318-595 statistics & reliability statistics and electronic reliability
TRANSCRIPT
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
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 failuresWearout failures are usually due to intrinsic failures
Reliability of Electronic Circuits
318-595 Statistics & Reliability PCB Assembly Failure Mechanisms
Stresses & Major FactorsI. 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
FR4 LaminateCTE = ~20e-6/C
Thin Epoxy Solder MaskNiAu Pad
Copper
Gold CTE = 14.2e-6/C
5 – 15 μ in.
Nickel CTE = 13.4e-6/C
> ~100 μ in.
Copper CTE = 16.5e-6/C
> ~1.2 mil
Si Die CTE = 2.8e-6/C
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 2.3.25The 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 g/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 ionograph-style 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 2.3.28This 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.
318-595 Statistics & ReliabilitySpecifying Warranty: Must Understand Reliability of Product (1, 5 yrs, etc)
• Life of Product should be less than wear out failure mode period
• Bathtub Reli Curve: (Failure Rate vs Time) Area under curve = total failures
Minimize or Precipitate using ESS in factory
~ Constant Failure Rate
Warranty Period Using ESS
Warranty Period
Infantile
Period
318-595 Statistics & Reliability
Basic Statistics and Reliability Statistics
0
2
5
8
10
12
15
18
20
22
25
1.238 1.240 1.242 1.244
318-595 Statistics & ReliabilityBasic Statistics ReviewBasic 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
i where X = index notation for each individual.where n = 7 people
i
Calculate the mean(average): m= X =X i
i = 1
n
n
where X = Sum of the individual times
where X and m = Average or Meani
n = 7 people Mean: X = (2+6+5+2+10+8+7)/7 = 5.7 minutes
Calculate the standard deviation: =s=( Xi - X )
2i = 1
n
n - 1
where = s = Standard DeviationSum or Variance
Step 1 Step 2 (Xi - X) (Xi - X) 2-5.7= -3.7 13.696-5.7= .3 .095-5.7 = -.7 .492-5.7 = -3.7 13.6910-5.7 = 4.3 18.498-5.7 = 2.3 5.297-5.7 = 1.3 1.69 (Xi - X) = 53.43
2
2
= s =7 - 1
53.43
= 2.98 minutes= s
Definition:Range = Max - Min Median = Middle number when arranged low to highMode = Most common number
This Example: Range = 10 - 2 = 8 minutesMedian = 6 minutesMode = 2 minutes
Equation
Equation
Standard Deviation:
Square each one
Then Add All
Step 4
Step 3
Std Deviation is a measure of the inherent spread in the data
318-595 Statistics & Reliability
Bar Chart or Histogram
Provides a visual display of data distributionProvides a visual display of data distribution
Shape of Distribution May be Key to IssuesShape of Distribution May be Key to Issues
1. Normal (Bell Shaped)2. Uniform (Flat)3. Bimodal (Mix of 2 Normal Distributions)4. Skewed left or right5. 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
0
2
5
8
10
12
15
18
20
22
25
1.238 1.240 1.242 1.244
318-595 Statistics & Reliability
• Normal (Gaussian) Distributions
318-595 Statistics & Reliability
Histogram vs Histogram vs Spec Limits Spec Limits
11
Specification LimitSpecification Limit
Area under curve Is probability of
failure
Z = 3
TargetTarget
Much Less Chance of
Failure11
Z = 6
Z is the number of Std Z is the number of Std Devs between the Mean Devs between the Mean and the spec limit. The and the spec limit. The higher the value of Z, higher the value of Z,
the lower the chance of the lower the chance of producing a defectproducing a defect
Z is the number of Std Z is the number of Std Devs between the Mean Devs between the Mean and the spec limit. The and the spec limit. The higher the value of Z, higher the value of Z,
the lower the chance of the lower the chance of producing a defectproducing a defect
66807ppmPPM = Part per Million Defects
3.4ppm** Assumes Z is 4.5 long term
33
Normal Normal DistributionDistribution
Normal Normal DistributionDistribution
318-595 Statistics & Reliability
Area under Distribution Curve Yields Probabilities
