Inference of the Optical Fiber Lifetime
for Mechanical Reliability
Osamu Aso*, Toshio Matsufuji*2, Takuya Ishikawa*,
Masateru Tadakuma*4, Soichiro Otosu*3, Takeshi Yagi*4, Masato Oku*5

Optical fiber communication has found applications in new fields, such as fiber
to the home (FTTH) optical interconnection systems and automobile
communication systems. In these fields of applications, the mechanical reliability of the opticalfiber is important. Since, the inference of the optical fiber lifetime has been usually discussed
based on the theory of the mathematical statistics, the discussion becomes complicated. In thispaper, we shall provide the statistical strength degradation map for intuitive understanding of thetheory.
To avoid the serious B-value issue, the lifetime of the fiber has been conventionally inferred by8), 9)
However,using some approximations of the exact lifetime formula derived by Mitsunaga et.al.
the approximations are violated in the case of short lifetime with large stress. To avoid the
difficulties, we shall develop an alternative approximation method to resolve the problem.

ABSTRACT1.

INTRODUCTION

In the new fields of the application of the optical fiber
communications, such as FTTH with indoor optical wiring, automobile multimedia system and the optical interconnection, the fiber wiring is required to be coiled morecompactly than ever. So far, several kinds of the novel
optical fibers have been developed to reduce the bending1) to 3).
loss
If the optical the fiber is used in the long-haul transmission systems, the accumulating transmission loss islarge, therefore, the minimum bending radius of the fiber
is designed as 30 mm or more to avoid the additional loss
in the cable splice boxes (closures). With such loose
bending, the mechanical reliability of the optical fibers is
not a concern. On the other hand, in the case of the use
for wiring, since the transmission distance is short, theallowable bending radius can be small. The combinationof the situation, with the development of the novel, low
bend-loss optical fibers as mentioned above leads to thewiring with few millimeters of bending radius in the applications. In this case, the mechanical load stress applied
to the optical fiber becomes quite large therefore the conventionally neglected failure mode regarding the fracture* Yokohama R&D Labs, R&D Div.
*2 Telecommunication and Network System Sales Dept.,
Telecommunications Company*3 Broadband Products Div., Telecommunications Company*4 FITEL Photonics Labs, R&D Div.
*5 Optical Fiber and Cable Products Div., Telecommunications
Company

occurring before the increment of the bending loss,
should be a serious problem. This is the reason why weshould pay attention to the the discussion of the reliability
4)
for the mechanical strength .
The discussion of the mechanical reliability of opticalfibers is also necessary for the future long-haul transmission line. Recently, given the dramatic expansion of thetransmission capacity, the spatial multiplex transmission
systems using the multicore optical fibers have been5), 6). Since the mechanical structure of the opticalstudiedfibers is different from the conventional one, the specificdiscussion will be necessary.
With respect to the lifetime expectancy of the opticalfibers for mechanical strength, the IEC Technical Report
7)(IEC / TR62048) is often referred as the typical literature.
The discussion in this technical report is based on thestatistical lifetime theory proposed by Mitsunaga and his8), 9), however the theory is mathematicallycolleagues
complicated thus the intuitive discussion seems difficult
for the general users.
In this paper, at first, we provide a technique named
statistical-strength degradation map, which leads us to
the intuitive understanding of the theory of the lifetime sta8), 9). Using the technique, we showtistics of optical fibers
a graphical interpretation of the discussion from
Mitsunaga, et al..
Secondly, we consider the B-value issue. The formulafor the lifetime expectancy which is proposed by
8)
Mitsunaga et. al. includes some parameters which must
be determined by the experiments. Throughout the manystudies in the past, it is recognized that the determination

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2012

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Inference of the Optical Fiber Lifetime for Mechanical Reliabilityof the B-value with sufficient accuracy is difficult. For thisreason, the approximated formula of B → 0 is conventionally used for the fiber lifetime expectancy. Depending on
the degree of approximations, the conventional approxi8), 9)
are classified. The approximated formated formulae
mulae derived by Mitsunaga et. al. known as "Mitsunaga's
Approximation" is used for the fibers for the long-haultransmission line. And the Griffioen’s formula is used forthe study of tight bending of the optical fiber used in wiring. We provide a novel approximation method (theparameter approximation) which is used to the exact formula with approximated (non-zero) B-value. We compare
the above three approximations based on the measured
data from the fatigue test on 1,960 pieces of an opticalfiber.
In this paper, the expressions of formulae and symbols
7)
are as defined in the IEC Technical Report .

