 0.368  63.2% of population will fail!
318-595 Statistics & Reliability
Intro to Reliability Evaluation
• Basic Series Reli Method of an Electronic System:
Component 1
Component 2
Component i
Component N
R1
R2
Ri
RN
• Each component also has an associated reliability R
• The System R is the product of all the component R
R = P Ri
• Recall, Reli R is a probability (0 to 1) expressed in percent
318-595 Statistics & Reliability
Reliability R Flowdown Example
Drive System,
needs R= 0.9 at
10 years
Power supply
R = 0.94
Control Card
R = 0.99
System Level
Subsystem Level
Motor
R = 0.97
Component Level
Part
Part
Part
R=0.9999
Part
R=0.9999
R=0.9999
R=0.999
Part
Part
Part
R=0.9999
R=0.9999
R=0.999
318-595 Statistics & Reliability
Reliability Requirements Flowdown- Example
•
•
•
Customer’s need: Meet R=90%@ 10 years
Partition requirements to subsystems
– Based on engineering analysis, experience, vendor
data, parts count, etc.
Allocation:
Rsystem = Rpower * Rcontroller * Rmotor
Rsystem = 0.94 * 0.99 * 0.97 = 0.90
Each of the 3 subsystems should in turn be allocated to
components
318-595 Statistics & Reliability
More Reason to use R(t) and not MTBF Example
• An electronics product team has a goal of warranty cost which requires that a
Minimum reliability after 1 year be 99% or higher, R(1yr) >= 0.99. Assume Constant
Failure Rates.
• What MTBF should the team work towards to meet the goal?
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.
318-595 Statistics & Reliability
Some Typical Stresses
• Environmental: Temp, Humid, Pressure, Wind, Sun, Rain
• Mechanical: Shock, Vibration, Rotation, Abrasion
• Electrical: Power Cycle, Voltage Tolerance, Load, Noise
• ElectroMagnetic: ESD, E-Field, B-Field, Power Loss
• Radiation: Xray (non-ionizing), Gamma Ray (ionizing)
• Biological: Mold, Algae, Bacteria, Dust
• Chemical: Alchohol, Ph, TSP, Ionic
318-595 Statistics & Reliability
Common Circuit Bd Temperature-Induced Failures
Failure Category
High temperature
degradation
Failure Mode
Root Cause
Environmental
Conditions
Susceptible Parts and Materials
Strength/insulation
degradation
degradation
Temperature +
Time
Plastic materials, resins
Heat disintegration
Chemical change
Temperature
Plastic materials, resins
Distortion
Softening, melting,
evaporation, sublimation
Temperature
Metals, plastics materials, thermal fuse
Oxide film formation
High temperature
oxidation
Temperature +
Time
Contact material
Broken wire
Thermal diffusion
Temperature +
Time
Metal plating involving different
metals, and contact areas
Creep
Fatigue, damage
Metal/Plastic under
mechanical stress
Temperature +
Stress + Time
Springs, structural parts
Migration
Disconnection, broken
wire
Electro-migration
Temperature +
Current
W, Cu, Al (especially Al wiring on IC)
Low temperature
brittleness
Damage
Chemical property of
metal
Low temperature
Body-centered cubic crystalline (Cu,
Mo, W), closed-packed cubic
crystalline (Zn, Ti, Mg) & alloys
Flux loose
Noise, imperfect
contact
Flux steam adheres to
cold metal surface
Low temperature
Parts attached to printed board (e.g.
switches, connectors)
Thermal Cycling
Change in conductor
resistance
PCB through holes
degradation; solder
cracking
Thermal cycling
Printed circuit board w/ solder
318-595 Statistics & Reliability
Intro to Reliability Estimation
• Each l may be impacted by other factors or stresses, p:
• Some commonly used factors




pT = Temperature Stress Factor
pV = Electrical Stress Factor
pE = Environmental Factor
pQ = Quality Factor
• Overall Component l = lB * pT * pV * pE * pQ
Where lB = Base Failure Rate for Component
318-595 Statistics & Reliability
Reliability Prediction Methods/Standards
• Bellcore (TR-TSY-000332):
– Developed by Bell Communications Research for general use in
electronics industry although geared to telecom.
