ICAF 2007 - On the Selection of Test Factors for the Determination of Safe Life

24th
ICAF Symposium - Naples, 16-18 May 2007
ON THE SELECTION OF TEST FACTORS
FOR THE DETERMINATION OF SAFE-LIFE
Guy Habermann1
1
Associate Technical Fellow – Boeing Australia Limited
Abstract: This paper has been written to assist analysts in the selection of
appropriate life-factors for the fatigue life evaluation of structural systems. The
need for this guidance has been highlighted by (1) the need to select life-factors
for structural materials and systems that were not considered when the
traditionally accepted techniques were developed and (2) the increasing scarcity
of documented guidance on the origins and interpretation of these techniques.
In particular, this paper identifies the assumptions and principles that underpin
the methods of calculating life-factors and provides some insight into the
parameter values that underpin the life-factors promulgated through the
literature and by a number of airworthiness authorities.
AN OVERVIEW OF SAFE LIFE
The safe-life certification of aircraft or their constituent components is based upon the
premise that the structural systems thus certified can withstand the effects of a defined service
environment for a specified safe-life with an acceptable level of risk that the static strength of
the structural system will not be reduced below design limits by fatigue or environmental
effects.
Experience with metallic structures has shown that analyses of the scatter associated with
fatigue life are greatly facilitated by working with the logarithm of time. In particular, when
viewed as a function of log-time, the scatter in fatigue lives is typically (1) stochastic in
nature, (2) symmetrically distributed and (3) independent of the mean life for low-cycle
fatigue (i.e. the region represented by the steep part of an Wöhler (S-N) curve). Accordingly,
the lower limit in a data distribution that corresponds to a specified probability of survival can
be calculated relative to the true median by deducting a constant offset in log-time or by
dividing by a life-factor when working in the time domain.
Historically, safe-life has been calculated by reducing the life demonstrated by test or
calculation by a life-factor that accommodates the uncertainty inherent in the variables that
affect the durability of the corresponding structural system. This life-factor is selected to
provide an acceptable level of risk of premature failure based upon the statistical distribution
of the observed scatter in fatigue life.

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REGULATORY REQUIREMENTS FOR LIFE-FACTORS
Full-scale fatigue tests are typically required by airworthiness regulations to capture the
loading effects of a complex structure and to verify the assumptions that underpin fatigue
calculations. Even when aircraft structure is certified on a basis other than safe-life – such as
by damage tolerance – the number of simulated service lifetimes that need to be demonstrated
through full-scale fatigue testing specified by airworthiness regulators is determined through
the use of life factors.
A persistent problem that is associated with the calculation of safe-life involves the collection
of sufficient data to establish confidence in statistical analyses of an unknown distribution.
Due to the excessive time and cost involved in full-scale fatigue testing, test programmes are
typically limited to a single full-scale fatigue test. However, a single test in isolation is
insufficient to establish the knowledge that is required to obtain a reliable estimate of safe-
life. Accordingly, this calculation must draw upon prior knowledge of the expected scatter
that may be gained from either previous test and service experience or from dedicated
component and coupon tests that are conducted to augment full-scale fatigue tests.
For many years, some airworthiness authorities have provided guidance on acceptable life-
factors that had been derived from largely undisclosed sources and statistical techniques.
However, in recent times, much of this guidance has been removed from the airworthiness
regulations in favour of a requirement for the use of “acceptable” life-factors. In order to build
a case to justify the suitability of a life-factor, one needs to understand the principles that
underpin existing techniques and the associated interpretation of the results.
SELECTING A METHOD FOR CALCULATING LIFE-FACTORS
The basic requirements for calculating life-factors are that both (1) the general form of the
distribution of scatter in fatigue life and (2) the parameters needed to define this distribution,
are known or can be estimated. In keeping with the traditional approach, the scatter that is
discussed in this paper does not reflect the uncertainty that arises from variations in loading.
