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Specifying Warranty: Must Understand Reliability of Product Bathtub Reli Curve : (Failure Rate vs Time) Area under curve = total failures Warranty Period << Useful Life Try to minimize total failures in warranty period  reduce field failures. Infantile Period. ~ Constant Failure Rate.

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slide2

Specifying Warranty: Must Understand Reliability of Product

  • Bathtub Reli Curve: (Failure Rate vs Time) Area under curve = total failures
  • Warranty Period << Useful Life
  • Try to minimize total failures in warranty period  reduce field failures

Infantile

Period

~ Constant Failure Rate

Minimize or Precipitate using ESS in factory

Warranty Period Using ESS (Environmental Stress Screening)

Warranty Period

slide3

n

X

S

i

i

=

1

m

=

=

X

n

n

2

S

(

X

-

X

)

i

s

i

=

1

=

s

=

n

-

1

Basic Statistics Review

Example: The following data represents the amount of time it takes 7 people to do a 355 exam problem.

X = 2, 6, 5, 2 ,10, 8, 7 in min.

n = 7

where X = index notation for each individual.

where n = 7 people

i

i

whereS X = Sum of the individual times

where X and m = Average or Mean

Calculate the mean(average):

Equation

i

n = 7 people Mean:X = (2+6+5+2+10+8+7)/7 = 5.7 minutes

where s = s = Standard Deviation

Sum or Variance

Calculate the standard deviation:

Equation

Step 1 Step 2

(Xi - X) (Xi - X)

2-5.7= -3.7 13.69

6-5.7= .3 .09

5-5.7 = -.7 .49

2-5.7 = -3.7 13.69

10-5.7 = 4.3 18.49

8-5.7 = 2.3 5.29

7-5.7 = 1.3 1.69

S(Xi - X) = 53.43

Step 4

Definition:

Range = Max - Min

Median = Middle number when arranged low to high

Mode = Most common number

This Example:

Range = 10 - 2 = 8 minutes

Median = 6 minutes

Mode = 2 minutes

2

53.43

Square each one

Then Add All

s

=

s

=

7

-

1

Standard Deviation:

= 2.98 minutes

s

=

s

2

Step 3

Std Deviation is a measure of the inherent spread in the data

slide4

25

22

20

18

15

12

10

8

5

2

0

1.238

1.240

1.242

1.244

Bar Chart or Histogram

Provides a visual display of data distribution

Shape of Distribution May be Key to Issues

  • 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
slide6

Target

Specification Limit

3s

Std Deviation vs

Spec Limits

Area under curve

Is probability of

failure

1s

66807ppm

PPM = Part per Million Defects

Z is the number of Std Devs between the Mean and the spec limit. The higher the value of Z, the lower the chance of producing a defect

Z = 3s

Much Less

Chance of

Failure

1s

3.4ppm*

* Assumes Z is 4.5 long term

Normal Distribution

Z = 6s

area under distribution curve yields probabilities
Area under Distribution Curve Yields Probabilities

34%

34%

2%

2%

14%

14%

-2s

-3s

+2s

+3s

-1s

m

+1s

Characterized by Two Parameters

m and s2

Normal Distribution = N( m,s2 )

life cycle of a component
Life Cycle of a Component

Standard Normal Distribution

Apply

Transformation

Standard Normal Distribution

Original Distribution

x-m

Z=

Area under Curve =1

s

m-s m m+s

-1 0 1 Z

X

Examples:

Z = +1.0 is one Standard Deviations above the mean

Z= -0.5 is 0.5 Standard Deviations below the mean

1 sided normal distribution probability table

Z

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

0.005.00e-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-001

0.10 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-001

0.20 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-001

0.30 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-001

0.40 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-001

0.50 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-001

0.60 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-001

0.70 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-001

0.80 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-001

0.90 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-001

1.10 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-001

1.20 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-002

1.30 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-002

1.40 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-002

1.50 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-002

1.60 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-002

1.70 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-002

1.80 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-002

1.90 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-002

2.10 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-002

2.20 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-002

2.30 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-003

2.40 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-003

2.50 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-003

2.60 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-003

2.70 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-003

2.80 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-003

2.90 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-003

3.10 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-004

3.20 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-004

3.30 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-004

3.40 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-004

3.50 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-004

3.60 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-004

3.70 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-005

3.80 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-005

3.90 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-005

4.10 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-005

4.20 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-006

4.30 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-006

4.40 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-006

4.50 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-006

4.60 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-006

4.70 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-007

4.80 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-007

4.90 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

normal distribution cont
Normal Distribution (cont.)