S(0) at t=0. In this case, the condition of the fracture KI =KIc is rewritten as S(t) =σ(t) and the time taken to the fracture is called the fiber lifetime. Figure 1 shows the conceptual schematic of the process of the fatigue fracture of
the brittle materials according to the power-low theory
11)
using the conventional strength degradation map . In
the map, the horizontal axis represents the elapsed time
and the vertical axis represents the stress or strength. t =tc in the Figure 1(b) corresponds to the lifetime.

Fiber strength
Load stress
No strength

S/σ degradation occurs.

S/σ

Si

Si
σ=0

2.

DEVELOPMENT OF THE STATISTICAL
STRENGTH DEGRADATION MAP FOR
AN INTUITIVE UNDERSTANDING OF
THE THEORY OF LIFETIME

2.1. The Statistical Theory of the Optical Fiber
Lifetime
At first, we outline the standard theory for the crack
growth in the fibers. It is known that the stress corrosion
cracking (SCC) is the physical origin of the crack growth
and the fracture of the brittle materials. For simplicity, we
solely conceive the type-I fracture that is the traverse frac10)
ture through the longitudinal direction of the fiber . The
conventional optical fiber lifetime theory is based on the8), 9)of crack growth and the Weibull stapower-law theory
tistics of the inert strength distribution.
According to the power-law theory, the crack growth isngoverned by the equation da/dt = KI , where a is the sizeof the crack in glass, KI is the stress intensity factor and n
is the stress corrosion factor. Here, t is time and A is the
proportional coefficient. This relation is confirmed by the8), 9). K I increases with the growth of theexperiments
crack, and the fracture occurs in the case where KI coincides with the fracture toughness KIc.
If the strength of the fiber is defined as S, KIc is repre1/2
sented in KIc = YSa where Y is a proportional coefficient
1/2
and KI is represented in KI = Yσa where the load stressis σ.
Using the relations above, the equation of the crack
growth is rewritten as the equation of the strength degradation as follows:.
ndS n-2（t） σ（t）
=
,
dt
B

2

t
(a) Without load stress

Figure 1

Si
Fractureσσ

Load stress

Load stress

Lifetime t c t(b) With load stress(c) With load stresst

It is apparent that the optical fiber lifetime strongly
depends on the initial condition Si = S(0), however, thedestructive inspection is necessary to know Si. It implies
that we cannot exactly know the lifetime of particular
products. This leads us to, the probabilistic discussion.
The strengths of the optical fibers, which are manufactured from the same materials and the same process, areassumed as belonging to the same population. The probabilistic distribution of the population is estimated by
fatigue tests from a random sampling. From the paststudies, it is known that the strength distribution of optical8), 13),fibers can be described by the Weibull distribution
The set of "formulae" for lifetime statistics is derived by
combining the power-law theory of the fracture and the7)
Weibull distribution of inert strength .
That is, if each failure probability F is defined as F=112)
exp(-H), the cumulative hazard function H becomes asfollowing.
・The initial strength distribution of optical fiber (Weibull
distribution)
=
H（S
i
i）

L Si m,
L0 S 0(2)

・The strength distribution after screening by prooftest
=
H（S
p
p）

Here, B=2/{AY (n-2)KIc } is called the B-value. The
equation (1) represents the deterministic nature. If the values of n and B are determined by measurements, thetemporal degradation of the strength S(t) under load
stress σ(t) can be calculated by using the initial strength

S/σ

Since inert strength islarge enough, the ﬁber
strength does notreach to fracture in
the observation time.

Conceptual schematic of the process of the fatigue
fracture of the brittle materials according to thePower-Low theory using the strength degradation
map.

(1)
n-2

The ﬁber strength
gradually degrades
according to
the equation (1).

L
ms
m
n
（BS n-2）s ,（σ np t p+ BS pn-2
p +σ p t p ） −
min
ß ms

(3)

・The lifetime distributionLBm= ms σ na t fp+ 2 +σ np tp ms−H）s ,（t fp ,σa）
（σ np t p+ BS pn-2
min
ß
σa

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Inference of the Optical Fiber Lifetime for Mechanical Reliability