The most widely accepted method for calculating life-factors is based upon a combined
probability distribution function that is derived using knowledge of the distribution of scatter
in fatigue life and the distribution associated with the estimation of unknown parameters from
test results. A derivation of this expression for life-factors has been provided below to provide
a clearer understanding of the interpretation and limitations of the factors thus derived.
A novel methodology, that estimates the mean fatigue life and safe-life as intermediate steps
in the calculation of life-factors, is also presented to show how the noted limitations of the
more widely used method can be overcome. Although the example used to demonstrate this
method employs specific assumptions with respect to the distribution of scatter in fatigue life,
the general methodology used in the derivation can be adopted to accommodate alternate
distributions and parameters.
From the perspective of ascertaining the appropriateness of a method for calculating life-
factors, it is a necessary but not sufficient requirement that the mathematical model is capable
of accommodating the relevant parameters – including a distribution of fatigue scatter that is
representative of the applicable structural systems and materials. Of greater importance is an

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understanding of the underpinning assumptions and limitations that are inherent in the model.
As this paper will show, the principal hazard associated with the selection and use of life-
factors is due more to the lack of understanding that leads to the incorrect interpretation of
results than the limitations of the selected statistical model.
Nomenclature
Whilst an effort has been made to maintain traditional naming conventions, it was not
possible to do so in all cases. For the purposes of consistency and clarity in this paper, the
following nomenclature has been used:
yα is the variate of the random variable Y that acts as the upper bound to a specified
percentage of the population, α. i.e. P(Y< yα) = α
μY corresponds to the mean of the random variable Y
σY corresponds to the standard deviation of the random variable Y
The most notable departure from standard conventions occurs in Eqn. 8, in which a negative
sign is introduced before the term zP. This is due to the conflict that exists between the
adopted nomenclature, in which the subscript corresponds to the area of the lower tail of a
distribution – i.e. the probability of premature failure (Z<zP) – as opposed to and the normal
convention within the literature of specifying the probability of survival (Z>zP).
To avoid confusion when referring to statistics corresponding to distributions described with
respect to time and the logarithm of time, the prefix “log-” will be used to denote results
calculated with respect to the logarithm of time. Accordingly, just as log-normal refers to the
normality of a distribution for a random variable that has undergone a logarithmic
transformation, the term log-mean has been used to refer to the algebraic average of the
logarithm of individual test results. From a practical perspective, the log-mean test life is
equivalent to the geometric mean of the individual test lives as measured in the time domain.
Combined Distribution Method
The foundations for the use of probability density functions that describe linear combinations
of independent random variables for the calculation of life-factors were laid by Bullen [1] in
1956. In particular, Bullen proposed three methods of calculating test factors that were based
upon combined probability distributions for test data drawn from normal distributions. These
methods correspond to cases where the standard deviation is either (1) unknown, (2) related to
the mean by a constant coefficient of variation or (3) known.
Although Bullen did not feel that the case of a known standard deviation was worthy of
consideration it was this case, that gained popular acceptance through the adoption of this
technique by British Ministry of Aviation in AvP 970 [2]. The following derivation
corresponds to this case, where a test programme consisting of n samples is used to calculate
an appropriate life-factor.
Consider X, a random variable describing the distribution of the logarithm of fatigue life of
the structural system of interest about the unknown mean μ with known standard deviation σ.
( )2
,~ σμNX (1)

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According to the Central Limit Theorem, the distribution of the mean of n samples taken from
X, which correspond to unbiased estimators of μ, can be described as follows:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
n
NX
2
,~
σ
μ (2)
By taking a linear combination of these independent normal random variables, it is possible to
define the random variable Y, which provides a measure of the difference between samples
drawn from each population.