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

5.002.87e-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-007

5.10 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-007

5.20 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-008

5.30 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-008

5.40 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-008

5.50 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-008

5.60 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-009

5.70 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-009

5.80 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-009

5.90 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-010

6.10 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-010

6.20 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-010

6.30 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-011

6.40 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-011

6.50 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-011

6.60 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-011

6.70 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-012

6.80 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-012

6.90 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-013

7.10 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-013

7.20 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-013

7.30 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-014

7.40 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-014

7.50 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-014

7.60 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-015

7.70 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-015

7.80 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-015

7.90 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-016

8.10 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-016

8.20 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-017

8.30 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-017

8.40 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-017

8.50 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-018

8.60 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-018

8.70 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-019

8.80 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-019

8.90 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-020

9.10 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-020

9.20 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-021

9.30 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-021

9.40 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-021

9.50 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-022

9.60 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-022

9.70 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-023

9.80 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-023

9.90 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

slide12

(with ± 1.5  shift)

PPM Defects

1,000,000

Tax Advice

(phone-in)

(140,000 PPM)

Restaurant Bills

100,000

Doctor Prescription Writing

Restaurant Checks

10,000

Average

Company

Airline Baggage Handling

1,000

100

AircraftCarrier Landings

10

Best-in-Class

1

6

2

3

4

5

7

Z

Domestic Airline Flight

Fatality Rate

(0.43 PPM)

Examples of Fault/Failure Rates on

The Sigma Scale

shift and drift
Shift and Drift

Short Term Capability Snapshots of the Product

Over time, a “typical” product process may shift or drift by ~ 1.5

. . . also called “short-term capability”

. . . reflects ‘within group’ variation

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

USL

Two Challenges:

Center the Process and Eliminate Variation!

slide14

Z Value vs Probability of Failure or Defect

1 Sided Normal Distribution

Industry Accepted 6 sigma quality level

slide15

Exponential Distributions

= Reliability

= Time

definitions
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: lis in failures/time, and t is time
  • Note: At T=0, R(0)=1.0 (100%)

lFIT = FITs = Failures per 109 hours

MTBF (years) = 1x109 / (lFIT * 8766 hours /year )

lMTBF = 1/MTBF = 1/Mean time between failure in time units

R(t) = e-lt, Note: lMTBF in hr-1 and t in hr

definitions1
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: lis in failures/time, and t is time

Note: At T=0, R(0)=1.0 (100%)

F(t) = (UnReliability at Time t or Failures at Time t) = Fraction of population that has failed at Time t, probability that a given system will fail for a time period “t,” assuming constant failure rate;

F(t) = 1-e-lt, Note: lis in failures/time, and t is time

Note: At T=0, F(0)=0.0 (0%)

weibull or 2 parameter distributions
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,”;

  • R(t) = e-(t/h)b, Note: his 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
    • = (/h)(t/h)-1
    • R(t) = e-(t/h)b
    • F(t) = 1-e-(t/h)b
typical reliability plot using weibull dist
Typical Reliability Plot using Weibull Dist
  • = (/h)(t/h)-1
  • F(t) = 1-e-(t/h)b

F(t) = (1 – R(t))100%

Time to Failure(s)

At some time, t, 100% of the population will fail

typical reliability plot assuming weibull dist
Typical Reliability Plot assuming Weibull Dist
  • = (/h)(t/h)-1
  • R(t) = e-(t/h)b
  • F(t) = 1-e-(t/h)b

Time to failure plot using Weibull tool

Decreasing

Failure Rates

<1

Increasing

Failure Rates

>1

The Bathtub Curve

Constant

Failure Rates

=1

Exponential Distribution

Failure Rate, 

Weibull slope indicates where the product may be on the bathtub curve.