34% 34%
14% 14%2% 2%
and 2
Characterized by Two Parameters
Normal Distribution = N( )
318-595 Statistics & ReliabilityLife Cycle of a Component
Standard Normal Distribution
Original Distribution
Apply
TransformationStandard Normal
Distributionx-Z=
-1 0 1 Z
Z = +1.0 is one Standard Deviations above the mean
Z= -0.5 is 0.5 Standard Deviations below the mean
Area under Curve =1
Examples:
X
318-595 Statistics & Reliability1 Sided Normal Distribution, Probability Table
ZZ 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.00 5.00e-001 4.96e-001 4.92e-001 4.88e-001 4.84e-001 4.80e-001 4.76e-001 4.72e-001 4.68e-001 4.64e-0010.10 4.60e-001 4.56e-001 4.52e-001 4.48e-001 4.44e-001 4.40e-001 4.36e-001 4.33e-001 4.29e-001 4.25e-0010.20 4.21e-001 4.17e-001 4.13e-001 4.09e-001 4.05e-001 4.01e-001 3.97e-001 3.94e-001 3.90e-001 3.86e-0010.30 3.82e-001 3.78e-001 3.74e-001 3.71e-001 3.67e-001 3.63e-001 3.59e-001 3.56e-001 3.52e-001 3.48e-0010.40 3.45e-001 3.41e-001 3.37e-001 3.34e-001 3.30e-001 3.26e-001 3.23e-001 3.19e-001 3.16e-001 3.12e-0010.50 3.09e-001 3.05e-001 3.02e-001 2.98e-001 2.95e-001 2.91e-001 2.88e-001 2.84e-001 2.81e-001 2.78e-0010.60 2.74e-001 2.71e-001 2.68e-001 2.64e-001 2.61e-001 2.58e-001 2.55e-001 2.51e-001 2.48e-001 2.45e-0010.70 2.42e-001 2.39e-001 2.36e-001 2.33e-001 2.30e-001 2.27e-001 2.24e-001 2.21e-001 2.18e-001 2.15e-0010.80 2.12e-001 2.09e-001 2.06e-001 2.03e-001 2.00e-001 1.98e-001 1.95e-001 1.92e-001 1.89e-001 1.87e-0010.90 1.84e-001 1.81e-001 1.79e-001 1.76e-001 1.74e-001 1.71e-001 1.69e-001 1.66e-001 1.64e-001 1.61e-001
1.00 1.59e-001 1.56e-001 1.54e-001 1.52e-001 1.49e-001 1.47e-001 1.45e-001 1.42e-001 1.40e-001 1.38e-0011.10 1.36e-001 1.33e-001 1.31e-001 1.29e-001 1.27e-001 1.25e-001 1.23e-001 1.21e-001 1.19e-001 1.17e-0011.20 1.15e-001 1.13e-001 1.11e-001 1.09e-001 1.07e-001 1.06e-001 1.04e-001 1.02e-001 1.00e-001 9.85e-0021.30 9.68e-002 9.51e-002 9.34e-002 9.18e-002 9.01e-002 8.85e-002 8.69e-002 8.53e-002 8.38e-002 8.23e-0021.40 8.08e-002 7.93e-002 7.78e-002 7.64e-002 7.49e-002 7.35e-002 7.21e-002 7.08e-002 6.94e-002 6.81e-0021.50 6.68e-002 6.55e-002 6.43e-002 6.30e-002 6.18e-002 6.06e-002 5.94e-002 5.82e-002 5.71e-002 5.59e-0021.60 5.48e-002 5.37e-002 5.26e-002 5.16e-002 5.05e-002 4.95e-002 4.85e-002 4.75e-002 4.65e-002 4.55e-0021.70 4.46e-002 4.36e-002 4.27e-002 4.18e-002 4.09e-002 4.01e-002 3.92e-002 3.84e-002 3.75e-002 3.67e-0021.80 3.59e-002 3.51e-002 3.44e-002 3.36e-002 3.29e-002 3.22e-002 3.14e-002 3.07e-002 3.01e-002 2.94e-0021.90 2.87e-002 2.81e-002 2.74e-002 2.68e-002 2.62e-002 2.56e-002 2.50e-002 2.44e-002 2.39e-002 2.33e-002
2.00 2.28e-002 2.22e-002 2.17e-002 2.12e-002 2.07e-002 2.02e-002 1.97e-002 1.92e-002 1.88e-002 1.83e-0022.10 1.79e-002 1.74e-002 1.70e-002 1.66e-002 1.62e-002 1.58e-002 1.54e-002 1.50e-002 1.46e-002 1.43e-0022.20 1.39e-002 1.36e-002 1.32e-002 1.29e-002 1.25e-002 1.22e-002 1.19e-002 1.16e-002 1.13e-002 1.10e-0022.30 1.07e-002 1.04e-002 1.02e-002 9.90e-003 9.64e-003 9.39e-003 9.14e-003 8.89e-003 8.66e-003 8.42e-0032.40 8.20e-003 7.98e-003 7.76e-003 7.55e-003 7.34e-003 7.14e-003 6.95e-003 6.76e-003 6.57e-003 6.39e-0032.50 6.21e-003 6.04e-003 5.87e-003 5.70e-003 5.54e-003 5.39e-003 5.23e-003 5.08e-003 4.94e-003 4.80e-0032.60 4.66e-003 4.53e-003 4.40e-003 4.27e-003 4.15e-003 4.02e-003 3.91e-003 3.79e-003 3.68e-003 3.57e-0032.70 3.47e-003 3.36e-003 3.26e-003 3.17e-003 3.07e-003 2.98e-003 2.89e-003 2.80e-003 2.72e-003 2.64e-0032.80 2.56e-003 2.48e-003 2.40e-003 2.33e-003 2.26e-003 2.19e-003 2.12e-003 2.05e-003 1.99e-003 1.93e-0032.90 1.87e-003 1.81e-003 1.75e-003 1.69e-003 1.64e-003 1.59e-003 1.54e-003 1.49e-003 1.44e-003 1.39e-003