XXY −= (3)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
+1
1
,0~ 2
n
NY σ (4)
To facilitate the use of the standard normal distribution tables, Y is transformed to the
standard normal distribution (Z) as follows:
1+
=
−
=
n
nYY
Z
Y
Y
σσ
μ
(5)
At this point, it will be assumed that the failure of the structural system is associated with the
failure of a single critical component, although the impact of multiple critical components will
be considered later. For a specified probability of premature failure (i.e. P(Z<zP)= Pspec) …
( )
11 +
−
=
+
=
n
nxx
n
ny
z PP
P
σσ
(6)
Traditionally, this result has been used to calculate the life-factor LF, which corresponds to
the ratio of the mean test life to the safe-life (where the mean test life is defined as the antilog
of the log-mean test life).
pxx
LF
−
=10 (7)
( ) n
n
z
xx p
P
LF
1
1010
+
−
−
==∴
σ
(8)
Eqn. 8, is the expression for LF that is widely referenced in the literature and is used as the
basis for the guidance provided in a number of airworthiness regulations [3, 4, 5].
A widely held interpretation of this result is that Pspec corresponds to the percentage of the
population that will have failed prior to the safe-life that is calculated by dividing the mean
test life by this life-factor. However, this is not the case, even when qualified by the common
assertion that the result can be expected on average. The problem with this determination of
life-factor is highlighted by Eqn. 9.
( ) PP xxxx −≠− (9)

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The random variable Y in Eqn. 3 measures the difference between the mean calculated from a
sample of size n drawn from the population X and an additional sampled value (variate)
drawn from the same population. Accordingly, the left side of Eqn. 9 corresponds to the value
yP for which P(Y<yP)=Pspec as calculated with respect to the total population. The term on the
right side of Eqn. 9, however, corresponds to one possible pairing of values that contributes to
the calculated value yP.
The accuracy of the life-factor calculated using Eqn. 8 depends upon the quality of the
calculated mean as an estimate of the true mean, which can be assured only in the limiting
case as the number of samples approaches infinity. As previously noted, this is not a practical
consideration when dealing with full-scale fatigue tests.
Although this realisation leads to an alternate approach that abandons the traditional
Combined Distribution Method, the preceding derivation has been presented to provide a
clearer understanding of a technique that has gained acceptance over a significant period.
Estimating the Log-Mean of Fatigue Life
A fundamental concept that underpins the alternate approach to calculating life-factors
described in this paper is the technique that is used to estimate the log-mean fatigue life with a
quantifiable level of confidence.
In the previous derivation, the Central Limit Theorem was invoked through Eqn. 2, which
describes the distribution of the mean of n samples taken from a normally distributed
population. However, it should be noted that the Central Limit Theorem also provides a good
approximation of the distribution of the mean of n samples taken from a population of any
shape as long as the sample space is sufficiently large (most commonly applied when n>30).
Furthermore, the Central Limit Theorem can be applied to smaller samples of non-Gaussian
distributions as long as the population does not differ significantly from a normal distribution.
As the mean of n samples is an unbiased estimator of the mean of the parent population from
which the original sample was drawn, it is evident that the Central Limit Theorem can be used
to infer knowledge about the true mean of fatigue life for a broad range of distribution shapes.
To assist in the manipulation of this information using standard probability distribution tables,
the random variable in Eqn. 2 can be transformed to the standard normal form as follows.
n
XX
Z
X
X
σ
μ
σ
μ −
=
−
= (10)
By equating the value zα, (corresponding to the probability αspec that Z<zα) with the
normalised form of the log-mean test result (Eqn. 11), it is possible to arrive at an estimate of
the true mean (Eqn. 12) for which the assertion can be made – at the specified level of
confidence (αspec) – that the estimate does not exceed the true value.
( )
n
x
zspec
σ
μ
α α
ˆ−
==Φ (11)
nzx σμ α−=∴ ˆ (12)

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A graphical representation of this technique has been provided as Figure 1.