Early

Life

Wear out

Useful Life

Time

slide21

Reliability Targets… Allocation & Flow-down

  • Stress Model…. Actual vs Accelerated
  • Failure Modes & Opportunities, Assess the Technology!
  • HALT… Test Capability of Design
  • Root Cause…Autopsy Failures, Understand the Physics!
  • Design-Process Changes
  • Qualification Testing
  • Fault Tolerant Design
  • Asm & Test Standards
  • ESS Strategy & Capabilities
  • Field Replaceable Modularity

POF Approach

POF = Physics of Failure

Additional Keys to High Reliability

Key Strategies in Design for Reliability (DFR)

slide22

Some Typical Stresses – Most Can be Accelerated

    • 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
overview of printed circuit board technology
Overview of Printed Circuit Board Technology
  • Basic Types of PCB-Component Assembly Technology
    • Thru Hole (TH) using prepackaged devices
    • Surface Mount (SMT) using prepackaged devices
    • Micro-electronics including bare die and prepackaged devices
  • 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)
  • PCB Surface Metalization Finishes
    • HASL – Hot Air Solder Leveling (SnPb solder 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
typical pcb interconnections
Typical PCB Interconnections

Device

NiAu Pad

Thin Epoxy Solder Mask

SnPb or SAC Solder Joint

Copper

FR4 Laminate

interconnection assembly processes
Interconnection Assembly Processes
  • Connectors and other Mechanical Interconnections
  • Soldering
    • Hand Soldering of wires and manually assembled devices
    • Reflow Soldering of Surface Mount on PCBs (SMT) using “solder paste” or preformed solder balls
    • Wave Soldering of Thru-Hole Devices on PCBs
  • Wire Bonding (Small Ag and Al wire-welding)
    • Inside IC Package from Die to Leadframe or Substrate
    • From Die to Die or Die to PCB Substrate as in Multi-Chip-Modules (MCM)
    • Inside Multi IC Packages from Die to Die
  • Adhesive Bonding
    • Conductive Epoxy (Au or Ag filled epoxy) used similar to solder
    • Compressive Displacement (CD); non-conductive epoxy shrinkage holds conductors together
    • Anisotropic Conductive Film (ACF); heat-pressure activated conductive adhesive strips sometimes used to bond flex circuits to flat-panels
slide26

Causes of Electronic Systems Failure

Reliability ofElectronic Circuits

  • 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
slide27

PCB Assembly Failure Mechanisms

  • Stresses & Major Factors
    • 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
    • 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
slide28

PCB Assembly Failure Mechanisms

  • Stresses & Major Factors - continued
    • 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.
printed circuit board assemblies
Printed Circuit Board Assemblies

CTE Mismatches in PCB Assemblies

Si Die CTE = 2.8e-6/C

Gold CTE = 14.2e-6/C5 – 15 μ in.

NiAu Pad

Thin Epoxy Solder Mask

Nickel CTE = 13.4e-6/C> ~100 μ in.

