reliability estimation from accelerated degradation testing

Reliability Estimation from Accelerated Degradation Testing基于加速退化试验的可靠性估

计

Guangbin Yang (杨广斌), Ph.D.©2011 ASQ & Presentation YangPresented live on Jan 08th, 2011

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Reliability Estimation from

Accelerated Degradation Testing

Guangbin Yang (杨广斌), Ph.D.

Ford Motor Company, Dearborn, Michigan, U.S.A.

Email: [email protected]

基于加速退化试验的可靠性估计

2

Overview

ALT (Accelerated Life Test) and ADT (Accelerated Degradation Test)

Reliability Estimation from Pseudo-Lifetimes

ADT with Destructive Inspections

Takeaways

3

ALT Purpose and Test Method

The primary purpose of ALT is to estimate the

reliability of a product at the design condition in a

shorter time.

To do an ALT, a number of units are sampled and

divided into two or more groups. Each group is

tested at a different accelerating condition.

The test at an accelerating condition continues

until all units fail, or until a pre-specified time or

number of failures is reached.

4

ALT Data Analysis

The life data of all groups are combined to

estimate the reliability at the design condition

through an acceleration relationship.

t

S2

S1

0

acceleration

relationship

S0

S

5

Why ADT?

The time allowed for testing is continuously

reduced, and thus the test at low stress levels

often yields few or no failures. This is especially

the case when we test high-reliability products.

With few or no failures, it is difficult or

impossible to analyze the life data and make

meaningful inferences about product reliability.

In these situations, we should consider ADT.

6

What Products Are Suitable for ADT?

Soft failure: failure is defined by a performance characteristic degrading to an unacceptable level.

Degradation is irreversible; that is, the performance characteristics monotonically increase or decrease with time.

For convenience of data analysis, a product should have a critical performance characteristic, which describes the dominant degradation process and is closely related to reliability. Such a characteristic is fairly obvious to identify for many products.

7

ADT Method

ADT are similar to ALT. During ADT, however,

measurements of the critical performance

characteristic are taken at various time intervals.

Most ADT apply constant stress.

Other types of stress (e.g., step stress) may be

used, but are not common in practice because of

complexity in data analysis and stress application.

8

Methods for Degradation Data Analysis

Degradation data obtained at higher stress levels are used to estimate the reliability at the design level.

The estimation requires a degradation model that relates performance characteristic to aging time and stress level.

The primary methods for reliability estimation include Pseudo-lifetime analysis.

Random-process method.

Random-effect method.

9

Advantages of ADT

An ADT allows reliability to be estimated even

before a test unit fails. Thus an ADT greatly

reduces the test time and cost.

An ADT often yields more accurate estimates

than those from life data analysis, especially when

a test is highly censored.

10

Disadvantages of ADT

Reliability estimation from degradation data often

requires intensive computations.

An ADT requires frequent measurement of

performance characteristics during testing. This

increases workload if it cannot be done

automatically.

11

Reliability Estimation from

Pseudo Lifetimes

伪寿命及可靠性估计

12

Pseudo Life

A pseudo life is not an observation.

A pseudo life is obtained by extrapolating a

degradation path.

t

y

G

t1 tnt20 t0

13

Estimation of Life Distributions

0

y

S1S2

t

G

t21 t23 t11t13

14

Reliability Estimation from Pseudo

Lifetimes at the Design Stress Level

The methods for ALT life data analysis apply to

pseudo lifetimes.

The analysis can be done using commercial

software.

t

S2

S1

0

acceleration

relationship

S0

S

15

Application Example: Electrical Connector

Problem statement

Electrical connectors fail often due to excessive stress relaxation.

Stress relaxation can be measured by the ratio (%), where s0 is the initial stress and s is the stress loss.

For an electrical connector, failure is defined by the stress relaxation exceeding 30%.

Estimate its failure probability at the design life of 15 years and the operating temperature of 40C.

0/ ss

16


Test method

A sample of 18 units was randomly selected from a

production lot and equally divided into three groups.

Each group had 6 units.

The test temperatures were 65, 85 and 100C.

The censoring times were 2848 hours at 65C, 1842

hours at 85C, and 1238 hours at 100C.

17


Stress relaxation data

0

5

10

15

20

25

30

0 500 1000 1500 2000 2500 3000

t (hr)

100C

85C

65C

0s

s

18


Degradation model

where Ea is the activation energy, k is the

Boltzmann’s constant, A and B are unknowns.