μ′ˆ μ ′′ˆμ
x′ x ′′αx
⎟
⎠
⎞
⎜
⎝
⎛
n
NX
σ
μ,~⎟
⎠
⎞
⎜
⎝
⎛
′
n
N
σ
μ ,ˆ ⎟
⎠
⎞
⎜
⎝
⎛
′′
n
N
σ
μ ,ˆ
specArea α=
( ) ( ) specxXPP αμμ α =<=<ˆ
Figure 1: Graphical representation of mean estimation using the Central Limit Theorem
In situations where the shape of the parent population from which the test data were drawn
differs significantly from the normal distribution this technique can be easily modified to
accommodate alternate distributions of the test mean, that can be derived from either
statistical theory or empirical analysis using computer modelling.
Mean Estimation Method
The Mean Estimation Method was independently developed by this author as a novel
approach to overcome the identified deficiencies of the Combined Distribution Method,
although the literature survey that was conducted to support this paper has subsequently
disclosed that the same approach was previously used by Abelkis [6] in 1967. This method
overcomes the complication of separating random variables bound in a single probability
density function by estimating the log-mean of fatigue life as an intermediate step in the
determination of the safe-life.
For populations for which the Central Limit Theorem describes the distribution of the mean of
n samples taken from that population, Eqn. 12 can be used to provide an upper bound on
estimates of the true mean of fatigue life to a confidence level of αspec.
To facilitate the comparison of the expressions for the calculation of life-factor derived from
the Combined Distribution Method and the Mean Estimation Method, the ensuing derivation
will consider the random variable X described by Eqn. 1.
Consider the normalised form of the random variable X and the value zP for which the
probability that Z<zP corresponds to a specified probability (Pspec).
σ
μ−
= P
P
x
z (13)
Substituting the estimate of μ from Eqn. 12 for μ in Eqn. 13 yields the following expression.
⎟
⎠
⎞
⎜
⎝
⎛
−−=−
n
z
zxx PP
α
σ (14)

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The life-factor that results from substituting Eqn. 14 into Eqn. 7 yields a conservative estimate
of safe-life that can be asserted at the specified level of confidence (αspec) for the specified
probability of premature failure (Pspec).
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−−−
== n
z
zxx P
p
LF
α
σ
1010 (15)
Figure 2 provides a visual representation of the calculation of the logarithm of safe-life xP.
Px μˆ μx
( )2
,σμN
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
n
N
2
,ˆ
σ
μ
( )2
,ˆ σμN
specArea α=
specPArea =
Logarithm of Test Life
Distribution of fatigue
scatter (μ unknown)
Figure 2: Graphical representation of the Mean Estimation Method
As previously noted, although this example assumed that the random variable X is normally
distributed, this assumption is not critical to the success of this technique. In fact, this method
can be used to derive an expression for the life-factor as long as both (1) the distribution of
the population of log-mean estimates calculated from n samples and (2) the general form of
the distribution of the scatter in fatigue-life, are either known or can be estimated.
Compliance with the first requirement has been previously discussed, whilst the second
condition can be satisfied by any number of probability density functions including non-
symmetric distributions and those represented by tabulated data collated from test or fleet
service data.
It should be noted that the confidence level associated with any expression for life-factor must
include the uncertainty surrounding the inherent assumptions. In this example, it was assumed
that the standard deviation of the scatter is known exactly and that the fatigue life is normally
distributed. Any uncertainty associated with these assumptions will result in a reduction in the
confidence level with which a safe-life can be asserted.
SELECTING INPUT PARAMETERS
The calculation of an appropriate life-factor requires the selection of input parameters that are
representative of the specific structural system being modelled. Accordingly, the
recommendation of the input parameters is a matter that is beyond the scope of this paper.
The following sections have been provided without prejudice to highlight some
considerations of relevance to the selection of these parameters and to identify some common
values that underpin the guidance provided by a number of airworthiness authorities.

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Distribution of Fatigue Life Scatter
An accurate description of the distribution of fatigue life requires significantly more samples
than are required to reliably estimate the standard deviation and mean of a population. Given
the cost of full-scale fatigue testing, it is not surprising that the empirical basis for describing
the distribution of fatigue scatter is still the subject of much debate.
Much of our understanding of the distribution of fatigue scatter can be attributed to a small
number studies involving large collections of test data – such as those documented in Table I.