Copper

FR4 Laminate

CTE = ~20e-6/C

Copper CTE = 16.5e-6/C> ~1.2 mil

SnPb Eutectic Solder Joint CTE = ~25e-6/C

common failure modes factors in electronics
Common Failure Modes & Factors in Electronics
  • PCB FAB VIA Cracking
  • Thermal Cycling Stress
  • Fab Insulation Materials
  • Optimize Aspect Ratio
  • Optimize Plating, Drill
  • Area Array (BGA) Voiding, Crack Propagations
  • Thermal Cycling Stress
  • Optimize Reflow Profile
  • Pad-Via Design
  • 100% 3D Xray Automatic Optical Inspection
  • Flex Trace Cracking
  • Mech Bend Stress
  • Cu Annealing Selection
  • Flex Adhesive Selection
  • Strain Relief Process
  • Materials Durability
  • Hi Temp-Humid, Shock & Vibration Stresses
  • Metal Interactions
  • Ionic Cleanliness
  • Bearing Designs in Fans
  • Vertical Height of COG of Components
rohs new materials new failure modes
RoHS  New Materials  New Failure Modes
  • Tin Migration
  • Voltage-Humidity Stresses
  • Caused by Pb Free (SAC305) Flux Residuals
  • High Density Interconnect Failures
  • Caused by Flux Residues
  • Voiding in Solder Joints, Underfills
  • Crack Propagations
  • Compromising Reliability
key elements design for reliability plan
Key Elements: Design-For-Reliability Plan
  • Allocation/Flowdown of Targets
  • Quantification of Technology/Failure Opps
  • Life Stress Quantification, Accel Factors
  • Fault Tolerance in Detailed Design
  • Modular Serviceability in Detailed Design
  • Use of Military & Industrial Hi Reli Stds & Guides – ex. MIL-STD-883, IPC-A-610 Class 3
  • Early Component & Asm Level HALT
  • Autopsy to Lowest Root Cause, Design Out
  • Formal HAST/ Life Qualification Testing
  • Environmental Stress Screening in Mfg (ESS)
slide33

100 %

75 %

50 %

25 %

0 %

100 %

75 %

50 %

25 %

0 %

Electronic Assembly Quality

key elements design for reliability plan1
Key Elements: Design-For-Reliability Plan
  • Allocation/Flowdown of Targets
  • Quantification of Technology/Failure Opps
  • Life Stress Quantification, Accel Factors
  • Fault Tolerance in Detailed Design
  • Modular Serviceability in Detailed Design
  • Use of Military & Industrial Hi Reli Stds & Guides – ex. MIL-STD-883, IPC-A-610 Class 3, AEC-Q100, etc
  • Early Component & Asm Level HALT
  • Autopsy to Lowest Root Cause, Design Out
  • Formal HAST/ Life Qualification Testing
  • Environmental Stress Screening in Mfg (ESS)
slide37

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 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 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.

statistics example ipc workmanship classes solder volume shape placement control

100 %

75 %

50 %

25 %

0 %

100 %

75 %

50 %

25 %

0 %

Statistics Example: IPC Workmanship Classes: Solder Volume, Shape, Placement Control
  • 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
  • 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
  • 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.

Min PTH Vertical Fill: Class 2 = 75% Class 3 = 100%

Ref: IPC-A-610, IPC-JSTD-001

bga void size and locations uniform void position distribution varying diameter
BGA Void Size and Locations,Uniform Void Position Distribution, Varying Diameter

Sampling_Grid

Position

Model

Solder_Joint_Radius

Void_Distance

Void_Radius

S

Void_Solder Interface Distance

S = Shell

Potential for Early Life Failure (ELFO) if S < D/10 = (solder_joint_radius)/10

S =Shell = solder_joint_radius – (void_distance + void_radius)

slide40

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 %

slide41
IPC (Void Size) Class vs Shell Size Relative Probabilities~ 2x more likely to exceed D/10 threshold with Class 2 vs Class 3

S = Shell

Depth

reliability prediction assume constant failure rate b 1 0
Reliability Prediction: Assume Constant Failure Rateb = 1.0
  • Basic Series Reli Method of an Electronic System:

Component 1

l1

Component 2

l2

Component i

li

Component N

lN

  • Each component has an associated reliability l
  • The System Reli lss is the sum of all the component l
  • lss = Sli
  • Reli l is expressed in “FITs” failure units
  • x FIT = x Failures/109 hours
  • Note: 109 hours = 1 Billion Hours
example mtbf not so good to use for reliability specification
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)
example mtbf not so good to use for reliability specification1
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!
intro to reliability evaluation
Intro to Reliability Evaluation
  • Basic Series Reli Method of an Electronic System:

Component 1

R1

Component 2

R2

Component i

Ri

Component N

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
slide46

Reliability R Flowdown Example

Drive System,

needs R= 0.9 at 10 years

System Level

Power supply

R = 0.94

Subsystem Level

Motor

R = 0.97

Control Card

R = 0.99

Component Level

Part

R=0.9999

Part

R=0.9999

Part

R=0.9999

Part

R=0.9999

Part

R=0.9999

Part

R=0.999

Part

R=0.999

slide47

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
more reason to use r t and not mtbf example
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.