Here H is the cumulative hazard function 12) and is related to the failure probability by the relation F=1-exp(-H).
Since the failure probability needs to be in the range of0≦F≦1, H≧0 is required.
In the formula (2), L0 is called the gauge length, m and
S0 represents the shape parameter and the effective scaleparameter of the Weibull distribution respectively.
The formula (3) represents the strength distribution ofan optical fiber that passed the screening test of strengthSp.
S pmin is the minimum strength of the optical fiber.
n-2
1/ms. It was pointed bym s =m/(n-2) and β=BS 0 L 0
Miyajima and Tachikura that the fiber parameter k is4), 14). According to the IEC
essential in the theory
Technical Report expression, the parameter k corresponds to β in the above formula, σp is the proof stresswhich is the maximum value of the stress applied at theprooftest. tp is the proof time in which the proof stress σp
is effectively applied during the test.
Eq. (4) is the commonly used formula and provides thefailure probability F after the time tfp is elapsed under theload of the application σa. These are the typical theories
of lifetime statistics, however, given in mathematicallycomplicated form, and it is difficult to see the physicalmeaning intuitively.
2.2. Graphical Interpretation of the Theory Using
Statistical-Strength Degradation Map
In this section, we attempt a visualization of the physicalcontents of the formulae (2) to (4) by introducing the statistical-strength degradation map which is the statisticalextension of the conventional strength degradation mapof Figure 1. Here, the initial strength is assumed to be thesame as its inert strength. To visualize the theory, we represent the probability distribution of the initial strength in
the strength degradation map. In this paper, we refer tothe map made in such way as the statistical strength-degradation map and its conceptual schematic is shown in
Figure 2.

stress/strength

Inert strength Strength passed
distribution, S i screening, S p
②
③

Smin
σp

Application
duration

Proof test

time

Lifetime ④
distribution
0 tfpminFigure 2

σa

Spmin

20yrs

tfp Application
duration

Conceptual Schematic of the statistical meanings ofthe lifetime distribution using the statistical strength
degradation map.

The horizontal axis in Figure 2 represents the elapsed

time from the drawing of the optical fiber and the verticalaxis represents the strength or the load stress of the optical fiber. The initial strength distribution of optical fiber
represented by formula (2) is shown on the extreme left in
Figure 2. This can be interpreted as the probability of theexistence of the inert strength of one optical fiber withlength L or as the fiber strength distribution of a manufactured lot of optical fibers. For the screening, the drawn
optical fiber is forced to be examined through the prooftest. This prooftest stress profile is shown as the trapezoidal shape which consists of the processes of load, dwell,and unload. Under the stresses, the optical fiber strength
degrades according to the formula (1) of the power-law
theory and the relatively weak parts of the optical fiber
fractures at the point where S(t) =σ(t). Since the portionsof the optical fiber with large strength have no fracture,they survive, and passes the screening. The red line in
the map shows the minimum strength of the optical fibersthat passed through the screening. Since the strength
degrades during the process, the minimum strength Spmin
is smaller than the corresponding initial strength Smin. Itshould be remarked that the fiber is also fatigued during
the unloading process, therefore generally Spmin＜σp. If thefatigue during the unloading process is large and the Spmin
is much smaller than the proof stress σp, the unexpectedly weak optical fiber will be admitted to the field. In thiscase, the proof test is inappropriate. The design of theappropriate prooftest condition was precisely studied by
8)
2
Mitsunaga, et.al. . They found the condition of α=σp tu /((n-2)B)＜1 for appropriate prooftest, with tu as unloadingtime.
The strength distribution of the optical fiber which
passed the screening is the strength distribution at the
point shown as ③ in Figure 2 and is represented by theformula (3). These optical fibers are weakened in accordance to the Eq. (1) under the load stress σa in the field.
The fiber is fractured at the point where S(tfp)=σa. The failure probability in operation is calculated by the Baye's formula considering the optical fiber which passed screening as a new population. In accordance with the initialstrength distribution, the lifetime is also distributed probabilistically as shown in the lower right ④ of Figure 2. This
corresponds to the lifetime probability distribution of theformula (4). As shown in the schematic, the no failure
time tfpmin exists in association with the existence of thefinite minimum strength Spmin.
The above schematic discussion is exactly the same as
the original theory of the lifetime statistics. By using only
the formula (1) of the strength degradation and theWeibull distribution (2), we could provide the more intui8)
tive interpretation of the theory from Mitsunaga et. al. (orequivalently IEC/TR62048).
2.3. High Strength Region and Low Strength Regionof the Fiber
The Weibull plot of the strength distribution is shown in
Figure 3. The results was obtained by the tensile test
which we have examined on 1,960 pieces of the
10m-length optical fiber.