– Highest Stress Factor is Electrical Stress
– Data based upon field results, lab testing, analysis, device mfg data
and US Military Std 217
– Stress Factors include environment, quality, electrical, thermal
• US Military Handbook 217F:
– Developed by the US Department of Defense as well as other
agencies for use by electronic manufacturers supplying to the military
– Describes both a “parts count” method as well as a “parts stress”
method
– Data is based upon lab testing including highly accelerated life testing
(HALT) or highly accelerated stress testing (HAST)
– Stress factors include environment and quality
318-595 Statistics & Reliability
318-595 Statistics & Reliability
Reliability Prediction Methods/Standards
• HRD4 (Hdbk of Reliability Data for Comp, Issue 4):
– Developed by the British Telecom Materials and Components Center
for use by designers and manufacturers of telecom equipment
– Stress factors include thermal as well as environment, quality with
quality being dominant
– Standard describes generic failure rates based upon a 60% confidence
interval around data collected via telecom equipment field
performance in the UK
• CNET:
– Developed by the French National Center of Telecommunications
– Similar to HRD4, stress factors include thermal as well as
environment and dominant quality
– Data is based upon field experience of French commercial and
military telecom equipment
318-595 Statistics & Reliability
Reliability Prediction Methods/Standards
• Siemens AG (SN29500):
– Developed by Siemens for internal uniform reliability predictions
– Stress factors include thermal and electrical however thermal
dominates
– Standard describes failures rates based upon applications data, lab
testing as well as US Mil Std 217
– Components are classified into technology groups each with tuned
reliability model
318-595 Statistics & Reliability
Reliability Prediction
• Basic Series Reli Method of an Electronic System:
Component 1
Component 2
Component i
Component N
l1
l2
li
lN
• Above Reliability Prediction Model is flawed because;
• Components may not have constant reliability rates l
lss = S li
• Component applications, stresses, etc may not be well
matched by the method used to model reliability
• Not all component failures may lead to a system failure
• Example: A bypass capacitor fails as an open circuit
318-595 Statistics & Reliability
595 Standard Failure Rates in FIT (Data is not accurate in all cases)
Component Type
Method A - l
Method B - l
Method C - l
Method D - l
Method E - l
BJT/FET
5.0
3.8
3.2
7.6
4.0
Switch
5.0
44.0
30.0
1.0
20.0
Metal Film Res
0.7
2.5
0.05
0.05
0.2
18.2
2.7
1.0
1.1
2.6
Varistor, tc Res
6.0
1.0
10.0
1.0
10.0
Electrolytic Cap
210
22.0
120
16.0
120
Polyester Cap
8.5
2.0
3.0
0.5
7.0
Tantalum Cap
15.0
7.0
8.0
4.0
10.0
Ceramic Cap
2.0
1.0
0.5
0.25
1.2
Si PN, Shottkey, PIN Diode
2.4
1.6
3.6
1.6
2.4
Zener Diode
3.2
13.6
17.4
18.8
70.0
LED
9.0
15.0
280
65.0
1.0
BJT Dig IC <100 Gates
20.0
138
2.3
1.0
6.7
BJT Dig IC < 1000 Gates
30.0
150
4.0
1.5
10.0
MOS Dig IC < 1000 Gates
27.3
301