3.00 1.35e-003 1.31e-003 1.26e-003 1.22e-003 1.18e-003 1.14e-003 1.11e-003 1.07e-003 1.04e-003 1.00e-0033.10 9.68e-004 9.35e-004 9.04e-004 8.74e-004 8.45e-004 8.16e-004 7.89e-004 7.62e-004 7.36e-004 7.11e-0043.20 6.87e-004 6.64e-004 6.41e-004 6.19e-004 5.98e-004 5.77e-004 5.57e-004 5.38e-004 5.19e-004 5.01e-0043.30 4.83e-004 4.66e-004 4.50e-004 4.34e-004 4.19e-004 4.04e-004 3.90e-004 3.76e-004 3.62e-004 3.49e-0043.40 3.37e-004 3.25e-004 3.13e-004 3.02e-004 2.91e-004 2.80e-004 2.70e-004 2.60e-004 2.51e-004 2.42e-0043.50 2.33e-004 2.24e-004 2.16e-004 2.08e-004 2.00e-004 1.93e-004 1.85e-004 1.78e-004 1.72e-004 1.65e-0043.60 1.59e-004 1.53e-004 1.47e-004 1.42e-004 1.36e-004 1.31e-004 1.26e-004 1.21e-004 1.17e-004 1.12e-0043.70 1.08e-004 1.04e-004 9.96e-005 9.57e-005 9.20e-005 8.84e-005 8.50e-005 8.16e-005 7.84e-005 7.53e-0053.80 7.23e-005 6.95e-005 6.67e-005 6.41e-005 6.15e-005 5.91e-005 5.67e-005 5.44e-005 5.22e-005 5.01e-0053.90 4.81e-005 4.61e-005 4.43e-005 4.25e-005 4.07e-005 3.91e-005 3.75e-005 3.59e-005 3.45e-005 3.30e-005
4.00 3.17e-005 3.04e-005 2.91e-005 2.79e-005 2.67e-005 2.56e-005 2.45e-005 2.35e-005 2.25e-005 2.16e-0054.10 2.07e-005 1.98e-005 1.89e-005 1.81e-005 1.74e-005 1.66e-005 1.59e-005 1.52e-005 1.46e-005 1.39e-0054.20 1.33e-005 1.28e-005 1.22e-005 1.17e-005 1.12e-005 1.07e-005 1.02e-005 9.77e-006 9.34e-006 8.93e-0064.30 8.54e-006 8.16e-006 7.80e-006 7.46e-006 7.12e-006 6.81e-006 6.50e-006 6.21e-006 5.93e-006 5.67e-0064.40 5.41e-006 5.17e-006 4.94e-006 4.71e-006 4.50e-006 4.29e-006 4.10e-006 3.91e-006 3.73e-006 3.56e-0064.50 3.40e-006 3.24e-006 3.09e-006 2.95e-006 2.81e-006 2.68e-006 2.56e-006 2.44e-006 2.32e-006 2.22e-0064.60 2.11e-006 2.01e-006 1.92e-006 1.83e-006 1.74e-006 1.66e-006 1.58e-006 1.51e-006 1.43e-006 1.37e-0064.70 1.30e-006 1.24e-006 1.18e-006 1.12e-006 1.07e-006 1.02e-006 9.68e-007 9.21e-007 8.76e-007 8.34e-0074.80 7.93e-007 7.55e-007 7.18e-007 6.83e-007 6.49e-007 6.17e-007 5.87e-007 5.58e-007 5.30e-007 5.04e-0074.90 4.79e-007 4.55e-007 4.33e-007 4.11e-007 3.91e-007 3.71e-007 3.52e-007 3.35e-007 3.18e-007 3.02e-007
318-595 Statistics & ReliabilityNormal 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 2.87e-007 2.72e-007 2.58e-007 2.45e-007 2.33e-007 2.21e-007 2.10e-007 1.99e-007 1.89e-007 1.79e-0075.10 1.70e-007 1.61e-007 1.53e-007 1.45e-007 1.37e-007 1.30e-007 1.23e-007 1.17e-007 1.11e-007 1.05e-0075.20 9.96e-008 9.44e-008 8.95e-008 8.48e-008 8.03e-008 7.60e-008 7.20e-008 6.82e-008 6.46e-008 6.12e-0085.30 5.79e-008 5.48e-008 5.19e-008 4.91e-008 4.65e-008 4.40e-008 4.16e-008 3.94e-008 3.72e-008 3.52e-0085.40 3.33e-008 3.15e-008 2.98e-008 2.82e-008 2.66e-008 2.52e-008 2.38e-008 2.25e-008 2.13e-008 2.01e-0085.50 1.90e-008 1.79e-008 1.69e-008 1.60e-008 1.51e-008 1.43e-008 1.35e-008 1.27e-008 1.20e-008 1.14e-0085.60 1.07e-008 1.01e-008 9.55e-009 9.01e-009 8.50e-009 8.02e-009 7.57e-009 7.14e-009 6.73e-009 6.35e-0095.70 5.99e-009 5.65e-009 5.33e-009 5.02e-009 4.73e-009 4.46e-009 4.21e-009 3.96e-009 3.74e-009 3.52e-0095.80 3.32e-009 3.12e-009 2.94e-009 2.77e-009 2.61e-009 2.46e-009 2.31e-009 2.18e-009 2.05e-009 1.93e-0095.90 1.82e-009 1.71e-009 1.61e-009 1.51e-009 1.43e-009 1.34e-009 1.26e-009 1.19e-009 1.12e-009 1.05e-009
6.00 9.87e-010 9.28e-010 8.72e-010 8.20e-010 7.71e-010 7.24e-010 6.81e-010 6.40e-010 6.01e-010 5.65e-0106.10 5.30e-010 4.98e-010 4.68e-010 4.39e-010 4.13e-010 3.87e-010 3.64e-010 3.41e-010 3.21e-010 3.01e-0106.20 2.82e-010 2.65e-010 2.49e-010 2.33e-010 2.19e-010 2.05e-010 1.92e-010 1.81e-010 1.69e-010 1.59e-0106.30 1.49e-010 1.40e-010 1.31e-010 1.23e-010 1.15e-010 1.08e-010 1.01e-010 9.45e-011 8.85e-011 8.29e-0116.40 7.77e-011 7.28e-011 6.81e-011 6.38e-011 5.97e-011 5.59e-011 5.24e-011 4.90e-011 4.59e-011 4.29e-0116.50 4.02e-011 3.76e-011 3.52e-011 3.29e-011 3.08e-011 2.88e-011 2.69e-011 2.52e-011 2.35e-011 2.20e-0116.60 2.06e-011 1.92e-011 1.80e-011 1.68e-011 1.57e-011 1.47e-011 1.37e-011 1.28e-011 1.19e-011 1.12e-0116.70 1.04e-011 9.73e-012 9.09e-012 8.48e-012 7.92e-012 7.39e-012 6.90e-012 6.44e-012 6.01e-012 5.61e-0126.80 5.23e-012 4.88e-012 4.55e-012 4.25e-012 3.96e-012 3.69e-012 3.44e-012 3.21e-012 2.99e-012 2.79e-0126.90 2.60e-012 2.42e-012 2.26e-012 2.10e-012 1.96e-012 1.83e-012 1.70e-012 1.58e-012 1.48e-012 1.37e-012