Authors Year Sample Size
Payne and Ford [7] 1959 230 test values including 178 Mustang half-wings
Rosenfeld [8] 1962 26 unused US Navy aircraft
Abelkis [6] 1967 1,180 fatigue test samples (6,659 specimens)
Stagg [9] 1976 Collation and analysis of several earlier studies.
Young and Ekvall
[10]
1981 553 S-N test groups (2,417 specimens) and 1,288 spectrum
test groups (~5,000 specimens)
Table I: Studies to determine the distribution of fatigue scatter
A common observation that was made by these studies, which considered a number of
alternate probability distributions (primarily log-normal and Weibull), was that no single
probability distribution function provided the best fit to all sets of test data. Several of these
reports [6,7,10] noted that the log-normal distribution was not representative at the extremities
of the distribution, with limits of validity being set at either the 10 and 90 percentiles [9,10] or
outside two standard deviations of the mean [6] (i.e. a premature failure rate of approximately
2%). Although Weibull distributions could be found to provide a better fit at the lower
extremities (upon which the interest in safe-life is focused), the parameters that describe these
distributions were found to be specific to the sample group being analysed and as such lacked
the generality and computational convenience of the log-normal distribution.
Accordingly, the log-normal distribution has gained wide acceptance as the distribution of
choice for modelling fatigue scatter through the adoption of Eqn. 8 even though the specified
probabilities of premature failure (typically of the magnitude of one in one thousand) tend to
fall outside the reported limits of validity for this distribution.
Another point of relevance to the suitability of this distribution is that these findings have
been based on the study of test programmes involving metallic structures. With the advent of
new materials and structural systems, such as those used in advanced composite structures, it
is worth considering the suitability of the traditional assumption that fatigue scatter possesses
log-normal distribution, when selecting an appropriate model for calculating life-factors.
Standard Deviation
Fatigue test results appear to be characterised by scatter – not just in the observed fatigue life
of test articles but also in the estimates of standard deviation that describe this scatter.
Significant factors that were found to contribute to the variability in standard deviation
estimates included the material tested (e.g. aluminium, steel, titanium), the nature of the test
article (e.g. notched and unnotched coupons, structural components and full-scale test articles)
and loading (e.g. constant amplitude and spectrum loading) [6,10].

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The literature provides evidence to support a broad range of standard deviation values. Whilst
most interest is focused on standard deviations within the range of 0.10 to 0.20, reports
providing evidence of values outside this range are not uncommon. Reference [11] provides a
detailed historical overview of the development of test factors with particular emphasis on the
origins and values of standard deviation of fatigue scatter used as the basis for life-factors.
The specific standard deviation values that underpin the life-factors recommended or implied
by a number of current airworthiness regulations have been summarised in Table II.
Airworthiness Regulation /
Regulatory Guidance
Standard
Deviation
Comments
US Navy [5] σ=0.10
DEFSTAN 00-970 [4] σ=0.1296 A precision not intended [11]
Federal Aviation Administration &
European Aviation Safety Agency
[3]
σ=0.14
σ=0.17
σ=0.25
σ=0.20
Aluminium
Steel (100-200ksi)
Steel (200-300ksi)
Titanium
Table II: Values of standard deviation of fatigue scatter accepted by some regulatory bodies
As previously noted, the majority of information on the standard deviation of fatigue lives is
based upon the testing of metallic structures. Despite more than three decades of experience
with advanced composites in military aircraft in particular, it is worthy of note that there is a
dearth of information on the standard deviation of fatigue scatter for advanced composite
materials.
Sample Size
Inspection of Eqn. 8 and Eqn. 15 reveals the dependence of life-factors upon the sample size
used to calculate the mean test life. Although the expense of full-scale fatigue testing limits
the number of tests that can be conducted, analysis of these equations reveals the benefit of
maximising the number of samples used to generate the test mean.
