Understanding the Technology

Guidance for accelerated testing and reliability—For electrical and electronic parts and equipment—
Toshio Yamamoto*Resources are continually being poured into efforts to improve the reliability ofelectrical and electronic parts and equipment. This has lead to the production ofa large number of highly reliable products, and brought about a sharp decline in
failure rates. Concretely evaluating product reliability requires extremely long periodsof time of environmental testing, specifically in the area of reliability testing. Thesetime constraints have created a need for accelerated testing that can produce effective
results in shorter periods of time. However, accelerated testing cannot be achieved bymerely ratcheting up the stress to shorten testing times, and this type of testing is notapplicable to every situation. Accelerated testing, just like other forms of reliability
testing, is a reliable test method supported by scientific logic.
In this report, we would like to present the logic behind accelerated testing in aneasily understandable way, from the standpoint of environmental testing used in thefields of electricity and electronics.

Contents
1. Introduction
2. Definitions, prerequisites, and fundamentals
3. Accelerated testing and the physical chemistry of product failure
3-1 Stress-strength model
3-2 Chemical kinetics model
3-3 Applying chemical kinetics
4. The relationship between accelerated testing and predicting product life
5. Constructing accelerated tests
5-1 The acceleration factor
5-2 Constructing conditions for an acceleration test (1)5-3 Constructing an acceleration test (2)6. Conclusion*Technical Planning Department
ESPEC TECHNOLOGY REPORT No. 8

11. Introduction
The details of environmental testing differ according
to the type of product, and no one test method can serve
for all products. We could go so far as to say that eachindividual product requires its own test procedure. Within
the category of reliability testing, environmental testingnormally focuses on determining whether a product canfully display and maintain its established functions
within the marketplace environment of actual use after
the product has been shipped from the factory. This
testing is done from the standpoint of technology directly
related to the product. However, even the same types of
products face a variety of environments in themarketplace, including how the individual product may
be used. Because products meet such conditions, eachtype of environmental test has its own significance.
However, accelerated testing is not created by merely
increasing the stress in a rush for results. Such methods
will simply create destruction testing. Because of this,
we must thoroughly understand the principles ofaccelerated testing, carefully construct the logic involved,
and create a method in which no contradictions arise in
the testing procedure.

2. Definitions, prerequisites, andfundamentals
According to “JIS (Japanese Industrial Standard)
Z 8115 Glossary of terms used in reliability”, accelerated
testing refers to “a test in which the applied stress levelis chosen to exceed that stated in the reference conditions
in order to shorten the time required to observe the stressresponse of the item.” In general, the more severe theconditions in relation to standard conditions, the more
quickly it is possible to complete the test. However, it
would be premature to conclude that we have proven the
excellence of a product simply because it has enduredan accelerated test. A product that has successfully
endured extremely severe conditions may fail in a
relatively short time under the same type of stressconditions that are considered extremely mild. We must
create a test plan for all methods of use and surrounding
environments that can be imagined, and we must carryout complete pre-test studies and check for
misconceptions in logic, and make sure we haven’t
missed anything.
To start with, there is always a cause for each type of
product failure. Unless there has been severe misuse,such failures do not merely appear out of the blue. Seenfrom a qualitative standpoint, the failure of electrical andelectronic products, and electronic equipment inparticular, begins when changes are experienced in thephysical and chemical characteristics of the materials
used in their production. Such changes can be caused byan intrusion from the external environment, or frominternal factors, or from a combination of both internaland external factors. These physical and chemical
reactions are affected by the surrounding environment(heat, in particular), speeding the reaction, and the
product functions are weakened are weakened orcompletely stopped in the course of achieving2