7.00 1.28e-012 1.19e-012 1.11e-012 1.03e-012 9.61e-013 8.95e-013 8.33e-013 7.75e-013 7.21e-013 6.71e-0137.10 6.24e-013 5.80e-013 5.40e-013 5.02e-013 4.67e-013 4.34e-013 4.03e-013 3.75e-013 3.49e-013 3.24e-0137.20 3.01e-013 2.80e-013 2.60e-013 2.41e-013 2.24e-013 2.08e-013 1.94e-013 1.80e-013 1.67e-013 1.55e-0137.30 1.44e-013 1.34e-013 1.24e-013 1.15e-013 1.07e-013 9.91e-014 9.20e-014 8.53e-014 7.91e-014 7.34e-0147.40 6.81e-014 6.31e-014 5.86e-014 5.43e-014 5.03e-014 4.67e-014 4.33e-014 4.01e-014 3.72e-014 3.44e-0147.50 3.19e-014 2.96e-014 2.74e-014 2.54e-014 2.35e-014 2.18e-014 2.02e-014 1.87e-014 1.73e-014 1.60e-0147.60 1.48e-014 1.37e-014 1.27e-014 1.17e-014 1.09e-014 1.00e-014 9.30e-015 8.60e-015 7.95e-015 7.36e-0157.70 6.80e-015 6.29e-015 5.82e-015 5.38e-015 4.97e-015 4.59e-015 4.25e-015 3.92e-015 3.63e-015 3.35e-0157.80 3.10e-015 2.86e-015 2.64e-015 2.44e-015 2.25e-015 2.08e-015 1.92e-015 1.77e-015 1.64e-015 1.51e-0157.90 1.39e-015 1.29e-015 1.19e-015 1.10e-015 1.01e-015 9.33e-016 8.60e-016 7.93e-016 7.32e-016 6.75e-016
8.00 6.22e-016 5.74e-016 5.29e-016 4.87e-016 4.49e-016 4.14e-016 3.81e-016 3.51e-016 3.24e-016 2.98e-0168.10 2.75e-016 2.53e-016 2.33e-016 2.15e-016 1.98e-016 1.82e-016 1.68e-016 1.54e-016 1.42e-016 1.31e-0168.20 1.20e-016 1.11e-016 1.02e-016 9.36e-017 8.61e-017 7.92e-017 7.28e-017 6.70e-017 6.16e-017 5.66e-0178.30 5.21e-017 4.79e-017 4.40e-017 4.04e-017 3.71e-017 3.41e-017 3.14e-017 2.88e-017 2.65e-017 2.43e-0178.40 2.23e-017 2.05e-017 1.88e-017 1.73e-017 1.59e-017 1.46e-017 1.34e-017 1.23e-017 1.13e-017 1.03e-0178.50 9.48e-018 8.70e-018 7.98e-018 7.32e-018 6.71e-018 6.15e-018 5.64e-018 5.17e-018 4.74e-018 4.35e-0188.60 3.99e-018 3.65e-018 3.35e-018 3.07e-018 2.81e-018 2.57e-018 2.36e-018 2.16e-018 1.98e-018 1.81e-0188.70 1.66e-018 1.52e-018 1.39e-018 1.27e-018 1.17e-018 1.07e-018 9.76e-019 8.93e-019 8.17e-019 7.48e-0198.80 6.84e-019 6.26e-019 5.72e-019 5.23e-019 4.79e-019 4.38e-019 4.00e-019 3.66e-019 3.34e-019 3.06e-0198.90 2.79e-019 2.55e-019 2.33e-019 2.13e-019 1.95e-019 1.78e-019 1.62e-019 1.48e-019 1.35e-019 1.24e-019
9.00 1.13e-019 1.03e-019 9.40e-020 8.58e-020 7.83e-020 7.15e-020 6.52e-020 5.95e-020 5.43e-020 4.95e-0209.10 4.52e-020 4.12e-020 3.76e-020 3.42e-020 3.12e-020 2.85e-020 2.59e-020 2.37e-020 2.16e-020 1.96e-0209.20 1.79e-020 1.63e-020 1.49e-020 1.35e-020 1.23e-020 1.12e-020 1.02e-020 9.31e-021 8.47e-021 7.71e-0219.30 7.02e-021 6.39e-021 5.82e-021 5.29e-021 4.82e-021 4.38e-021 3.99e-021 3.63e-021 3.30e-021 3.00e-0219.40 2.73e-021 2.48e-021 2.26e-021 2.05e-021 1.86e-021 1.69e-021 1.54e-021 1.40e-021 1.27e-021 1.16e-0219.50 1.05e-021 9.53e-022 8.66e-022 7.86e-022 7.14e-022 6.48e-022 5.89e-022 5.35e-022 4.85e-022 4.40e-0229.60 4.00e-022 3.63e-022 3.29e-022 2.99e-022 2.71e-022 2.46e-022 2.23e-022 2.02e-022 1.83e-022 1.66e-0229.70 1.51e-022 1.37e-022 1.24e-022 1.12e-022 1.02e-022 9.22e-023 8.36e-023 7.57e-023 6.86e-023 6.21e-0239.80 5.63e-023 5.10e-023 4.62e-023 4.18e-023 3.79e-023 3.43e-023 3.10e-023 2.81e-023 2.54e-023 2.30e-0239.90 2.08e-023 1.88e-023 1.70e-023 1.54e-023 1.39e-023 1.26e-023 1.14e-023 1.03e-023 9.32e-024 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
3 4 5 6 7
1,000,000
100,000
10,000
1,000
100
10
1
2
Examples of Fault/Failure Rates onThe Sigma Scale
PPM Defects
•
Restaurant Bills
Doctor Prescription Writing
Restaurant Checks
Airline Baggage Handling
Domestic Airline Flight
(0.43 PPM)
Fatality Rate
Tax Advice (phone-in)
(140,000 PPM)
(with ± 1.5 shift)
Best-in-ClassBest-in-Class
Average Company
Average Company
Z
AircraftCarrier Landings
318-595 Statistics & Reliability
Shift and DriftShift and Drift
Over time, a “typical” product process may shift or drift by ~ 1.5
LSL USLT
Time 1
Time 2
Time 3
Time 4
Short Term Capability Snapshots of the Product
Actual Sustained Capability of the Process
. . . also called “short-term capability”