Here A usually varies from unit to unit, and B is a

fixed effect parameter.

kT

EAt

s

s aB exp0

19


Linearized degradation model

At a given temperature, the degradation model

can be written as

where and

),ln()ln( 210 tss

,/)ln(1 kTEA a .2 B

20


The linearized degradation model is fitted to each

of the 18 degradation paths. 1 and 2 are

estimated for each unit using the least squares

method.

The pseudo lifetime of each test unit is calculated

from

.ˆ

ˆ)30ln(expˆ

2

1

t

21


The lifetimes at the three temperatures are

lognormal.

The shape parameter is reasonably constant.

22


Acceleration relationship

From the degradation model, we can assume the

acceleration relationship as

where is the lognormal scale parameter, T is the

absolute temperature, 0 and 1 are unknown

parameters.

,/10 T

23


Estimation of acceleration model parameters

Using Minitab (or other software), we obtain the

ML estimates:

,56.14ˆ0 ,35.83731 .347.0ˆ

24


Failure Probability at the Use Temperature

The estimate of the scale parameter at 40C is

Then the failure probability at 15 years (131,400 hours) is

.179.1215.313/35.837356.14ˆ

.129.0347.0

179.12)131,400ln()131,400(

F

25

ADT with Destructive Inspections

破坏性加速退化试验

26

Destructive Inspections

For some products, inspection to measure

performance characteristics must damage the

function of the test units.

Example 1: A solder joint must be sheared or pull off to

get its strength.

Example 2: An insulator must be broken down to

measure its dielectric strength.

After destructive inspection, units cannot restart

with the same function as before the inspection,

and are removed from testing.

27

Destructive Inspections

A unit is inspected once and generates only one

measurement.

The performance characteristics usually are

monotonically decreasing strengths.

The degradation analysis methods described

earlier are not applicable. Instead, the random-

process method can be used.

28

Test Method, Degradation Data, and

Analysis

t

y

G

t0

S2

S1

S0

29

Application Example: Copper Wire Bond

Problem statement

To reduce cost, it was planned to replace gold wire

with copper wire to provide an electrical

interconnection for a new semiconductor device.

The shear strength of wire bonds is the critical

characteristic. If it is less than 15 grams force, a bond is

said to have failed.

We wanted to estimate the reliability of the wire bonds

after the use of 8500 cycles at a temperature profile of

–25C to 75C.

30

Application Example: Copper Wire Bonds

Test plan

GroupSample

Size

High T

(C)

Low T

(C)Inspection Cycles

A 100 125 –55 50, 100, 300, 600, 900

B 100 110 –45 100, 300, 600, 900, 1200

C 100 95 –35 300, 600, 900, 1200, 1500

31


Shear strength dataShear

Str

ength

(gf)

C1500

C1200

C900

C600

C300

B1200

B900

B600

B300

B100

A900

A600

A300

A100

A50

100

80

60

40

20

0

15

32


Lognormal fits to the strength data of group A

Shear Strength

Per

cent

12080604020105

99

95

90

80

70

60

50

40

30

20

10

5

1

A50

A100

A300

A600

A900

33


Lognormal fits to the strength data of group B

Shear Strength

Per

cent

1201008060402010

99

95

90

80

70

60

50

40

30

20

10

5

1

B100

B300

B600

B900

B1200

34


Lognormal fits to the strength data of group C

Shear Strength

Perc

ent

1201008060402010

99

95

90

80

70

60

50

40

30

20

10

5

1

C300

C600

C900

C1200

C1500

35


Plots of estimates of µy vs. log inspection cycles

for all groups

2

2.5

3

3.5

4

4.5

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

Group A

Group B

Group C

ln(t)

y

36


Degradation model

The effect of thermal cycling is often described by the

Coffin-Manson relationship. From the previous plots,

we have

where T is the temperature range.

Multiple linear regression analysis suggests this model

is reasonable.

),ln()ln( 321 Tty

37


Estimation of model parameters

Consider the degradation model as a two-variable

acceleration relationship, where t is also treated as

a stress. Using Minitab, we obtain

,1165.28ˆ1 ,6445.0ˆ

2 ,1416.4ˆ3 .2205.0ˆ y

38


Reliability at the use temperature profile

The estimate of y after 8500 cycles at the use

condition (T = 100C) is

The reliability at 8500 cycles is

9889.02205.0

2124.3)15ln(1

ˆ

ˆ)ln(1)Pr()8500(

y

yGGyR

212.3ˆ y

39

Takeaways

ADT is more efficient than ALT, and should be used whenever possible.

Pseudo-lifetime method applies to nondestructive

inspections.

Random-process method can be used for both

destructive and nondestructive inspections.

reliability estimation from accelerated degradation testing

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