intro to reliability estimation
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

reliability prediction methods standards
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
reliability prediction methods standards1
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
reliability prediction methods standards2
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
reliability prediction
Reliability Prediction
  • Basic Series Reli Method of an Electronic System:

Component 1

l1

Component 2

l2

Component i

li

Component N

lN

  • Above Reliability Prediction Model is flawed because;
    • Components may not have constant reliability rates l
  • lss = Sli
    • 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
595 standard stress factors
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
slide59

Part

Max Tr

Max Vr

pT

pV

pE

pQ

C1

105C

 50V

 2.082

 0.186

 2.5

 1.25

C2

105C

 50V

 2.082

 0.186

 2.5

 1.25

C3

85C

 15V

 3.773

 0.223

 2.5

 1.25

C4

125C

50V 

 1.548

 0.151

 2.5

 1.25

R1

120C

20V

 1.643

 0.232

 2.5

 1.25

R2

150C

6V

 1.249

 0.549

 2.5

 1.25

Zener Diode

100C

N/A

 2.318

1.0

 2.5

 1.25

Op Amp

125C

36V

 1.548

 1.0

 2.5

 1.25

74HCT14

125C

7V

 1.548

 1.649

 2.5

1.25 

LED

85C

N/A

 3.773

1.0

 2.5

  1.25

Example: Method A, 0-50C Ambient, Indoor Mobile, Distributor Components

+5VDC

C1 0.1uf 50V

Polyester

+12VDC

C4 0.1uf 50V

Ceramic

+5VDC

LED

Vf=1.5V

R1 2KW 1/4W

Brand A Metal Film

Vin

BPLR

OP AMP

R2 150W 1/4W

Brand B Metal Film

C2 0.1uf 50V

Polyester

74HCT14

5V 1W

Zener

C3 10uf 15V

Electrolytic

-12VDC

lFITS

10.29

10.29

552.2

1.46

0.83

1.50

23.18

67.73

217.77

106.16

991.37 Fits  115.1 Yrs MTBF

stress factors drive simple 595 standard deratings
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.
slide61

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 CLParts Quality:Select Either: Mil-Spec or Commercial/BellcoreQuantity 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

slide62

Example Reliability calculation using actual MIL-HDBK-217F

Failure rate of a Metal Oxide Semiconductor (MOS) can be expressed as

Parameters are listed in MIL Data base.

Temperature factor is modeled using Arrhenius type Eqn

595 charts are greatly simplified from actual parts count Reli

slide63

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 | | | |

parts count method reliability prediction drawbacks
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.
key elements design for reliability plan2
Key Elements: Design-For-Reliability Plan
  • Allocation/Flowdown of Targets
  • Quantification of Technology/Failure Opps
  • Life Stress Quantification, Accel Factors
  • Fault Tolerance in Detailed Design
  • Modular Serviceability in Detailed Design
  • Use of Military & Industrial Hi Reli Stds & Guides – ex. MIL-STD-883, IPC-A-610 Class 3
  • Early Component & Asm Level HALT
  • Autopsy to Lowest Root Cause, Design Out
  • Formal HAST/ Life Qualification Testing
  • Environmental Stress Screening in Mfg (ESS)
slide68

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

Repeat

slide69

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

slide70

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

slide72

Svante August Arrhenius

High Temperature Acceleration Factor

Modified Arrhenius Equation:

AT = Acceleration Factor

Ea = Activation Energy Depends on failure modes; incl electromigration, contamination, etc.

slide74

Voltage Stress Acceleration Factor

Modified Arrhenius Equation:

slide75

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

Au

Al fracture in wire bonds

4.0

4

PQFP Delamination / Bond Failure

4.2

ASTM 2024 Aluminum Alloy

4.2

Copper

5.0

Au Wire Bond Heel Crack

5.1

ASTM 6061 Aluminum Alloy

6.7

Alumina Fracture

5.5

Interlayer Dielectric Cracking

4.8-6.2

Silicon Fracture

5.5

Silicon Fracture (cratering)