. . . reflects ‘within group’ variation
. . . also called “long-term capability”
. . . reflects ‘total process’ variation
Two Challenges: Two Challenges:
Center the Process and Eliminate Variation!Center the Process and Eliminate Variation!
318-595 Statistics & ReliabilityStatistics 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.
• Requirement for Aero-Space, Certain Military, Certain Medical
4. 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.
• Requirement for High Eng Telecom, COTS Military, Medical
5. 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.
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
100 %
75 %
50 %
25 %
0 %
100 %
75 %
50 %
25 %
0 %
Min PTH Vertical Fill: Class 2 = 75% Class 3 = 100%
Ref: IPC-A-610, IPC-JSTD-001
318-595 Statistics & Reliability
Solder_Joint_Radius
Void_Distance
Void_Radius
Void_Solder Interface Distance
Sampling_Grid
PositionModel
Potential for Early Life Failure (ELFO) if S < D/10 = (solder_joint_radius)/10
S =Shell = solder_joint_radius – (void_distance + void_radius)
BGA Void Size and Locations, Uniform Void Position Distribution, Varying Diameter
S
S = Shell
318-595 Statistics & Reliability
CLASS 3 - BESTSolder Joint_Radius: 0.225 mmVoid_Radius: 0.0675 mmVoid_Area: 9% of Joint AreaFailure criteria: D/10
CLASS 2 - BETTERSolder Joint_Radius: 0.225 mmVoid_Radius: 0.1013 mmVoid_Area: 20% of Joint AreaFailure criteria: D/10
P(D<10) = 81.11 %
P(D<10) = 52.21 %
P(D<10) = 27.00 %
CLASS 1 - GOODSolder Joint_Radius: 0.225 mmVoid_Radius: 0.135 mmVoid_Area: 36% of Joint AreaFailure criteria: D/10
318-595 Statistics & ReliabilityClass 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 & ReliabilityDefinitions
General Failure Rate Variable:
Recall the Bathtub Curve- Failure Rate () 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-t, Note: is in failures/time, and t is time
Note: At T=0, R(0)=1.0 (100%)
FIT = FITs = Failures per 109 hours
MTBF (years) = 1x109 / ( FIT * 8766 hours /year )
MTBF = 1/MTBF = 1/Mean time between failure in hours
R(t) = e-t, Note: MTBF in hr-1 and t in hr
318-595 Statistics & ReliabilityDefinitions
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-t, Note: 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-t, Note: is in failures/time, and t is time
Note: At T=0, F(0)=0.0 (0%)
318-595 Statistics & ReliabilityWeibull 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,”;
R(t) = e-t/ ), Note: is the dimensionless scale parameter (stretches)
is the shape or slope parameter (exponent)
Note: At T=0, R(0)=1.0 (100%)
Relationship of Weibull parameters to Failure Rate
= (/)(t/)-1
R(t) = e-t/ )
F(t) = 1-e-t/ )
318-595 Statistics & ReliabilityTypical Reliability Plot using Weibull Dist
= (/)(t/)-1
F(t) = 1-e-t/ )
1.00
5.00
10.00
50.00
90.00
99.00
1.00 100000.0010.00 100.00 1000.00 10000.00
Generated by: ReliaSoft's Weibull++ 5.0 - www.Weibull.com - 888-886-0410
Probability Plot
Time, (t)
Unr
elia
bilit
y, F
(t)
1:31:22 PM2/22/00GE AppliancesDouglas C. Kemp
WeibullSupplier 1
P=2, A=RRX-S F=10 | S=0
Supplier 2
P=2, A=RRX-S F=10 | S=0CB/FM: 90.00%2 Sided-BC-Type 2
Time to Failure(s)
F(t) = (1 – R(t))100%
At some time, t, 100% of the population will fail
318-595 Statistics & ReliabilityTypical Reliability Plot assuming Weibull Dist
= (/)(t/)-1
R(t) = e-t/ )
F(t) = 1-e-t/ )
1.00
5.00
10.00
50.00
90.00
99.00
1.00 100000.0010.00 100.00 1000.00 10000.00
Generated by: ReliaSoft's Weibull++ 5.0 - www.Weibull.com - 888-886-0410
Probability Plot
Time, (t)
Unr
elia
bilit
y, F
(t)
1:31:22 PM2/22/00GE AppliancesDouglas C. Kemp
WeibullSupplier 1
P=2, A=RRX-S F=10 | S=0
Supplier 2
P=2, A=RRX-S F=10 | S=0CB/FM: 90.00%2 Sided-BC-Type 2
Time to failure plot using Weibull tool
Fai
lure
Rat
e,
Constant Failure Rates
=1Exponential Distribution
Time
The Bathtub Curve
Useful LifeEarlyLife Wear out
DecreasingFailure Rates
<1
IncreasingFailure Rates
>1
Weibull slope indicates where the product may be on the bathtub curve.