9.0
1.0
13.3
MOS Dig IC => 1000 Gates
55.0
550
16.0
2.2
31.0
EM Coil Relay
385
302
220
715
44.0
SSR, Optocoupler
120
105
47.0
190
12.0
BJT Linear IC < 1000 Transistors
14.0
27.0
4.3
1.0
50.0
MOS Linear IC < 1000 Transistors
19.0
54.0
9.0
1.0
13.3
Transformer < 1VA
33.0
90.0
70.0
60.0
50.0
Transformer > 1VA
3.0
9.0
7.0
6.0
5.0
Carbon Res
318-595 Statistics & Reliability
595 Standard Failure Rates in FIT (Data is not accurate in all cases)
Component Type
Method A - l
Method B - l
Method C - l
Method D - l
Method E - l
Plastic Shell Connector, Plug, Jack
100.0
55.0
150.0
120.0
105.0
Metal Shell Connector, Plug, Jack
33.0
18.0
57.0
40.0
35.0
7.0
1.0
50.0
8.0
22.0
115.0
113.8
113.2
117.6
114.0
Quartz Crystal SMT
15.0
34.0
30.0
51.0
20.0
Quartz Oscillator Module CMOS
10.0
12.5
10.5
20.0
15.0
Diode Bridge
4.8
1.6
3.6
1.6
2.4
LED Display
19.0
115.0
280
165.0
21.0
LCD Display
119.0
215.0
380
1165.0
206.0
BJT Linear IC > 1000 Transistors
114.0
217.0
41.3
91.0
150.0
MOS Linear IC > 1000 Transistors
29.0
74.0
19.0
21.0
113.3
Pb, NCd, Li, Lio, NmH Battery
Quartz Crystal Thru Hole
318-595 Statistics & Reliability
595 Standard Stress Factors
• Factor Definitions (may not represent standard models)
 pT = Temperature Stress Factor = e[Ta/(Tr-Ta)] – 0.4
 Where Ta = Actual Max Operating Temp, Tr = Rated Max Op Temp, Tr>Ta
 pV = Cap/Res/Transistor Electrical Stress Factor = e[(Va)/Vr-Va]-2.0
 Where Va = Actual Max Operating Voltage, Vr = Abs Max Rated Voltage, Vr>Va
 pE = Environmental (Overall) Factor >>>





Indoor Stationary = 1.0
Indoor Mobile = 2.5
Outdoor Stationary = 3.0
Outdoor Mobile = 5.0
Automotive = 7.0
 pQ = Quality Factor (Parts and Assembly)





Mil Spec/Range Parts = 0.75
100 Hr Powered Burn In = 0.75
Commercial Parts Mfg Direct = 1.0
Commerical Parts Distributor = 1.25
Hand Assembly Part = 3.0
318-595 Statistics & Reliability
Example:
Method A, 0-50C Ambient, Indoor Mobile, Distributor Components
+5VDC
+12VDC
C1 0.1uf 50V
Polyester
+5VDC
C4 0.1uf 50V
Ceramic
LED
R1 2KW 1/4W
Brand A Metal Film
Vin
Vf=1.5V
BPLR
OP AMP
C2 0.1uf 50V
Polyester
74HCT14 R2 150W 1/4W
5V 1W
Zener
Brand B Metal Film
C3 10uf
15V
Electrolytic
-12VDC
Max Tr
Max Vr
pT
pV
pE
pQ
lFITS
C1
105C
50V
2.082
0.186
2.5
1.25
10.29
C2
105C
50V
2.082
0.186
2.5
1.25
10.29
C3
85C
15V
3.773
0.223
2.5
1.25
552.2
C4
125C
50V
1.548
0.151
2.5
1.25
1.46
R1
120C
20V
1.643
0.232
2.5
1.25
0.83
R2
150C
6V
1.249
0.549
2.5
1.25
1.50
Zener Diode
100C
N/A
2.318
1.0
2.5
1.25
23.18
Op Amp
125C
36V
1.548
1.0
2.5
1.25
67.73
74HCT14
125C
7V
1.548
1.649
2.5
1.25
217.77
LED
85C
N/A
3.773
1.0
2.5
1.25
106.16
Part
991.37 Fits  115.1 Yrs MTBF
318-595 Statistics & Reliability
Stress Factors Drive Simple:
595 Standard Deratings
• Resistors, Potentiometers <= 50% maximum power
• Caps/Res <= 60% maximum working voltage
• Transistors <= 50% maximum working voltage
• Note: Most discrete devices as well as linear IC’s have
parameters which will vary with temperature which is
expressed as Tc (temp coefficient). Typically a delta or
percent of change per deg C from ambient.