Given the broad definition of safe-life provided at the beginning of this paper (or even the
more limited definition associated with the detection of cracks in metallic structure) it is
apparent that in the absence of a significant redistribution of load within the structural system
due to structural failure or altered stiffness, fatigue events at separate locations can be treated
as being statistically independent. Accordingly, all indications of the initiation of fatigue
failure can be counted as separate samples that contribute to both the calculation of the mean
test life and its quality as an estimate of the true mean fatigue life for the appropriate
structural systems. This realisation reinforces the benefit of regular structural inspection and
the early repair of detected damage to facilitate the continuation of testing as significant
mechanisms for maximising the calculated safe-life by reducing the magnitude of life-factors
and thereby enhancing the value of a full-scale fatigue tests.
It is important to reiterate that the benefit of an increased sample size is a direct consequence
of the reduction in uncertainty associated with the estimation of the mean fatigue life. Whilst
the existence of a large historical database of fatigue test results or fleet service data can
contribute to an improved understanding of the distribution of fatigue scatter, a reduction in

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uncertainty in the estimate of mean fatigue life can only be achieved if (1) the data are
representative of the structural system and usage under consideration and (2) the data have
been used to contribute to the calculation of the mean test life. The rationale that has been
provided to justify the United States Navy’s use of a life factor of 2.0 [5] represents an
incorrect interpretation of Eqn. 8 in that the mean test life, which is calculated without
reference to these historical data, is used in the limiting form of this equation that results as
the sample size n approaches infinity.
This approach is equivalent to assuming that the calculated mean test life is not less than the
true mean fatigue life, which can only be asserted at a confidence level of 50%. As noted by
Hoffman and Hoffman [5], the risk associated with this low confidence level is mitigated by
routine maintenance, however, this rationale is inconsistent with the safe-life philosophy,
which obviates the need for an underpinning inspection programme.
Probability of Premature Failure
The determination of an acceptable probability of premature failure for the determination of
safe-life is highly subjective and falls within the domain of risk management. Whilst some
airworthiness authorities mandate acceptable probabilities of failure, others are content to
provide guidance on the probabilities that they would deem to be acceptable. In cases where
an acceptable probability is not explicitly stated, it is frequently possible to infer this value
from the promulgated life-factors. A review of the guidance provided by a number of
airworthiness regulators [3,4,5] revealed a general level of acceptance for a probability of
premature failure of one in one thousand (i.e. Pspec=0.001), although it is worthy of note that
Reference [3] also cites a value of approximately one in five thousand (i.e. Pspec =0.000223).
Number of Critical Components
An important consideration in the selection of an acceptable probability of failure is the
cumulative effect of the probability of component failures upon the overall probability of
failure of the structural system. Bayesian theory describes how the probability of system
survival is equal to the product of the probabilities of survival of all of statistically
independent scenarios that can result in a system failure.
( i
C
i
spec PP −=− Π=
11
1
) (16)
In simple terms, the existence of multiple failure modes requires that the probability of failure
of each must be less than or equal to the specified acceptable level of failure. This
requirement for a lower probability of premature failure results in the specification of a higher
life-factor.
Consider the simplest case where C denotes the number of critical components, P denotes a
common probability of failure for each component and Pspec<<1.
CPPP spec
C
spec ≈−−= 11 (17)
In this context, P is the probability that should be used to calculate zP in both Eqn. 8 and Eqn.
15. Consideration of Eqn. 16 reveals that the use of Pspec in the original derivation is only
appropriate when considering a single critical component. A practical application of this
result arises when considering similar components such as left and right wings.

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Confidence Level
The 95% confidence level has achieved broad acceptance by the engineering community for
static strength analyses as demonstrated through the wide-spread use of A and B-basis values
for material properties. In the field of fatigue life evaluation, the precedent for the use of this
confidence level has been provided by the Civil Aviation Authorities of several countries
through their requirement for the use of life-factors that provide a 99.9% probability of
survival with 95% confidence [3].