7.1

Thin Film Cracking

8.4

Thermal Cycle Stress Accelerations

Primarily used to stress CTE mismatch, accumulated fatigue damage failures

Basic Coffin-Manson Equation – Temperature Cycle

SnPb Eutectic (single melting point) Solder Joint Creep Failure Application

AF = (DTs/ DTa)E

Where;

DTs = Stress Test Thermal Excursion Range oK

DTa = Application Thermal Excursion Range oK

E = Material Dependent Exponent

E = 1.9 – 2.7 for 63/37 SnPb Eutectic Solders

AF = Per Cycle Stress Test Acceleration Factor

slide76

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

slide77

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

slide78

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

slide79

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)

slide80

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)

Repeat

slide81

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

Repeat

reliability bathtub curve

LFailures/Time

infant mortality constant failure rate wearout

Time

Reliability Bathtub Curve
  • 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
slide83

Life Stress Models and Qualification

  • Specify Device Storage/Shipment Profiles:
  • Specify Device Heavy User Profiles:
    • Number of Power Cycles
    • Number of Thermal Cycles and Min-Max Excursion (oC) per cycle
    • Number, Amplitude (G force) and Direction of Mechanical Shocks
    • Amplitude (Grms), Duration (Hrs), Freq Range (Hz) and Direction (1, 2 or 3 axis) Mechanical Vibration
    • Total airflow volume (M3) and particulates (Kg)
slide84

The AEC-Q100 Standard

  • Developed by the Automotive Electronics Council (Mfgs and Suppliers)
  • Auto Manufacturers Pushing Infantile Defects from PPM (106) to PPB (109) levels
  • Based on understanding of physics of failures of integrated circuits and packages
  • Tests require specific sample sizes, lot numbers and have predefined acceptance criteria. Standard allows for “family” qualifications
  • Specific Life Stress Tests Include
      • Accelerated Environmental Stress
      • Accelerated Lifetime Simulations
      • Package Assembly Integrity
      • Die Fab Reliability
      • Electrical Verification
      • Defect Screening
      • Cavity Package Integrity
other industry quality reliability standards
Other Industry Quality/Reliability Standards
  • JESD22 Integrated Circuit Quality and Test Standard
  • TS16949 APAP-PPAP (Level 3) Automotive: Advanced Product Quality Plan, Production Part Approval Process
  • MIL-STD-883 Devices and Microelectronic Assemblies
slide87

More on Component DeratingIntentional limiting of usage stress vs rated capabilityVoltagePower

slide90

Physics of Failure: Accumulated Fatigue Damage (AFD) is related to the number of stress cycles N, and mechanical stress, S, using Miner’s rule

Exponent Bcomes from the S-N diagram. It is typically between 2 and 20

Example: Solder Joint

Shear

Force

voids

Effective cross-sectional

Area: D/2

Effective cross-sectional

Area: D

F

Applied stress:

Applied stress:

Let  = 10, then

AFD with voids will “age” about

1000x faster than AFD with no voids

Voids in solder joints

slide91

a

=

N

cycles

D

b

T

Failure Mechanism/Material

b

316 Stainless Steel

1.5

4340 Steel

1.8

Solder (97Pb/03Sn) T > 30°C

1.9

Solder (37Pb/63Sn) T < 30°C

1.2

Solder (37Pb/63Sn) T > 30°C

2.7

General Failure Mechanism

b

Solder (37Pb/03Ag & 91Sn/09Zn)

2.4

Ductile Metal Fatigue

1 to 2

Aluminum Wire Bond

3.5

Commonly Used IC Metal Alloys and

Au

Al fracture in wire bonds

4.0

3 to 5

4

Intermetallics

PQFP Delamination / Bond Failure

4.2

Brittle Fracture

6 to 8

ASTM 2024 Aluminum Alloy

4.2

Copper

5.0

Au Wire Bond Heel Crack

5.1

ASTM 6061 Aluminum Alloy

6.7

Alumina Fracture

5.5

Interlayer Dielectric Cracking

4.8-6.2

Silicon Fracture

5.5

Silicon Fracture (cratering)

7.1

Thin Film Cracking

8.4

Physics of failure: Thermal Fatigue Models

Coefficients for Coffin

-

Manson Mechanical Fatigue Model

The Coffin

-

Manson model is most often used to model mechanical failures

caused by thermal cycling in mechanical parts or electronics.