equilibrium in that reaction. Therefore, accelerated
testing consists of speeding up this physical and chemical
process with suitable ambient environments, causing
malfunctions to appear.
Accelerated testing characteristically entails knowing
in advance the results of testing when deciding to run
the tests, because one must establish what is being
accelerated in relation to what, and clearly establish theitems that serve as the basis for acceleration. Essentially,
accelerated testing is not a means for ferreting out newmodes of failure, but rather serves as a time-saving meansof confirming phenomena that have already been
identified. Therefore, major premises have already been
proposed concerning the factors involved in failure andthe mechanism leading to failure. Only when expected
results are obtained do the conclusions form accelerated
testing. Then, by recording the test preparations andaccumulating the data, it finally becomes possible toapply the procedures to similar products. However, there
are no accelerated tests that can be applied indiscriminately to all products and failure modes. For
example, if the relation between the failure mode andthe acceleration mechanism is not known and we justexpose a new product to severe conditions and cause theproduct to fail, the only result will be that we havedestroyed the product. We will not be able to obtain any
scientifically valid data at all from such testing. We must
remember that accelerated testing, as one form of
reliability testing, is a very specific technical method.
To sum up, accelerated testing consists of, “accelerating the mechanisms causing product failure by using
conditions that are more severe than standard conditions,and saving testing time by utilizing the systematic natureexisting between the standard conditions and theaccelerated conditions in the identical mode of failure.”
In other words, the absolute prerequisites to accelerated
testing are:(1) Having the same product failure mode, and(2) Having a systematic relationship between standard
conditions and accelerated conditions.
Care must also be taken in the following matters when
performing accelerated testing.
(1) The test must be based on the main points whose
results have been predicted by thoroughly examining
the problems.
(2) The test conditions must be constructed on the basisof thoroughly grasping the usage conditions and theambient environment of the product.
(3) When special prerequisites exist, they must be dealt
with, but one should always try to gather universal
data that can be applied in the future.
The most important condition of all is to clarify exactly
the purpose for running the test. In other words:(1) The test presumes a correlation with conditions in
the field. (Conditions are within the product ratings,
and the test aims at forecasting or reproducing failuresthat occur in the field.)(2) The test attempts to detect the characteristic
weaknesses of the product. (With the aim of collecting
data to discover and improve product weaknesses)
ESPEC TECHNOLOGY REPORT No. 8

(3) The test simply attempts to confirm productdurability. (Durability is confirmed outside theproduct rating.)

expresses the thermal transition. In 1899, S.T. Arrehnius
proposed the formulaK = Λ [exp (–B/T )]3. Accelerated testing and the physicalchemistry of product failure
The physical chemistry of product failure in electricaland electronic equipment can be broadly grouped into
approximately 30 categories, or more specificallyclassified into about 70 categories. The mechanisms
leading to failure have mostly been elucidated.
Therefore, the method of planning accelerated testingor analyzing product failure quite often consists of
selecting the appropriate mechanism leading topredicted failure from among these categories, and thenverifying the pre-selected or pre-constructed failure
model.
First of all, to capture the general concept of failure
occurrence, the stress-strength model is briefly checked,
and then great emphasis is placed on the chemical
kinetics model, which is extremely easy to understandfor accelerated testing.

3-1 Stress-strength modelThis model explains the process leading to failure
through the relationship between the characteristic
durability of the product and the stress from the ambientenvironment. (Failure occurs in the areas in which
deterioration of durability and distribution of stressoverlap.)

Strength-stressth n
ng tiore ribuh ont
gt rati
S ist
n
d
re io
St eterd S

Strength distributiontdisrength
wid tributio
ens n

Wide
margin ofsafetyFailure occurrence(Section with overlapping distribution)

Failure occurrence

Stress distribution
0

Stress distributiontTimeFig. 1 Stress-strength model

3-2 Chemical kinetics modelThis model is based on the chemical reactions
between the molecules of matter within a solid, andutilizes the principle that the existence of backgroundheat strongly influences the initiation and the progressof the reaction. For example, when hydrogen and oxygen
react to form water, the higher the temperature, thegreater the speed of the chemical reaction.
The Arrehnius model is the model that most directly
ESPEC TECHNOLOGY REPORT No. 8(3.1)

