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Effects of Error, Variability, Testing and Safety Factors on Aircraft Safety
REC2004
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Effects of Error, Variability, Testing and Safety Factors on Aircraft Safety


E. Acar, A. Kale and R.T. Haftka
Department of Mechanical and Aerospace Engineering,University of Florida, Gainesville, FL
32611-6250
e-mail: eacar@ufl.edu, akale@ufl.edu and haftka@ufl.edu

Abstract:
In this paper we aim to clarify the interaction between error, variability, testing and
safety factors on the safety of aircraft structures by using an error model that includes errors made
in the calculation of loads and stresses, and also errors in material and geometric parameters. The
effect of various representative safety measures taken while designing aircraft structures follow-
ing the deterministic approach codes in the FAA regulations is investigated. Uncertainties include
errors, such as in predicting the response (stress, deflection etc.) of the structure and variability in
materials, loading and geometry. Two error models, one is simple and the other is more detailed,
are used and the results of these two models are compared. We use a simple model of failure of a
representative aircraft structure. In addition, we explore the effectiveness of certification tests for
improving safety. It is found that certification tests reduce the calculated failure probabilities by
updating the modeling error. We find that these tests are most effective when safety factors are
low and when most of the uncertainty is due to systemic errors rather than variability.
Nomenclature
c.o.v.
= Coefficient of variation
e
m,
e
P
, e
,
e
t
and e
w

= Error factor for material failure stress, load, stress, thickness
and width
e
total

= Cumulative effect of various errors
P
act
, P
calc
and P
d

= Actual, calculated and design load f design
, t
design
and w
design

= Design values of failure stress, thickness and width f built
, t
built
and w
built

= Average values of failure stress, thickness and width of the
components built by an aircraft company f actual
, t
actual
and w
actual

= Actual values of failure stress, thickness and width
S
F avg

= Fleet-average safety factor
k
= Error
multiplier
nt
P
and
t
P

= Average value of probability of failure without and with certifi-
cation
MEF and SEF Cases
= Multiple Error Factor and Single Error Factor Cases

REC2004
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1. Introduction
Aerospace structures have traditionally been designed using a deterministic approach based on
FAA regulations. The safety of the structures has been achieved by combining safety factors with
tests of material and structural components. There is a growing interest to replace safety factors
by reliability-based design. However, there is no consensus on how to make transition from de-
terministic design to reliability-based design. An important step in this transition is to understand
the way safety is built into aircraft structures now, via explicit safety factors, use of conservative
material properties and by testing. Safety measures are intended to compensate for errors and
variability. Errors reflect inaccurate modeling of physical phenomena, errors in structural analysis,
errors in load calculations, or use of materials and tooling in construction that are different from
those specified by the designer. Thus, the errors affect all copies of structural components in the
entire fleet of aircraft of the same model. On the other hand, variability reflects variation in mate-
rial properties, geometry, or loading between different copies of the same structure on different
aircraft in the fleet.
Our previous paper (Kale et al, 2004) sought to clarify the interaction between the error, vari-
ability and testing on the overall probability of failure. We started with a structural design em-
ploying all considered safety measures. The effect of variability in geometry, loads, and material
properties was incorporated by the appropriate random variables. For errors we used a simplified
model that represented the overall error by a single random variable used in the calculation of
stress. In this paper, we use a more detailed model in which we consider individual error compo-
nents in load calculation, stress calculation, material properties and geometry parameters. The
objective of the paper is to observe differences between the use of the simple model and the more
detailed model.
As in our previous paper, we transform the errors into random variables by considering the de-
sign of multiple aircraft models. As a consequence, for each model the structure is different. It is
as if we pretend that there are hundreds of companies (Airbus, Boeing, Bombardier, Embraer etc.)
each designing essentially the same airplane, but each having different errors in their structural
analysis and manufacturing. For each model we simulate certification testing. If the airplane
passes the test, then an entire fleet of airplanes with the same design is assumed to be built with
different members of the fleet having different geometry, loads, and material properties based on
assumed models for variability in these properties. That is, the uncertainty due to variability is
simulated by considering multiple realizations of the same design, and the uncertainty due to er-
rors is simulated by designing different structures to carry the loads specified by the FAA.
We consider only stress failure due to extreme loads, which can be simulated by an unstiff-
ened panel designed under uniaxial loads. No testing of components prior to certification is ana-
lyzed for this simple example.
2. Structural uncertainties
A good analysis of different sources of uncertainty is provided by Oberkampf et al. (2000). Here
we simplify the classification with a view to the question of how to control uncertainty. We pro-
pose in Table 1 a classification that distinguishes between (1) uncertainties that apply equally to
the entire fleet of an aircraft model and (2) uncertainties that vary for the individual aircraft. The
distinction is important because safety measures usually target one or the other.
Similarly, the uncertainty in the failure of a structural member can also be divided into two
types: systemic errors and variability. Systemic errors reflect inaccurate modeling of physical
phenomena, errors in structural analysis, errors in load calculations, or use of materials and tool-
ing in construction that are different from those specified by the designer. Systemic errors affect
REC2004
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all the copies of the structural components built using the same model and are therefore fleet-
level uncertainties. The other type of uncertainty reflects variability in material properties, ge-
ometry, or loading between different copies of the same structure and is called here individual
uncertainty.
Table 1. Uncertainty Classification
Type of
uncertainty
Spread Cause
Remedies
Systemic error
(modeling errors)
Entire fleet of compo-
nents designed using
the model
Errors in predicting struc-
tural failure and differ-
ences between properties
used in design and aver-
age fleet properties.
Testing and simula-
tion to improve math
model and the solu-
tion.
Variability Individual
component
level
Variability in tooling,
manufacturing process,
and flying environments.
Improve tooling and
construction.
Quality control.
3. Safety Measures
Aircraft structural design is still done by and large using code-based design rather than probabilis-
tic approaches. Safety is improved through conservative design practices that include use of
safety factors and conservative material properties. It is also improved by tests of components and
certification tests that can reveal inadequacies in analysis or construction. In the following we
detail some of these safety measures.
Safety Margin: Traditionally all aircraft structures are designed with a safety factor to withstand
1.5 times the limit load without failure.
A-Basis Properties: In order to account for uncertainty in material properties, the Federal Avia-
tion Administration (FAA) recommends the use of conservative material properties. This is de-
termined by testing a specified number of coupons selected at random from a batch of material.
The A-basis property is determined by calculating the value of a material property exceeded by
99% of the population with 95% confidence.
Component and Certification tests: Component tests and certification tests of major structural
components reduce stress and material uncertainties for given extreme loads due to inadequate
structural models. These tests are conducted in a building block procedure. First, individual cou-
pons are tested, and then a sub assembly is tested followed by a full-scale test of the entire struc-
ture. Since these tests cannot apply every load condition to the struct