318-595 Statistics & ReliabilityReliability Prediction: Assume Constant Failure Rate
= 1.0
• Basic Series Reli Method of an Electronic System:
Component 1
1
• Each component has an associated reliability • The System Reli ss is the sum of all the component
ss = i
• Reli is expressed in “FITs” failure units
x FIT = x Failures/109 hoursNote: 109 hours = 1 Billion Hours
Component 2
2
Component i
i
Component N
N
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-t
• = 1/MTBF = 1/20000 hr• = 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-t
• = 1/MTBF = 1/20000 hr• = 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 yearsBut … 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
R1
• Each component also has an associated reliability R• The System R is the product of all the component R
R = Ri
• Recall, Reli R is a probability (0 to 1) expressed in percent
Component 2
R2
Component i
Ri
Component N
RN
318-595 Statistics & Reliability
Reliability R Flowdown Example
Power supplyR = 0.94
Drive System,needs R= 0.9 at
10 years
Subsystem Level
System Level
MotorR = 0.97
PartR=0.9999
Control CardR = 0.99
PartR=0.9999
PartR=0.9999
PartR=0.999
PartR=0.9999
PartR=0.9999
PartR=0.999
Component Level
318-595 Statistics & Reliability
• 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
Reliability Requirements Flowdown- Example
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 aMinimum 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 -t and MTBF = 1/
Solve for MTBF: MTBF = 1/ = 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 & ReliabilityCommon Circuit Bd Temperature-Induced Failures
Failure Category Failure Mode Root Cause Environmental Conditions
Susceptible Parts and Materials
High temperature degradation
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 may be impacted by other factors or stresses, :• Some commonly used factors
T = Temperature Stress Factor V = Electrical Stress Factor E = Environmental Factor Q = Quality Factor
• Overall Component = B * T * V * E * Q
Where B = 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
1
• Above Reliability Prediction Model is flawed because;• Components may not have constant reliability rates
ss = i
• 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
Component 2
2
Component i
i
Component N
N
318-595 Statistics & Reliability595 Standard Failure Rates in FIT (Data is not accurate in all cases)
Component Type Method A - Method B - Method C - Method D - Method E -
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
Carbon Res 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
318-595 Statistics & Reliability595 Standard Failure Rates in FIT (Data is not accurate in all cases)
Component Type Method A - Method B - Method C - Method D - Method E -
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
Pb, NCd, Li, Lio, NmH Battery 7.0 1.0 50.0 8.0 22.0
Quartz Crystal Thru Hole 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
318-595 Statistics & Reliability595 Standard Stress Factors
• Factor Definitions (may not represent standard models)
T = Temperature Stress Factor = e[Ta/(Tr-Ta)] – 0.4 Where Ta = Actual Max Operating Temp, Tr = Rated Max Op Temp, Tr>Ta
V = 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
E = Environmental (Overall) Factor >>> Indoor Stationary = 1.0 Indoor Mobile = 2.5 Outdoor Stationary = 3.0 Outdoor Mobile = 5.0 Automotive = 7.0
Q = 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
C3 10uf 15VElectrolytic
C4 0.1uf 50VCeramic
C2 0.1uf 50VPolyester
C1 0.1uf 50VPolyester
74HCT145V 1W Zener
R1 2K 1/4WBrand A Metal Film
R2 150 1/4WBrand B Metal Film
BPLROP AMP
+12VDC
-12VDC
Vin
+5VDC
LEDVf=1.5V
+5VDC
Example: Method A, 0-50C Ambient, Indoor Mobile, Distributor Components
Part Max Tr Max Vr T V E Q
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
FITS
10.29
10.29
552.2
106.16
1.50
23.18
1.46
0.83
991.37 Fits 115.1 Yrs MTBF
217.77
67.73
318-595 Statistics & ReliabilityStress 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
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: 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 InputList of components, their number,Environment conditions, components quality
MTBF Data Input Sheet for e-Reliability.com COST: $500 per report
318-595 Statistics & Reliability
Example Reliability calculation using actual MIL-HDBK-217F
Failure rate of a Metal Oxide Semiconductor (MOS) can be expressed as
hoursLQECTCp60failures/1 )21(
Parameters are listed in MIL Data base.Temperature factor is modeled using Arrhenius type Eqn
base. data MILin listed is Ea componentsmany For
eV. 0.35Ea MOSFor energy. activation theis Ea where
)]/1/1(5617.8/exp[1.0
workingTaccelTeEaT
595 charts are greatly simplified from actual parts count Reli
318-595 Statistics & Reliability
---------------------------------------------------------------------------------------| | | | | 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 | | | |
Example Reliability report
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
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
Reliability Growth Methods: HALT
Rep
eat
318-595 Statistics & Reliability
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
2 Types of Acceleration
318-595 Statistics & ReliabilityExample 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 fatiguefailure 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
test time, days
1 3.53 10.55 17.5
10 35
318-595 Statistics & Reliability
Stress Accelerations
* High Temperature
* High Voltage
* Thermal Cycling
* Vibration
318-595 Statistics & Reliability
High Temperature Acceleration Factor
Svante August Arrhenius
Modified Arrhenius Equation:
AT = Acceleration Factor
Ea = Activation Energy Depends on failure modes; incl electromigration, contamination, etc.