318-595 Statistics & Reliability
MTBF Data Input Sheet for e-Reliability.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 CL
Parts Quality:
Select Either: Mil-Spec or Commercial/Bellcore
Quantity
Description
---------Bipolar Integrated Circuits
IC / Bipolar, Digital 1-100 Gates
IC / Bipolar, Digital 101-1000 Gates
IC / Bipolar, Digital 1001-3000 Gates
IC / Bipolar, Digital 3001-10000 Gates
IC / Bipolar, Digital 10001-30000 Gates
IC / Bipolar, Digital 30001-60000 Gates
IC / Bipolar, Linear 1-100 Transistors
IC / Bipolar, Linear 101-300 Transistors
IC / Bipolar, Linear 301-1K Transistors
IC / Bipolar, Linear 1001-10K Transistors
, etc.
EXAMPLE: Actual Reli Tool Input
List of components, their number,
Environment conditions, components quality
318-595 Statistics & Reliability
Example Reliability calculation using actual MIL-HDBK-217F
Failure rate of a Metal Oxide Semiconductor (MOS) can be expressed as
l p  (C1p T + C2p E )p Qp L failures/106 hours
Parameters are listed in MIL Data base.
Temperature factor is modeled using Arrhenius type Eqn
p T  0.1exp[- Ea / 8.617e - 5(1 / Taccel - 1 / Tworking)]
where Ea is theactivationenergy.For MOS Ea  0.35eV.
For manycomponentsEa is listed in MIL data base.
595 charts are greatly simplified from actual parts count Reli
318-595 Statistics & Reliability
Example Reliability report
--------------------------------------------------------------------------------------|
|
|
|
| Failure Rate in
|
|
|
|
|
| Parts Per Million Hours |
| Description/
| Specification/ | Quantity | Quality |-------------------------|
| Generic Part Type
| Quality Level |
| Factor |
|
|
|
|
|
| (Pi Q) | Generic
|
Total
|
|
|
|
|
|
|
|
|=====================|================|==========|=========|============|============|
| Integrated Circuit/ | Mil-M-38510/
|
16
|
1.00 |
0.07500 |
1.20000 |
| Bipolar, Digital
| B
|
|
|
|
|
| 30001-60000 Gates
|
|
|
|
|
|
|
|
|
|
|
|
|
| Integrated Circuit/ | Mil-M-38510/
|
8
|
1.00 |
0.01700 |
0.13600 |
| Bipolar, Linear
| B
|
|
|
|
|
| 101-300 Transistors |
|
|
|
|
|
|
|
|
|
|
|
|
| Diode/
| Mil-S-19500/
|
2
|
2.40 |
0.00047 |
0.00226 |
| Switching
| JAN
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Diode/
| Mil-S-19500/
|
4
|
2.40 |
0.00160 |
0.01536 |
| Voltage Ref./Reg.
| JAN
|
|
|
|
|
| (Avalanche & Zener) |
|
|
|
|
|
|
|
|
|
|
|
|
| Transistor/
| Mil-S-19500/
|
4
|
2.40 |
0.00007 |
0.00067 |
| NPN/PNP
| JAN
|
|
|
|
318-595 Statistics & Reliability
Reliability Prediction Drawbacks
318-595 Statistics & Reliability
Parts Count Method Reliability Prediction Drawbacks
• Prediction Methods not always effective in representing future reality of a
product. Tend to be pessimistic, however they are generally inaccurate.
• Best utilized for design comparison and order of magnitude reliability
prediction (must use same methods for comparisons)
• Single Stress Factors must be employed to represent a composite average or
worst case of the population. Difficult to predict average stress levels, peak
stress levels
• Methods give an overall average failure rate, one dimensional
• Time to failure distributions (Weibull) are two dimensional describing
infantile failures as well as end of life failures
• Reli growth using actual stress testing is a much more effective process
(however also more expensive approach)
• MIL-STD-217F Notice 2 was the last revision of this long used standard
(Jan 1995), No further releases planned.
