A systematic approach to defining margin in a manner that incorporates statistical information and accommodates data uncertainty but does not require assumptions about specific forms of the tails of distributions is developed. A margin that is insensitive to the character of the tails of the relevant distributions (tail insensitive margin, TIM) is defined. This is complemented by the calculation of probability of failure (PoF) where the load distribution is augmented by a quantity equal to the TIM. This approach avoids some of the perplexing results common to traditional reliability theory where, on the basis of very small amounts of data, one is led to extraordinary claims of infinitesimal probability of failure. Additionally, this approach permits a more meaningful separation of statistical and engineering issues.

References

References
1.
Freudenthal
,
A. M.
,
Garrelts
,
J. M.
, and
Shinozuka
,
M.
,
1966
, “
The Analysis of Structural Safety
,”
J. Struct. Div., Proc. Am. Soc. Civ. Eng.
,
92
(
ST1
), pp.
267
325
.
2.
Ang
,
A.-S.
, and
Amin
,
M.
,
1968
, “
Reliability of Structures and Structural Systems
,”
ASCE J. Eng. Mech. Div.
,
94
, pp.
671
691
.
3.
Madsen
,
H. O.
,
Krenk
,
S.
, and
Lind
,
N. C.
,
2006
,
Methods of Structural Safety
,
Courier Corporation
, Dover Publications, New York.
4.
Wu
,
Y.-T.
, and
Wirsching
,
P. H.
,
1987
, “
New Algorithm for Structural Reliability Estimation
,”
J. Eng. Mech.
,
113
(
9
), pp.
1319
1336
.
5.
Rosenblatt
,
M.
,
1956
, “
Remarks on Some Nonparametric Estimates of a Density Function
,”
Ann. Math. Stat.
,
27
(
3
), pp.
832
837
.
6.
Rackwitz
,
R.
,
2001
, “
Reliability Analysis—A Review and Some Perspectives
,”
Struct. Saf.
,
23
(
4
), pp.
365
395
.
7.
Der Kiureghian
,
A.
,
2008
, “
Analysis of Structural Reliability Under Parameter Uncertainties
,”
Prob. Eng. Mech.
,
23
(
4
), pp.
351
358
.
8.
Der Kiureghian
,
A.
,
1989
, “
Measures of Structural Safety Under Imperfect States of Knowledge
,”
J. Struct. Eng.
,
115
(
5
), pp.
1119
1140
.
9.
Krishnamoorthy
,
K.
, and
Mathew
,
T.
,
2009
,
Statistical Tolerance Regions: Theory, Applications, and Computation
, Vol.
744
,
Wiley
, Hoboken, NJ.
10.
Fisher
,
R. A.
,
1934
, “
Two New Properties of Mathematical Likelihood
,”
Proc. R. Soc. London, Ser. A
,
144
(
852
), pp.
285
307
.
11.
Ang
,
A. H.-S.
, and
Tang
,
W. H.
,
1975
,
Probability Concepts in Engineering Planning and Design: Volume I—Basic Principles
,
Wiley
, Hoboken, NJ.
12.
Benjamin
,
J. R.
, and
Cornell
,
C. A.
,
1970
,
Probability Statistics and Decision for Civil Engineers
,
McGraw-Hill Book
, New York.
13.
Weibull
,
W.
,
1951
, “
A Statistical Distribution Function of Wide Applicability
,”
ASME J. Appl. Mech.
,
18
(
3
), pp.
293
297
.
14.
Committee of the National Research Council
,
2008
,
Evaluation of Quantification of Margins and Uncertainties Methodology for Assessing and Certifying the Reliability of the Nuclear Stockpile
,
The National Academies Press
, Washington, DC.
15.
Parzen
,
E.
,
1962
, “
On Estimation of a Probability Density Function and Mode
,”
Ann. Math. Stat.
,
33
(
3
), pp.
1065
1076
.
16.
Efron
,
B.
,
1979
, “
Computers and the Theory of Statistics: Thinking the Unthinkable
,”
SIAM Rev.
,
21
(
4
), pp.
460
480
.
17.
Efron
,
B.
,
1979
, “
Bootstrap Methods: Another Look at the Jackknife
,”
Ann. Stat.
,
7
(
1
), pp.
1
26
.
18.
Aven
,
T.
,
2013
, “
On the Meaning of a Black Swan in a Risk Context
,”
Saf. Sci.
,
57
, pp.
44
51
.
19.
Paté-Cornell
,
E.
,
2012
, “
On ‘Black Swans' and ‘Perfect Storms': Risk Analysis and Management When Statistics Are Not Enough
,”
Risk Anal.
,
32
(
11
), pp.
1823
1833
.
20.
Feynman
,
R. P.
,
1988
,
What Do You Care What Other People Think?: Further Adventures of a Curious Character
,
W. W. Norton & Company
, New York.
You do not currently have access to this content.