318-595 Statistics & Reliability
Examples of Arrhenius Temperature Acceleration
0
1
2
3
4
5
6
7
20 40 60 80
Temp (deg C)
Rela
tive f
ailu
re r
ate Ceramic Caps
Resistors- Film
Bipolar transistors
Bipolar IC
RAM, CMOS
318-595 Statistics & Reliability
Voltage Stress Acceleration Factor
Modified Arrhenius Equation:
318-595 Statistics & Reliability
AF = (Ts/ Ta)E
Where;
Ts = Stress Test Thermal Excursion Range oK
Ta = 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
Basic Coffin-Manson Equation – Temperature CycleSnPb Eutectic Solder Joint Creep Failure Application
Thermal Cycle Stress AccelerationsPrimarily used to stress CTE mismatch, accumulated fatigue damage failures
Failure Mechanism/Material E316 Stainless Steel 1.54340 Steel 1.8Solder (97Pb/03Sn) T > 30°C 1.9Solder (37Pb/63Sn) T < 30°C 1.2Solder (37Pb/63Sn) T > 30°C 2.7Solder (37Pb/03Ag & 91Sn/09Zn) 2.4Aluminum Wire Bond 3.5Au4Al fracture in wire bonds 4.0PQFP Delamination / Bond Failure 4.2ASTM 2024 Aluminum Alloy 4.2Copper 5.0Au Wire Bond Heel Crack 5.1ASTM 6061 Aluminum Alloy 6.7Alumina Fracture 5.5Interlayer Dielectric Cracking 4.8-6.2Silicon Fracture 5.5Silicon Fracture (cratering) 7.1Thin Film Cracking 8.4
318-595 Statistics & Reliability
AF = (Ts/ Ta)1.9
Application, 1 Cycle/Day;
Tmin = 10 oC = 283 oK, Tmax = 50 oC = 323 oK
ExampleSnPb Eutectic Solder Joint Creep Failure Application, Conservative Acceleration
Stress Test Design;
Tmin = -40 oC = 233 oK, Tmax = 125 oC = 398 oK
Ts = 165 oK, Ta = 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
AF = (Ts/ Ta)E (Fa/Fs)
1/3 e(Tsa/100)
Where;
Ts = Stress Test Thermal Excursion Range oK
Ta = 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
Tsa = 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 Coffin-Manson Equation – Temp and Temp GradientSnPb Solder Joint Creep Failure
318-595 Statistics & Reliability
AF = (Ts/ Ta)E (Fa/Fs)
1/3 e1414(1/Tamax – 1/Tsmax)
Where;
Ts = Stress Test Thermal Excursion Range oK
Ta = 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
Tsa = 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 Coffin-Manson Equation (Common)Norris-Landsberg Equation for Solder Joint Creep Failure
318-595 Statistics & Reliability
Example
Application;
Tmin = 10 oC = 283 oK, Tmax = 50 oC = 323 oK, Ta = 40 oK
Fa = 1 cycle/day
Stress Test Design;
Tmin = -40 oC = 233 oK, Tmax = 125 oC = 398 oK, Ts = 165 oK
Ts(max) = 398 oK, Ta(max) = 323 oK, Tsa = 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
Modified Coffin-Manson EquationSnPb Solder Joint Creep Failure
1 Stress Test Day = Fs X AF = 259.2 Application Cycles
(Taking thermal gradient into account is more conservative)
318-595 Statistics & Reliability
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)
Reliability Growth Methods: HAST
Rep
eat
318-595 Statistics & Reliability
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
Reliability Growth Methods: HASS
Rep
eat
318-595 Statistics & Reliability
Reliability Bathtub Curve
Fai
lure
s/T
ime
Time
infant mortality constant failure rate wearout
• 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 & ReliabilityLife 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 DeratingIntentional limiting of usage stress vs rated capability
VoltagePower
318-595 Statistics & Reliability
318-595 Statistics & Reliability
318-595 Statistics & ReliabilityPhysics of Failure: Accumulated Fatigue Damage (AFD) is related to the number of stress cycles N, and mechanical stress, S, using Miner’s rule
SNAFD *Exponent B comes from the S-N diagram. It is typically between 2 and 20
Example: Solder JointShear Force
FApplied stress:
D
FS
Effective cross-sectional Area: D
Let = 10, then10* voids)( SNnoAFD
voids Effective cross-sectionalArea: D/2
Applied stress: SD
FS *2
*2
voids)(*102410**1024 noAFDSNAFD
AFD with voids will “age” about1000x faster than AFD with no voids
Voids in solder joints
318-595 Statistics & Reliability
Physics of failure: Thermal Fatigue ModelsCoefficients 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 electronicfailures are mechanical in nature)
• The values of the coefficient b for various failure mechanisms and materials(derived or taken from empirical data)
bcycles T
aN
N cycles = number of cycles to failure at reference condition
b = typical value for a given failure mechanism, a = prop constant