318-595 Statistics & Reliability
Reliability Growth Methods
318-595 Statistics & Reliability
Reliability Growth Methods: HALT
HALT Strategy: Highly Accelerated Life Testing
• One or more stresses used at accelerated amplitudes from
what the product would see during application
• Stress level is gradually increased until failure is detected
• Failure is then autopsied to fundamental root cause
• Corrective/Preventive action taken to remove chance of
recurring failure
• Test is then restarted
• Must be prepared to destroy prototypes, spend money
• Failure must be detectable, identifiable
318-595 Statistics & Reliability
2 Types of Acceleration
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
318-595 Statistics & Reliability
Example of Time Accelerated Life Test (595 Team Project):
“Rotating Bicycle Apparatus Project”
Potential reliability stress is the periodic g-load (start-stop cycles). This causes fatigue
failure mode (cracks in ceramic material, creep of plastics, adhesives, solder electrical contacts failure).
Estimation of the test protocol, plan and execution time.
The start-stop requirements for cycle:
•10 s to accelerate from 0 to 5 rev/sec max rotational speed (60 mph)
•5 s to decelerate from 5 rev/sec to 0.
•35 starts-stops cycles per day
•One cycle time (from start to stop) is going to be: T = 10+5+5=20s,
where 5 s is added as a lag time to accommodate the transition from stopping back to starting
Assuming the throughput 35 start-stops/day for 365 days/year
the total number of rotation cycles for 1 year is 35*365=12775 cycles /year (=12775 start-stops).
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
life time,
years
1
3
5
10
test time,
days
3.5
10.5
17.5
35
318-595 Statistics & Reliability
Stress Accelerations
* High Temperature
* High Voltage
* Thermal Cycling
* Vibration
318-595 Statistics & Reliability
High Temperature Acceleration Factor
Modified Arrhenius Equation:
Svante August Arrhenius
AT = Acceleration Factor
Ea = Activation Energy
Depends on failure modes;
incl electromigration,
contamination, etc.
318-595 Statistics & Reliability
Examples of Arrhenius Temperature Acceleration
7
Relative failure rate
6
Ceramic Caps
Resistors- Film
5
Bipolar transistors
4
Bipolar IC
RAM, CMOS
3
2
1
0
20
40
60
Tem p (deg C)
80
318-595 Statistics & Reliability
Voltage Stress Acceleration Factor
Modified Arrhenius Equation:
318-595 Statistics & Reliability
Thermal Cycle Stress Accelerations
Primarily used to stress CTE mismatch, accumulated fatigue damage failures
Basic Coffin-Manson Equation – Temperature Cycle
SnPb Eutectic 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
Failure Mechanism/Material
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
Au4Al fracture in wire bonds
4.0
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
4.8-6.2
Silicon Fracture
5.5
Silicon Fracture (cratering)
7.1
Thin Film Cracking
8.4
318-595 Statistics & Reliability
Example
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
318-595 Statistics & Reliability
Modified Coffin-Manson 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
318-595 Statistics & Reliability
Alternate Form Modified Coffin-Manson Equation (Common)
Norris-Landsberg 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
318-595 Statistics & Reliability
Modified Coffin-Manson 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)
318-595 Statistics & Reliability
Reliability Growth Methods: HAST
HAST Strategy: Highly Accelerated Stress Testing
• One or more stresses used at accelerated amplitudes from
what the product would see during application
• Stress level is constant, time to failure is primary
measurement
• Failure may also be autopsied to fundamental root cause
• Corrective/Preventive action NOT necessarily taken
• Test is then restarted using higher or lower stress
amplitude to get additional data points
• Used to find empirical relationship between stress level
and time to failure (life)
318-595 Statistics & Reliability
Reliability Growth Methods: HASS
HASS Strategy: Highly Accelerated Stress Screening
• Used in production to accelerate infantile failures and keep
them from shipping to customers
• Must have HAST data to understand how much life is
expended with stress screen
• One or more stresses used at slightly accelerated
amplitudes from what the product would see during
application
• Common application is powered burn-in time during
which electronics are powered and thermal cycled.