(Most electronic

failures are mechanical in nature)

N cycles = number of cycles to failure at reference condition

b = typical value for a given failure mechanism, a = prop constant

The values of the coefficient b for various failure mechanisms and materials

(derived or taken from empirical data)

Reference: “EIA Engineering Bulletin: Acceleration Factors”, SSB

1.003, Electronics

-

Industries Alliance, Government Electronics andInformation

Technology Association

Engineering Department, 1999.

slide92

a

=

N

cycles

D

b

T

Normal operating conditions cycling 15C to 60C (T=45C)

Plan for N Stress (Accelerated) cycles –40 to 125 C (T=165C)

Find Mean life at stress level MTTF=4570 hrs=0.5 yrs

Calculated acceleration factor and MTTF (and B10) @ normal stress:

AF = Nstress / Nuse = (DT/DT)b = (165/45)2.7 = 33.4

MTTF (use)=MTTF(stress)*AF = 4570*33.4 = 152638hrs = 17.4 yrs

slide93

b

- ( )

t / h

F(t) = 1 - e

Reliability Distributions are non-Normal, require 2 parameters

beta, b - slope/shape parameter

Intro: Weibull Distribution

ln ln (1 / (1 – F(t))) = b ln(t) – b ln(h)

F(t) = Cumulative fraction of parts that have failed

at time t

Y = b X + a

eta, h – characteristic life or

scale parameter

when t = h

F(t) = 63.2%

Knowing the distribution Function allows to

address the following problem (anticipated future failure):

What is the probability, P , that the failure will occur for the

period of time T if it did not occur yet for the period of time t ? (T>t)

P={F(T)-F(t)}/[1-F(t)]=

slide94

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)

= h G ( 1 + 1/b )

When b = 1.0, MTTF = h

When b = 0.5, MTTF = 2h

Cumulative Failure (%)

F(t)

MTBF = mean time between failure (repairable)

(MTBSC)

b

Slope =

= total time on all systems / # of failures

10

When there is no suspension data, MTBF = MTTF

B10

100

1

10

Time to Failure (t)

The slope parameter, Beta (b), indicates failure type

b < 1 rate of failure is decreasing infantile (early) failure

b = 1 rate of failure is constant random failure

b > 1 rate of failure is increasing wear out failure

slide95

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 / c2
  • 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%)
slide96

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
slide97

The calculations are based on the Binomial Distribution and the following formula:

where:

n

=

sample size

p

=

proportion defective

r

=

number defective

Confidence Level CL = 

=

probability of k or fewer failures occurring in a test of n units

Pass/Fail Test Sample Sizes?

Example:

Suppose that 3 failed parts have been observed in the test equivalent to 1 year life, what minimum sample size is needed to be 95% confident that the product is no more than 10% defective?

Inputs in the formula are:

p =0.1(10%), r = 3, CL = 0.95(95%), P(r<k) = 0.05 and calculate n.

The minimum sample size will be 76.

Reliability test should start using just a few parts in order to get preliminary number of failed parts. Using this data a required sample size can then be estimated.

slide98

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

slide100

Linear Correlation of Input to Output

1.4

1.2

1

0.8

mArms

0.6

Vrms

0.4

Output

0.2

0

0

0.5

1

1.5

Input

Plot or Scatter Plot

Used to Illustrate Correlation or Relationships

slide101

Pareto Chart

Root Cause Failures Example

Used to Illustrate Contributions of Multiple Sources

Excellent when data is abundant

slide102

Fishbone Diagram

Ambient Temp

Load Res

Line Voltage

Effect:

Temp

Of Amp

For example

Line Frequency

Volume

Input Amplitude

Illustrates Cause & Effect Relationship

slide103

Year to Date Summary

Replacement Parts Example

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