Many of the Weibull articles are copies from other bad copies, thus
legibility is a little difficult in preserving these old, important, historical,
documents pertaining to Weibull analysis.
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1.
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Waloddi Weibull author, Professor,
Royal Technical University, Stockholm, 1939
”A Statistical Theory Of The Strength
Of Materials”, Ingeniörsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens
Litografiska Anstalts Förlag, Stockholm.
This document, in English, was provided by Isamu Yoshimoto, 1-26-23-301 Kamiyoga, Setagaya-ku, Tokyo,
158-0098, JAPAN to Dr. Abernethy. This
document shows the mean rank Y-axis plotting position used by Dr.
Weibull. Later, Dr. Weibull adopted Benard’s median rank plotting position.
Download this 2.8Meg
PDF file which includes 45 pages.
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2.
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Waloddi Weibull author, 1939
”The Phenomenon of Rupture in Solids”,
Ingeniörs Vetenskaps Akademien-Handlingar, Nr 153, 1939, Generalstabens
Litografiska Anstalts Förlag, Stockholm.
Document Search/Request:
Download this 12.8
Meg PDF file which includes 54 pages. Thanks to Markus Wesoly
for finding this old paper from Dr. Weibull.
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3.
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Waloddi Weibull author, 1948
“En Statistisk Teori
För Utmattmingshallfastheten”,
Report TM 344 written for AB Bofors (in Swedish)
dated 2.9.1948 [If you could translate this to English, please send
a copy to Paul Barringer for
posting] This 23 page report is
broken into three sections for easier download.
The
first section includes pages 1-8
779KB PDF file
(8 pages)
The
second section includes pages 9-17
891KB PDF file
(9 pages)
The third section includes
18-23
362KB PDF file
(6 pages)
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4.
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Waloddi Weibull author, 1949
“A Statistical Representation Of Fatigue Failures In Solids”,
Transactions Of The Royal Institute Of Technology, Stockholm, Sweden, Number
27,
This report is broken into four sections for easier download.
The
first section includes the Introduction and Statistical Aspects
554KB PDF file
(12 pages)
The
second section includes Complete Fatigue Diagram and S-N Curves
633KB PDF file
(17 pages)
The third section includes
P-S Curves Size Effect, Computation of the Parameters, and Numerical Examples
790KB PDF file
(15 pages)
The fourth section includes
Appendix by Bengt W. Weibull, Punched-Card Methods
790KB PDF file
(9 pages)
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5.
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Waloddi Weibull author, 1950
“Explosion of Spherical Charges in
Air: Travel Time, Velocity of Front, and Duration of Shock Waves”
Abstract-
Travel times of shock waves
emitted from bare spherical charges of high explosives have been
measured. The experimental
arrangements are described. Observed
values may be reproduced with great precision by the formulae given in
Figures 4 and 5.
The scaling laws have been
verified over the whole range.
The relations between the front
velocity and the ambient density of the surrounding atmosphere have been
determined.
The front velocities of shocks
from PETN and from different mixtures of TNT and A1 have been determined.
(Figure 8).
The resulting data do not verify
the theories of Rüdenberg and Sedov.
Report Number: X-127
Referenced as AD-0704695
BALLISTIC RESEARCH LABS ABERDEEN PROVING GROUND MD
TI (6) EXPLOSION OF SPHERICAL CHARGES
IN AIR: TRAVEL TIME, VELOCITY OF
FRONT, AND DURATION OF SHOCK WAVES (Detonation av Klotformiga Laddningar iLuft; Gangtid, Fronthastighet och Vaglangd hos den Ustsanda Stotvagen)
Prof. Waloddi Weibull
Feb 1950, 27 Pages
Unclassified report
Trans. from Tidskrift fuer
Kustartilleriet (Sweden) n1 1947, by Lars Niclas Enequist.
Download this 1.3 meg file as AD-0704695.
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6.
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Waloddi Weibull author, 1951
“A Statistical Distribution Function
of Wide Applicability”,
Journal Of Applied Mechanics ASME Paper.
4 Meg
PDF file (7 pages)
ßThis is THE hallmark Weibull paper and includes
discussion in this one file!