Although the Mean Estimation Method provides a method for calculating life-factors for a
specified probability of premature failure with a specified level of confidence, the absence of
a term to accommodate confidence levels in the Combined Distribution Method, may explain
the past tendency for many airworthiness regulators to refrain from specifying acceptable
confidence levels for the calculation of life-factors. Not withstanding this, the use of the 95%
confidence level as a basis for comparison of the life-factors [3,4] would appear to provide
tacit approval by these particular regulatory authorities for the use of this confidence level,
despite the fact that these promulgated life-factors are frequently associated with lower
confidence levels.
By equating Eqn. 8 and Eqn. 15 it is possible to identify a relationship between confidence
level, probability of premature failure and sample size for life-factors calculated by the
Combined Distribution Method, that is independent the standard deviation of fatigue scatter
used in the calculation. It is interesting to note that the confidence level associated with life-
factors calculated using this method decreases as the number of sample points used to
calculate the life-factor increases. For an acceptable probability of premature failure of one in
one thousand, it can be shown that the confidence level starts at 90% for a single sample point
before dropping as successive sample points are added (i.e. 84% for n=2, 80% for n=3, 77%
for n=4, …). This trend is an undesirable artefact of the Combined Distribution Method that is
avoided by techniques that facilitate the specification of confidence level.
SUMMARY
The calculation of life-factors has evolved over the last half century, during which time, the
basis for the life-factors enshrined in many airworthiness regulations has become increasingly
hard to discern. A recent trend by airworthiness authorities to require the use of appropriate
life-factors has highlighted the difficulty of this task, especially when attempting to do so for
structural materials and systems that were not considered at the time when these techniques
were developed.
A review of the origins of the Combined Density Method that underpins the calculation of
life-factors in many airworthiness regulations highlighted a number of deficiencies in this
technique that can be attributed to either the inherent limitations or the incorrect interpretation
of the statistical model. The Mean Estimation Method was introduced as an alternate method
for calculating life-factors that is capable of redressing these deficiencies.
The major benefit of this statistically based method lies in the simplicity of the technique and
its ability to be tailored to accommodate user-specified parameters such as the probability
density functions describing fatigue scatter and estimates of the mean fatigue life, the standard
deviation of the fatigue scatter, the number of samples, the acceptable probability of
premature failure, the number of critical components and the desired confidence level.

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REFERENCES
[1] Bullen, N. I. (1956), A note on test factors, Reports & Memoranda No. 3166,
Aeronautical Research Council.
[2] Ministry of Aviation (1959), An acceptable procedure for estimating the fatigue life of
an aeroplane structure, In: Design requirements for service aircraft, Aviation
Publication (AvP) 970, vol. 1, chapter 200, section 7 and leaflet 200/7.
[3] Federal Aviation Administration (2005), Fatigue, fail-safe, and damage tolerance
evaluation of metallic structure for normal, utility, acrobatic, and commuter category
airplanes, Advisory Circular (AC) 23-13A.
[4] Ministry of Defence (2007), Fatigue safe-life substantiation, In: Design and
airworthiness requirements for service aircraft, DEF STAN 00-970 part 1, issue 5
section 3, leaflet 35.
[5] Hoffman, M.E., Hoffman, P.C. (2001), Corrosion and fatigue research – structural
issues and relevance to naval aviation, Int Jnl of Fatigue, vol 23 p.1-10.
[6] Abelkis, P.R. (1967), Fatigue strength design and analysis of aircraft structures. Part I
- Scatter factors and design charts, AFFDL-TR-66-197.
[7] Payne, A.O., Ford, D.G., et al (1959), Fatigue characteristics of riveted 24S-T
aluminium alloy wing, Part V: Discussion of results and conclusions, Aeronautical
Research Laboratory Report SM 268, Melbourne.
[8] Rosenfeld, M.S. (1962), Navy research of structural fatigue, In: Fatigue of aircraft
structures, Special Technical Publication (STP) 338 p.216, American Society for
Testing and Materials.
[9] Stagg, A.M. (1976), Scatter in fatigue:- Elements and sections from aircraft structures,
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