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Inference of the Optical Fiber Lifetime for Mechanical Reliability

Low strength region10

H 2= Np L

H=ln (1/(1-F))

1
F=0.1
10 -2

F=0.01
F=10 -3

10 -4

F=10 -4
1

Figure 3

2

Strength, (GPa)5

10Weibull plot of the tension test on the 1,960 fibers.

From the result of Figure 3, it is found that the strength
distribution of the optical fiber in practice is not a simple
Weibull distribution but it consists of two Weibull distributions. The high strength region is the inherent strength ofglass and the low strength region is attributed to defects
in the optical fiber or cracks developed at manufacturing8), 13). In spite of the complex fact, it is not necessary tochange the discussion of the lifetime statistics except for
rewriting the initial strength distribution to the extended
distribution shown in ② of Figure 2. Concretely, we conceive the whole cumulative Weibull hazard H=H 1+H 2
where H1 and H2 are the cumulative Weibull hazard of thehigh strength region and low strength region respectively.

3.

THE LIFETIME FORMULAE WITH
AVOIDING THE B-VALUE ISSUE AND
THEIR COMPARISON

3.1. The B-value Issue and Approximated Formulaewith B→0
Since the B-value is related to the inert strength, to estimate this parameter, the tensile test should be examinedin an ambient of liquid nitrogen or in an extremely highspeed. It is known that in spite of the efforts by many
researchers, the reported B-value of the conventional single-mode fibers vary in the range of eight-digit as 2 ×-82
2
10 GPa ・ s ≦ B ≦ 0.5 GPa ・ s. This is known as the17)
B-value issue . To avoid the issue, the approximate
equation of B→0 is conventionally used instead of theexact lifetime formula (4). Depending on the degree ofapproximations, there are two types of approximations:
the Griffioen’s formula and the Mitsunaga’s approximation.
The cumulative hazard of the Griffioen’s formula is4), 16).
given as follows
High strength region
H1=

L σ na t fp ms1
Lms1= ms1（σ na tfp ）,ß1
L0 BS01n-2

(5)

ms2
σ na t fp
L
ms2
m+1 −1 = ms2（σ na tfp+σ np tp ）−,（σ np t p）s2 (6)nσ p tpß2Here, ms1=m1/ (n-2) and ms2=m2/ (n-2). The two regions
correspond to the two strength distributions which compose the Weibull distribution. S01 appearing in the formula(5) is the Weibull effective scale parameter of the highstrength region. Np is the break rate and the value which
represents the number of fiber fractures per unit length
during the prooftest. The Griffioen’s formula (6) for the
low strength region is usually understood as the approximation as B→0 in the formula (4) but it could be alsointerpreted as the approximation for the case whenn
Spmin→0 and the fatigue in operation σa tfp is sufficiently
large. Likewise, the formula (5) is almost the same form
as the eq. (6) with the subscript of the parametersnchanged from 2 to 1 and also σp tp→0, and it is assumed
that the high strength region is subjected to a small
fatigue from the prooftest. It is an appropriate assumption, considering that the prooftest as the test thatremoves the defect part at the manufacturing. If theparameters except B, such as n, β1, β2, ms1, and ms2, aredetermined from the experiments, it is possible to infer
the lifetime prediction by the Griffioen’s formula. In fact
the n-value is determined from the dynamic fatigue tests
and the other parameters are defined from the tensile test7)
as shown in Figure 3 .
It is known that the Mitsunaga’s approximation is theapproximation of the low strength region and is derived
from the eq.(6) of the Griffioen's formula by assuming thefatigue in operation is sufficiently small, that is, the formunnla (7) as σa tfp ＜＜σp tp in the formula (6).
H= H 2= ms2 Np L

σ na t fp,
σ nptp(7)

Since the Griffioen’s formula is the approximation in thencase where σa tfp is large, the approximation will be violated if the time tfp is short even if σa is large. Usually, the discussion for the lifetime expectation of the optical fiber isused for evaluating the lifetime after the optical fiber
installation for a period duration over 10 years. On theother hand, considering the fracture during fiber assembly operation, the lifetime expectancy during short periodof assembly operation is necessary. In this case, as discussed above, the Griffioen’s formula will not be applicable. This is the serious problem of the conventional
approximation of B→0.
3.2. Introduction of the Parameter Approximation
We will provide an alternative approximation method toresolve the problem associated with the approximation
B→0. As discussed in the section 2.2, the condition of the2
appropriate prooftest is given by α=σp t u/((n-2)B) ＜ 1.
Using this relation, the lower limit for B-value can bederived as follows:

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Inference of the Optical Fiber Lifetime for Mechanical Reliability(8)