(Example MIL-STD-883) Assemblies tested during or after
burn-in for failure inducements
318-595 Statistics & Reliability
LFailures/Time
Reliability Bathtub Curve
infant mortality
constant failure rate
wearout
Time
• Infant mortality- often due to manufacturing defects ….. Can be screened out
• In electronics systems, prediction models assume constant failure rates
(Bellcore model, MIL-HDBK-217F, others)
• Understanding wearout requires knowledge of the particular device failure physics
- Semiconductor devices should not show wearout except at long times
- Discrete devices which wearout: Relays, EL caps, fans, connectors, solder
318-595 Statistics & Reliability
Life Stress Models and Qualification
• Specify Device Storage/Shipment Profiles:
•
Specify Device Heavy User Profiles:
1.
Number of Power Cycles
2.
Number of Thermal Cycles and Min-Max Excursion (oC) per cycle
3.
Number, Amplitude (G force) and Direction of Mechanical Shocks
4.
Amplitude (Grms), Duration (Hrs), Freq Range (Hz) and Direction (1, 2 or 3
axis) Mechanical Vibration
5.
Total airflow volume (M3) and particulates (Kg)
318-595 Statistics & Reliability
Appendices
318-595 Statistics & Reliability
More on Component Derating
Intentional limiting of usage stress vs rated capability
Voltage
Power
318-595 Statistics & Reliability
318-595 Statistics & Reliability
318-595 Statistics & Reliability
Physics of Failure: Accumulated Fatigue Damage (AFD) is related to the number
of stress cycles N, and mechanical stress, S, using Miner’s rule
b
AFD  N * S
Exponent B comes from the S-N diagram. It is typically between 2 and 20
Example: Solder Joint
Shear
voids
Effective cross-sectional
Effective
cross-sectional
Force
Area: D/2
Area: D
F
F
Applied stress: S 
D
Let  = 10, then
AFD(no voids)  N * S10
Applied stress: S 
2* F
 2* S
D
AFD  1024* N * S10  1024* AFD(no voids)
AFD with voids will “age” about
1000x faster than AFD with no voids
Voids in solder joints
318-595 Statistics & Reliability
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 
a
DT b
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)
General Failure Mechanism
b
Ductile Metal Fatigue
1 to 2
Commonly Used IC Metal Alloys and
3 to 5
Intermetallics
Brittle Fracture
6 to 8
Reference: “EIA Engineering Bulletin:
Acceleration Factors”, SSB 1.003, Electronics
-
Industries Alliance, Government Electronics and Information
Engineering Department, 1999.
Technology Association
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
Solder (37Pb/03Ag & 91Sn/09Zn)
2.4
Aluminum Wire Bond
3.5
Au4Al fracture in wire bonds
4.0
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
4.8-6.2
Silicon Fracture
5.5
Silicon Fracture (cratering)
7.1
Thin Film Cracking
8.4
318-595 Statistics & Reliability
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
N cycles 
MTTF (use)=MTTF(stress)*AF = 4570*33.4 = 152638hrs = 17.4 yrs
B(10)use  h * AF * 0.1051 / b  4768*15.3 * 0.1051 / 12  6.9 yrs
a
DT b
318-595 Statistics & Reliability
Reliability Distributions are non-Normal, require 2 parameters
beta, b - slope/shape parameter
Intro: Weibull Distribution
- ( t / h )b
F(t) = 1 - e
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=bX+a
eta, h – characteristic life or
scale parameter
Knowing the distribution Function allows to
address the following problem (anticipated future failure):
when t = h
F(t) = 63.2%
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)
T b
t b
P={F(T)-F(t)}/[1-F(t)]= 1 - exp{-[( ) - ( ) ]}
h
h
318-595 Statistics & Reliability
Physical Significance of Weibull Parameters
When Weibull distribution parameters are defined, B10 and MTTF can be computed.