Where T represents temperature (absolute temperature) and K represents the speed of the chemical
reaction. This formula shows strong conformity to test
results.
Formula (3.1) can also be written in the followingway.
K = Λ [exp (–E/RT )](3.2)
Here, Λ and E represent individual constants for thereaction conditions. Λ is called the frequency factor, andE is called the apparent activation energy. R is theBoltzmann constant, and by writing this another way, it
can be done in the same manner as the MaxwellBoltzmann distribution, which specifies the energy
distribution of the gas molecules. When the chemical
reaction is primary, contains the [time]–1 dimension,
so it is called the frequency factor. The fact that E ispositive in this formula means that rising temperature
increases the speed of the chemical reaction, and thegreater the value of E, the greater the speed of thechemical reaction.
As the temperature of a gas rises, the motion velocity
increases in the molecules that make up the gas.
However, the gas contains a mixture of fast-moving andslow-moving molecules, and if we posit that the velocity
distribution conforms to the negative exponential
distribution in relation to (1/T), then in particular theactivated molecules abounding in energy are what is
actually contributing to the reaction, and the proportionof activated molecules increases markedly along withrising temperature. It has been proposed that thechemical reaction between two gases can only becontributed to by molecules with relative motion energythat exceeds activation energy level E. Therefore, in
isothermal reactions in this type of molecular collision
between two gases, the explanation of formula (3.1)
applies to the proportion of exp(–E/RT), which is the
proportion of activated molecules with energy above acertain energy limit value. However, because this theory
cannot be properly applied to more complex reactions
in which numerous molecules participate, in 1935 H.
Eyring and E.H. Eyring proposed the absolute reaction
theory that was developed from this approach.
This approach holds that activation energy is the main
factor in reaction velocity, and that this can be separated
into activation energy and activation entropy. When T
represents temperature stress and S represents otherstress, reaction velocity K becomesV

Details and procedures will vary, depending on the
purpose of the test, and different types of test andmeasurement equipment will be used.

K = Λ [exp (–B/T )]S α(3.3)

This is known as the Eyring formula. This formula isfrequently used in the field of electrical and electronicequipment. However, no theory has yet been establishedthat can account for all chemical reactions. Here, α
becomes the constant.

3

3-3 Applying chemical kinetics
Let’s try to adapt these formulas to the field ofelectrical and electronic equipment reliability. Using
the aforementioned stress-strength model, we canconceptually grasp the process in which physicalchanges resulting from stress such as temperature andvoltage reduce durability and lead to failure. Can
chemical kinetics be applied to explain this type ofphenomenon?
If we express the level of stress applied to a productas x and the level of resulting deterioration as y, and if
we regard y as a function of x, then we can express thefollowing relationship.

L2 = L1 exp[B(1/T2 –1/T1)]= L1 exp[E/R(1/T2 –1/T1)]

When there are multiple sources of stress, we must
regard x as a vector, but to simplify matters, we canmake it scalar.
Deterioration with age dy/dt signify reaction
velocity, so we can express this as
dy
—=K
dt

(3.4)

Here, when K is a constant, if we integrate formula(3.4), we get y = Kt. Now, if we set L as the time inwhich deterioration level y reaches product proof stresslimit r, then the y = Kt relationship yields therelationshipL = r/K(3.5)
Next, if we substitute formula (3.3) for this formula,
we getL = [(r/Λ )exp(B/T )]S –α(3.6)
At this point, we can think of the product being
operated. If we have the following two instances,(1) Stress voltage is V 1 , operating temperature is T1
and the corresponding life is L 1, and the failure
rate is λ1(2) Stress voltage is V 2 , operating temperature is T2
and the corresponding life is L 2, and the failure
rate is λ2
Using formula (3.6), we can show both relationshipsas
V2 –α
L2 = L1 exp[B(1/T2 –1/T1)] • —
V
1

(3.7)

If we attempt to express this as a failure rate, themean life L and the failure rate λ of the electrical andelectronic equipment have an inverse function
relationship, and so the above formula becomesV2 α
λ 2 = λ 1 exp[–B(1/T2 –1/T1)] • —
V1