Failure Mechanism/Material b316 Stainless Steel 1.54340 Steel 1.8Solder (97Pb/03Sn) T > 30°C 1.9Solder (37Pb/63Sn) T < 30°C 1.2Solder (37Pb/63Sn) T > 30°C 2.7Solder (37Pb/03Ag & 91Sn/09Zn) 2.4Aluminum Wire Bond 3.5Au4Al fracture in wire bonds 4.0PQFP Delamination / Bond Failure 4.2ASTM 2024 Aluminum Alloy 4.2Copper 5.0Au Wire Bond Heel Crack 5.1ASTM 6061 Aluminum Alloy 6.7Alumina Fracture 5.5Interlayer Dielectric Cracking 4.8-6.2Silicon Fracture 5.5Silicon Fracture (cratering) 7.1Thin Film Cracking 8.4
General Failure Mechanism bDuctile Metal Fatigue 1 to 2Commonly Used IC Metal Alloys and Intermetallics
3 to 5
Brittle Fracture 6 to 8
Reference: “EIA Engineering Bulletin: Acceleration Factors”, SSB
-
1.003, Electronics
Industries Alliance, Government Electronics and Information
Technology Association Engineering Department, 1999.
318-595 Statistics & Reliability
Calculated acceleration factor and MTTF (and B10) @ normal stress:
AF = Nstress / Nuse = (b(165/45)2.7 = 33.4
MTTF (use)=MTTF(stress)*AF = 4570*33.4 = 152638hrs = 17.4 yrs
yrsAFuseB 9.612/1105.0*3.15*4768/1105.0**)10(
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
bcycles T
aN
318-595 Statistics & Reliability
Intro: Weibull Distribution
F(t) = Cumulative fraction of parts that have failedat time t
F(t) = 1 - e- ( )t /
ln ln (1 / (1 – F(t))) = ln(t) – ln()
Y = X + a
beta, - slope/shape parameter
eta, – characteristic life or scale parameter
when t = F(t) = 63.2%
Reliability Distributions are non-Normal, require 2 parameters
Knowing the distribution Function allows toaddress the following problem (anticipated future failure):
What is the probability, P , that the failure will occur for theperiod of time T if it did not occur yet for the period of time t ? (T>t)
P={F(T)-F(t)}/[1-F(t)]= ]})()[(exp{1
tT
318-595 Statistics & ReliabilityPhysical Significance of Weibull Parameters
99
10
Cu
mu
lati
ve F
ailu
re (
%)
F(t
)
Time to Failure (t)1 10 100
Slope =
B10
When Weibull distribution parameters are defined, B10 and MTTF can be computed.
The slope parameter, Beta (), indicates failure type
< 1 rate of failure is decreasing infantile (early) failure = 1 rate of failure is constant random failure> 1 rate of failure is increasing wear out failure
MTTF = mean time to failure (non-repairable)
MTBF = mean time between failure (repairable)(MTBSC)
= ( 1 + 1/ )
When = 1.0, MTTF = When = 0.5, MTTF = 2
When there is no suspension data, MTBF = MTTF
= total time on all systems / # of failures
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 / 2
In this equation, 2 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 2 = 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 & ReliabilityThe calculations are based on the Binomial Distribution and the following formula:
Confidence Level CL =
where:
n = sample size
p = proportion defective
r = number defective
= 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.
318-595 Statistics & Reliability
Number of subsystems: 3Equal Allocation
SystemB(10), years
SystemMTTF, years
SubsystemMTTF years
1 9.5 28.55 47.5 142.4
10 94.9 284.7
System Reliability Target Must be Allocated
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.
318-595 Statistics & Reliability
• Commonly Used Methods to Present and Analyze Data
318-595 Statistics & Reliability
Plot or Scatter Plot
Used to Illustrate Correlation or RelationshipsUsed to Illustrate Correlation or Relationships
Linear Correlation of Input to Output
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5
Input
Ou
tpu
t mArms
Vrms
318-595 Statistics & Reliability
Failure Root Causes
0
10
20
30
40
50
60
70
Dehumidif ier Pow er Supply No Defect Found Workmanship Other
Root Cause
#
OW
IW
Used to Illustrate Contributions of Multiple Sources
Excellent when data is abundant
Used to Illustrate Contributions of Multiple Sources
Excellent when data is abundant
Pareto ChartRoot Cause Failures Example
318-595 Statistics & Reliability
Fishbone Diagram
Effect:TempOf AmpFor example
Load ResLoad Res Line VoltageLine Voltage
VolumeVolumeLine FrequencyLine Frequency Input AmplitudeInput Amplitude
Ambient TempAmbient Temp
Illustrates Cause & Effect Relationship
318-595 Statistics & Reliability
Warranty Replacements
0
5
10
15
20
25
30
35
40
J F M A M J J A S O N D
Tota
l Uni
ts
0%
5%
10%
15%
20%
25%
30%
35%
40%
> W
arra
nty
Rate
Units
Rate
Year to Date SummaryReplacement Parts Example