According to the studies by Mitsunaga and colleagues,
the lifetime formula (4) indicates that the more the B-value
becomes large, the more the estimated failure probability8), 9). So the lifetime expectancy withbecomes as smalllarge safety factor is achieved when using approximate
value of B=Bmin together with the exact formula. The accuracy of the approximation is improved compared to theapproximation B→0. In using the exact formula, σa and tfp
will have no limitation for the domain of applicability.
3.3. The Lifetime Expectancy of the Optical Fiber andComparison of Each Approximations
In this section, we discuss the lifetime expectancy using
the parameters evaluated from the actual test of opticalfibers. Using the method mentioned in the section 3.1, we
evaluated the parameters required for the calculation of
the lifetime formula from the test result. Using theseparameters, the failure probability is calculated. In general, we wish to know the followings. The first (a) is theallowable load stress(or equivalently the bending radius)in the operation that does not have a fiber fracture until a
specified lifetime. The second (b) is the time until the fracture occurs with a specified load stress for the application.
= E0
σ R）
（

af
9a
1+ f ,
R0
4R

by manufacturing exist in the bending section becomeslow. On the other hand, the increase of the load stressmakes the fracture of glass (in the high strength region)
dominant. The above characteristics are the particulars
when considering the tight bending radius as shown in3)
the Tomita and Kurashima’s result . If the required failure
rate is about 0.1 FIT, the minimum bending radius isdefined at the high strength section.
Contribution of
the high strength section

Contribution of the low
strength section

1
10 -2
Failure Probability

σ 2p t u
,
n-2

10FIT
1FIT
0.1FIT

10 -5
10 -8
Parameter approximation
Griﬃoenʼs approximation
Mitsunagaʼs approximation

10 -11
10 -141

Figure 42

510
Bend Radius, (mm)20Inferred relations between the bend radius and thefailure probability after 15 years in the application.

(9)Here, the bending stress formula (9) represents theeffective maximum stress and for the sake of calculation,
the effective length is used instead of the actual practical
7)
fiber length . In eq. (9), E0 is the Young’s modulus of the
optical fiber, a f is the radius of the glass region of the optical fiber and R is the bending radius.
Figure 4 shows the comparison of the inferred failure
probabilities with respect to the bending radius R after
time in the operation tfp=over 15 years. We assume theoptical fiber has 2.5 turns of the bend around each radius.
As discussed in section 3.1, the Mitsunaga’s approximation shown in dark solid line coincides with to the
Griffioen’s formula (dashed blue line) when the stress issmall in the application as R is about 15 mm. On the other
hand, the difference between parameter approximation(red solid line) and the Griffioen’s formula appears in case
R＞Rmax～16 mm. In this region, the failure probability ofthe parameter approximation becomes F=0. The smaller
the load in the application σa becomes, the longer the no
failure time tfpmin shown in section 2.2 becomes. The facts
lead us to the result that the radius R=Rmax which satisfies
tfpmin=15 years exists. In other words, the failure probability
becomes zero with bending stress of R＞Rmax during the
15 years operation time.
n
In the region where the σa tfp is large, the Griffioen’s formula coincide with the parameter approximation. It isfound that the high strength region is dominant up to
R＜2.4 mm. In this region, since the part of optical fiber isshort, and the probability that cracks and others caused

The results of the failure probability calculation for some
proof-strain εp(εp =σp/E0) values are shown in Figure 5.
When the required failure rate is assumed about 0.1FIT or
more, the large proof strain is not significant for the assurance of the mechanical reliability of the fiber. This result is
3)
consistent with the result in the literature .

1

Parameter approximation
Griﬃoenʼs approximation

10 -2
Failure Probability

B = B min =

10FIT
1FIT
0.1FIT

10 -5
10 -8

εp =0.5%
εp=1.5%

10 -11

εp =2%
εp =2.5%

εp=1%

10 -141

Figure 5

2

5
10
20
Bend Radius, (mm)50Inferred results of the failure probability after 15
years in the application.  2.5-turn bending around thebend radius is considered. Some proof-strain cases
are shown.

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Inference of the Optical Fiber Lifetime for Mechanical Reliability

The results about (b) in the section 3.3 are shown in
Figure 6 and 7. These are the results with 2.5 turns ofbending with radius R=6 mm. As discussed at the end ofsection 3.1, the difference of Griffioen’s formula and theparameter approximation is large if the short time in thefield tfp is short as tfp is about 3days. The difference in the
failure probability seems small, however it appears aslarge in the discussion about failure rate. From this result,
it is considered that using Griffioen’s formula for the discussion of the failure rate in short-time, such as fiber
assembly operation or cable installation underestimates
the lifetime of the fiber, and possibility influences thedesign of the process or the products including opticalfibers.