(3.8)

In the above formula, V2/V1 = S is called the stressratio.
When α = 0 in formula (3.7), this becomes the
Arrhenius formula, and is often adapted to(3.9)

In other words, the rate of acceleration (the acceleration
factor) can be found with the following formula.
L2
E 1
1
Ac = —= exp — — – —
L1
R T2
T1
L2
E 1
1
or ln —
= — — –—
L1
R T2
T1

y = φ (x)4temperature-dependent deterioration phenomena, and isuseful for establishing the acceleration factor when
performing accelerated testing.
In other words, formula (3.7) can be rewritten in thefollowing way.

(3.10)The Arrehnius model is widely applied to reliability
testing and failure analysis of electrical and electronicequipment, especially to semiconductor devices. That is
to say, semiconductor devices are manufactured using
physical and chemical changes in the surface layers ofmaterial, and rather than having a structure of complete
crystallization or solidification, they are combined in an
amorphous state. Because of this, the changes that appear
tend to be chemical rather than physical changes, and sochemical theory is considered easier to apply.

4. The relationship between accelerated
testing and predicting product life
At this point, we would like to take up a very simple
example and examine it using numerical values.
From the standpoint of environmental conditions, weshall set the following theme. “What levels of acceleration
are possible if instead of using a TH (Temperature and
Humidity) test with test conditions of 85°C and 85 percent
RH, we substitute a HAST (Highly Accelerated
Temperature and Humidity Stress Test) with test conditionsof 120 to 140°C and 85 percent RH? Also, using thoseresults, to what level of reliability can we predict productlife in the field?”
As a precondition, these are temperature and humidity
tests, and in detailed analysis the water vapor pressure
differential is required as an environmental condition.
However, to simplify the explanation, let’s say the relative
humidity is proportional to the temperature, and utilize
the common value and just do away with the humidity
parameters. (There has yet to be a theory establishedproving the humidity relationship. Perhaps water vapor
pressure corresponds to the amount of intruding water
vapor. Water vapor and water are physical matter, and so
this activity level is thought to correspond to the temperature.)First of all, let’s look at the first of the two formulas informula (3.10).
E 1
1
L2
Ac = —= exp — — – —
L1
R T2
T1

ESPEC TECHNOLOGY REPORT No. 8

If we say that R = 8.615 × 10 –5 (eV/K), the above
formula becomes the following.

5. Constructing accelerated tests
5-1 The acceleration factor

1
1
Ac = exp 1.16 × 104 × E × — – —273 + T85 273 + THAST(3.11)
If we insert the various temperatures into this formulaand do the calculations, we obtain the acceleration
factors in Table 1 depending on the different values for
E.
Table 1 Acceleration factors for TH tests in HAST
E (e V)

HAS T

0.6

0.8

1.0

1.2

1.5

110°C

3.56

5.43

8.29

12.7

23.9

120°C

5.65 10.1

17.9

31.9

75.8

130°C

8.77 18.1

37.3

76.6

228

140°C

13.3

74.8

177

647

31.6

Note: The values of E, the activation energy, are values obtained fromtypical failure modes of semiconductor devices, but please regard
these numerical values as strictly hypothetical.

Next, from the results of HAST (130°C and 85 percent
RH), let’s try to predict the corresponding product life
for a product submitted to the test, and let’s say that the
product will be used in Japan in a typical Japanesesummer environment of 35°C and 85 percent RH. Let’stake the lower limit for the value of E as 0.8 and theupper limit as 1.0.
Predicted life when E = 0.8