99
MTTF = mean time to failure (non-repairable)
Cumulative Failure (%)
F(t)
= h G ( 1 + 1/b )
When b = 1.0, MTTF = h
When b = 0.5, MTTF = 2h
Slope = b
MTBF = mean time between failure (repairable)
(MTBSC)
= total time on all systems / # of failures
10
When there is no suspension data, MTBF = MTTF
1
B10
10
Time to Failure (t)
100
The slope parameter, Beta (b), indicates failure type
b<1
b=1
b>1
rate of failure is decreasing
rate of failure is constant
rate of failure is increasing
infantile (early) failure
random failure
wear out failure
318-595 Statistics & Reliability
Estimating Reliability from Test Data
• In testing electronics assemblies or parts, there are frequently few (or no) failures
• How do you estimate the reliability in this case?
• Use the chi-squared distribution and the following equation:
MTBF = 2 * Number of hours on test * Acceleration factor / c 2
In this equation, c2 is a function of two variables
n, the degrees of freedom, defined as n= 2 * number of failures + 2
and F, the confidence level of the results (e.g. 90%, 95%, 99%)
318-595 Statistics & Reliability
Example
The following test was conducted:
• A new design was qualified by testing 20 boards for 1000 hours
• The test was conducted at elevated temperatures, where the test would accelerate
failures by 10X the usage rate
• One board failed at 500 hours, the other 19 passed for the full 1000 hours
What is the MTBF of the board design at 90% confidence?
Solution:
• First, determine n = 2 * number of failure + 2 = 4; so c2 = 7.78 (at 90% confidence)
• Second, determine number of hours = 19 samples * 1000 + 1 * 500 = 19, 500 hours
• So, the answer is:
MTBF = 2 * 19500 (total hours) * 10 (acceleration factor) / 7.78 = 50, 128 hours
318-595 Statistics & Reliability
The calculations are based on the Binomial
Distribution and the following formula:
Pass/Fail Test Sample Sizes?
where:
Confidence Level CL =
n
=
sample size
p
=
proportion defective
r
=
number defective
=
probability of k or fewer failures occurring in a test
of n units
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.
318-595 Statistics & Reliability
Number of subsystems:
3
Equal Allocation
System
B(10),
years
System
MTTF,
years
1
5
10
Subsystem
MTTF years
9.5
28.5
47.5
142.4
94.9
284.7
MTTF~=10 years (B10=1 year) results in failure rate 1-F=1-exp(-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 1-F=1-exp(-1/47.5*10)=0.19,
i.e. 19% of units on average will fail for 10 years.
System Reliability Target Must be Allocated
318-595 Statistics & Reliability
• Commonly Used Methods to Present and Analyze Data
318-595 Statistics & Reliability
Plot or Scatter Plot
Linear Correlation of Input to Output
1.4
1.2
1
Output
0.8
mArms
0.6
Vrms
0.4
0.2
0
0
0.5
1
1.5
Input
Used to Illustrate Correlation or Relationships
318-595 Statistics & Reliability
Pareto Chart
Root Cause Failures Example
Failure Root Causes
70
60
50
OW
40
#
IW
30
20
10
0
Dehumidifier
Pow er Supply
No Defect Found
Workmanship
Other
Root Cause
Used to Illustrate Contributions of Multiple Sources
Excellent when data is abundant
318-595 Statistics & Reliability
Fishbone Diagram
Ambient Temp
Load Res Line Voltage
Effect:
Temp
Of Amp
For example
Line Frequency
Volume
Input Amplitude
Illustrates Cause & Effect Relationship
318-595 Statistics & Reliability
Year to Date Summary
Replacement Parts Example
Warranty Replacements
35
Units
40%
Rate
35%
30
30%
> Warranty Rate
Total Units
40
25
20
15
25%
20%
15%
10
10%
5
5%
0
0%
J
F
M
A
M
J
J
A
S
O
N
D