3days

Failure Probability

10 -8

10 -10

10 -12
Parameter approximation
Griﬃoenʼs approximation
Mitsunagaʼs approximation

10 -1410 -3

Figure 6

10 -1
10Times in year

10
5

Parameter approximation

2

Mean Failure Rate, FIT

20

3days

Griﬃoenʼs approximation

1

Mitsunagaʼs approximation

Figure 7

10 -1
Times in days

CONCLUSION

We shall summarize the discussion of this paper. First, in
Chapter 2, we provided the statistical strength degradation map for the intuitive understanding of the theory of
the lifetime statistics. The statistical strength-degradation
map would enable us to see intuitively, not only the resultof the lifetime statistics but also the processes to the failure without using mathematics. In Chapter 3, we
explained that the difficulties of the B-value issue, and the
Mitsunaga's approximation and the Griffioen's formulawere introduced to avoid this problem. And then, from thecondition of no over-fatigue during unloading at the prooftest, we provided a novel parametric approximation method where the appropriate B-value is evaluated by B=Bmin.
Also, in the discussion of the lifetime reliability in shorttime which ensures the reliability during the optical fiber
installation, there is a possibility of underestimation of thereliability when using the Griffioen’s formula. It becomes
more pronounced especially at the discussion using the
failure rate. In such case, it can be considered that theparametric approximation is effective.
On this study, the discussions with Mr. Hiroshi
Nakamura, Mr. Yoshihiro Arashitani, Dr. Misao Sakano, Mr.
Hiroshi Ono, Mr. Shinji Asao, Mr. Shinichi Arai, and Mr.
Keisuke Ui were essential for understanding the subject.
We, hereby, would like to express to them our gratitude.

10 3

Inference of the temporal growth of the failure probability under the condition of the 2.5-turn bending of
the bend radius R=6 mm.

10 -3

4.

10

Inference of the temporal growth of the mean failure
rate under the condition of the 2.5-turn bending of thebend radius R=6 mm.

REFERENCES
1) R. Sugizaki, R. Miyabe, T. Yagi, Furukawa Denko Jiho No.116(2005), 2. in Japanese.
rd2) T. Yasutomi, F. Nakajima, and Y. Rintsu : Proc. 53 Int. wire andcable symp., (2004), 11.
3) S. Tomita, T. Kurashima, Journal of IEICE, 91 , (2008), 689 in
Japanese.
4) M. Tachikura, IEICE Transactions, J94-B, (2011), 738 in Japanese.
5) K. Imamura, K. Mukasa, R. Sugizaki, Furukawa Denko Jiho No. 128,(2011), 11. in Japanese.
6) K. Imamura, K. Mukasa, T. Yagi, Proc.optical fiber communication
conference, (2009), paper OTuC3.
7) IEC, Technical Report, TR62048, first edition, (2002).
8) Y. Mitsunaga, Y. Katsuyama, H. Kobayashi, Y. Ishiida, J. Appl. Phys.,
53 (1982), 4847.
9) Y. Mitsunaga, Y. Katsuyama, H. Kobayashi, Y.Ishiida, Electronics andCommunications in Japan, 66, (1983), 79.
10) Y. Tanimura, Etoki Hakaikougaku Kiso No Kiso, NIKKAN KOGYOSHIMBUN, LTD., (2009). in Japanese.
11) E. R. Fuller Jr., S. M. Wiedrehorn, J. E. Ritter Jr., P. B. Oates, J.
Mater. Sci, 15 (1980) 2282.
12) Union of Japanese Scientists and Engineers, Reliability Seminar
Basic Course text, (2009).
13) R. Olshansky and R. D. Maurer, J. Appl. Phys., 47. (1976), 4497.
14) Y. Miyajima, J. Lightwave Technol., LT-1, (1983), 340.
15) TIA/EIA Standard, FOTP31 TIA/EIA-455-31C, (1994).
16) P. Matthijsse, W. Griffioen, Optical Fiber Technol., 11 (2005), 92.
17) T. Volotinen, A. Breuls, N. Evanno, K. Kemeter, C. Kurkjian, P.
Regio, S. Semjonov, T. Svenson, S. Glaessemann, Proc. 47th Int wireand cable symp., (1998), 881

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