11
LE=0.8 = exp 1.16 × 104 × 0.8 × — – —273 + 35 273 + 130=1268.512

approximately 1200 times

Predicted life when E = 1.0

11
LE=1.0 = exp 1.16 × 104 × 1.0 × — – —273 + 35 273 + 130=7570.39

When we discuss accelerated testing, our immediate
greatest concern is the acceleration factor.
By the way, we are often told, “We would like toperform humidity endurance testing for a certain product,
but at what level should we estimate the acceleration
factor, and what test conditions should we use?” Well,there is no acceleration test that corresponds unconditionally even to any one product, and moreover, there
is no acceleration factor that can be applied unconditionally with no preconditions at all. The related
references and research papers contain notations ofacceleration factors as test results for specific products,
and for those of you who are considering testing this may
look like something you just “gotta have”, but wait just a
minute. Previously, we introduced the matter of“preconditions”. Do those references and research papers
include the details of those “preconditions”? Unfortunately, in most cases those preconditions simply don’t
exist, and the details of the course and conditions of thetest have been omitted. As these are not completely
hypothetical discussions, they should serve as a reference,but they are, after all, other people’s data, and you’ll haveto decide for yourself whether you can rely on them inyour own circumstances.
There are three variables (E, T 1, and T 2) in formula(3.10), given earlier for finding the extremely simple
acceleration factor. We have nothing to say at this point
about T 1 and T 2 , but E is crucial. It is the value foractivation energy, and as we saw in the previous example,
even a slight change in this value can yield a prediction
for product life that is about six times longer. Therefore,
the actual value of E must be found at all costs from theexperimental data itself.
Well, how should we go about finding the value of E?

5-2 Constructing conditions for an
acceleration test (1)First of all, rather than indulge in excessive
explanations, let’s try to solve the following example.

approximately 7500 times

Therefore, if we perform a 48-hour test using theabove test conditions, and we say that failure did notoccur, the product life in the field would be:
For E = 0.8: 48 × 1200 = 57,600 hours = 6.5 equivalent
years
For E = 1.0: 48 × 7500 = 360,000 hours = 41.0
equivalent years

ESPEC TECHNOLOGY REPORT No. 8

Question
Preliminary testing of a certain product found that the
MTTF (mean time to failure) was 310 hours at 150°C,
1000 hours at 125°C, and 4000 hours at 100°C. Let’s
hypothesize that the failure mechanism for this productdoes not change at temperatures between 75 and 150°C,
and answer the following questions.
(1) Find the activation energy, then find the MTTF at
75°C.
(2) Indicate whether a test should be run to find how many
hours MTTF will be at 125°C to prove that MTTF is
5000 hours at 75°C.

5Answers(1)a) First of all, arrange the preconditions as follows.
L150 = 310-hour life at 150°C
L125 = 1000-hour life at 125°C
L100 = 4000-hour life at 100°Cb) Next, using the second of the two formulas in(3.10), change the formula to find E.
L2
E 1
1
ln—
= — —–—L1
R T2 T1
R(ln L100 / L150)
E =—
1
1
—–—
T100 T150(3.11)
If we substitute the actual values in formula (3.11),
we get
8.615 × 10–5(1n 4000 /310)
E=—
1
1
—–—
273 + 100 273 + 150= 0.68(eV) ... the activation energyc) Since we have found the activation energy, let’s
see what sort of ratio exists between L100 (T = 100°C)
and L75 (T = 75°C).
L75
0.68
1
1
ln—
=— — – —L100 8.615 × 10–5 273 + 75
273 + 100
= 1.523∴L75/L100 = exp 1.523=4.59 (the acceleration level
between L75 and L100)
Since the MTTF is 4000 hours when T = 100°C, we
can find the MTTF when T = 75°C by calculating
4000(hr) × 4.59 = 18,360(hr).
(2)
Using the MTTF for T = 75°C found above in part(1), find the acceleration factor between L75 and L125.

Ac = L75/L125 = 18,360hr/1,000hr = 18.36

Therefore, to prove that MTTF is 5000 hours attemperature conditions of 75°C, the conditions at
125°C would be 5000(hr)/18.36 = 272.33(hr). In otherwords, a test of approximately 272 hours would be
required.
(When solving this sort of problem, in addition tomethods such as the above relying entirely upon using
formulas to calculate the answers, one can also use
the Arrehnius plot using semi-logarithmic paper. Dueto space limitations we cannot deal with that methodin this report.)

6

5-3 Constructing an acceleration test (2)From the example in section 5-2, we have seen an
overview of how to construct an acceleration test.
Namely,(1) Since product tolerances for the ambient environment
are set in the product planning and design stage,
pretesting should be done, and just as in this example,
test conditions should be separated into several stages
to find the MTTF.
(2) In an attempt to shorten testing time, these pretests
are begun from temperatures thought to be at theupper limits of product heat endurance. However, youhave a small number of specimens and you arecollecting a wide variety of technical data in thecourse leading up to product failure, then you should
start from low temperatures. In the example,
acceleration testing was constructed for tests at low
temperatures, but if the product has a hightemperature tolerance, then high temperatures can beused to find test times.
(3) Perform failure analysis for products that fail at eachstage, and analyze the mechanism leading to failure.
Since obtaining identical failure modes is aprecondition for accelerated testing conditions, it isextremely important to check analysis work andresults. (At this time, it is also important to analyze
products that did not lead to failure. A comparison ofgood products with failed products can be aconclusive factor in determining product quality, andcan also be a basis for improvement measures.)(4) As you can see, the conditions for accelerated testing
are determined at the stage of pretesting and analyzing
the pretest results. More time is required forconstructing an accelerated test than for carrying out
the test. When there are no systematic relations, there
can be no accelerated testing.
(5) The following two methods are used to reveal
acceleration. In the example, we used method number
1 below to calculate acceleration.
1. One method is to use proportionate time and attainan equivalent cumulative failure rate to compare
accelerated testing and tests run at standard
conditions.
Time required at standard
Degree of = conditions
acceleration
Time required at accelerated
conditions

2. Another method is to use proportionate time forthe failure rate at a specific time to compare
accelerated testing and tests run at standard
conditions.
Failure rate at accelerated
Degree of = conditions
acceleration
Failure rate at standard
conditions
In general, the first method is more widely used.

ESPEC TECHNOLOGY REPORT No. 8

6. Conclusion
When considering accelerated testing from thestandpoint of the reliability of an individual product, thepreceding examples show that it can be relatively
dangerous to assume that you can just use the same test
conditions that another company has used. In particular,when applying the chemical kinetics model, the key tosuccess is the value of E, the activation energy, and thisvalue can be assumed to vary with different products.
Even among products with the same types of functions,
there will be slight variance among different manufacturers in raw materials, design details, andmanufacturing methods. This “slight variance” can havea considerable impact on the value of E.
If you should feel that, “It’s the same type of product,and seen from the current level of technology, there
should be very little difference from our company inmaterials, design details, and manufacturing methods,”
we must concede the possibility of opening reference
literature or other research papers and utilizing the valuesof E given there. However, it will not be possible toascertain whether these values are actually applicable toyour company’s product. You should keep in mind thatthe reliability testing results and the predicted life
calculated using these values may be lacking in accuracy.
Up to this point we have been discussing individual
accelerated tests, but actually it is possible to predict the
failure rate without relying on testing, though this islimited to electronic parts. This can be done by using
such procedures as MIL-HDBK-217F Reliability
prediction of electronic equipment, and the Bellcore
TR332 ISS05 Reliability prediction procedure. The
former, being “MIL” naturally is used by the US militaryfor electronic parts, but since it is based on field data, it
has a high level of precision, and is very useful as areference. However, it requires some modification for
application to civilian parts. The latter is based on MILHDBK-217, and consists of purchasing specifications
establishing an independent evaluation method.

[Bibliography]
1) Hisashi Mine, “Reliability Technology to Make Troubles Zero”,
Union of Japanese Scientists and Engineers Publication, (1990)
2) Hisashi Mine, Kiyoshige Echikawa, “Reliability Test of Electronics
Components”, Union of Japanese Scientists and Engineers, (1985)

ESPEC TECHNOLOGY REPORT No. 87