See Weibull’s Example
1. ßYield strength
See
Weibull’s Example 2 . ßFly ash size distribution
● Also see Goren
Weibull’s comments about his father’s 1951 paper from the Garfield
Library classics of 1981 (thanks to Fritz Scholz for this reference).
● Also
see the Birnbaum
tribute by Sam Saunders , page xxi, top paragraph, of why the Weibull
distribution may have gained much wide use (thanks to Fritz Scholz for this
reference).
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7.
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Benard, A and Bos-Levenbach, E.
C. authors, 1953
“Het uitzetten van waarnemingen op waarschijnlijkheidspapier” (The
Plotting of Observations on Probability Paper), Statististica
Neerlandica, Volume 7, Issue 3, September 1953, pages 163-173. Translated from Dutch into English by Ronald Schop in 2001 (In Weibull’s later papers, Dr.
Weibull acknowledged the superiority
of using Benard’s median rank equation as providing
a better plotting position for ranked data on Weibull probability paper).
This
paper is available for download as a 191
KB PDF file (8 pages)
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8.
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Waloddi Weibull author, May 1955
“Basic
Aspects Of Fatigue”
A paper presented at the Stockholm
Colloquium On Fatigue, 6 pages.
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9.
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Waloddi Weibull author, September 1959
“Statistical Evaluation Of Data From Fatigue And Creep-Rupture Tests
Part 1. Fundamental Concepts And General Methods”,
Wright Air Development Center Report 59-400, Report # AD229450—September 1959,
1
This report is broken into four sections for easier download.
The
first section includes Introduction, Classification of Test Series, and
Statistical Methods and Tools.
1.438MB PDF file
(25 pages)
The
second section includes Estimation Of Distribution Parameters.
1.088MB PDF file
(22 pages)
The third section includes
Fitting Curves To Observations and Bibliography.
368KB PDF file (8
pages)
The fourth section includes
Tables and Figures.
1.165MB PDF file
(25 pages)
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10.
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Waloddi Weibull author, 1960
“Size Effects On Fatigue Crack Initiation and Propagation In Aluminum
Sheet Specimens Subjected To Stresses Of Nearly Constant Amplitude”,
Report 86 to Flygtekniska Försöksanstalten
The Aeronautical Research Institute Of Sweden.
Summary:
Fatigue tests on axially-loaded
24S-T and 75S-T aluminum sheet specimens of various sizes were conducted with
a constant nominal stress amplitude, established by a stepwise reduction of
the load in proportion to the remaining cross-sectional area.
Earlier observations were
confirmed, showing that, in this type of test, the crack propagates with a
constant, stable rate of growth after a---generally short---transition period
has been passed. This transition
period was found to increase with the number of cycles necessary to initiate
a visible crack.
A law, deduced by means of
dimensional considerations and stating that the stable rate of growth should
be proportional to the size of geometrically similar specimens, was well
substantiated, which implies that the relative rate of growth is, for a given
stress amplitude and mean stress, a material constant.
For geometrically similar
specimens, the period of crack initiation was observed to depend on the size
of the notch and to increase with decreasing size, which is in accordance
with the statistical theory of strength.
Stockholm, June, 1960.
2.4Meg
PDF file (30 pages)
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11.
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Waloddi Weibull author, 1961
Fatigue Testing And Analysis Of
Results
published for and on behalf of Advisory Group For Aeronautical Research and
Development North Atlantic Treaty Organization..
This old book is broken into chapters for easier downloading as PDF files.
The
first section contains a title page with a hand written note from Waloddi
Weibull “To Professor A. M. Freudenthal with best
wishes from the author.” , Table of Contents, Forward by Theodore von Kármán, Chapter 1 on Symbols and Nomenclature, Chapter 2
on Fatigue Testing Methods
1.833MB PDF
file (18 pages)
The
second section contains Chapter 3 on Fatigue Testing Machines And Equipments
3.075MB PDF
file (21 pages)
The
third section contains Chapter 4 on Instruments And Measuring Devices
1.063MB PDF
file (8 pages)
The
fourth section contains Chapter 5 on Test Pieces: Design, Preparation,
Measurement And Protection
799KB PDF
file (6 pages)
The
fifth section contains Chapter 6 on Factors Affecting Test Results
2.878MB PDF
file (20 pages)
The
sixth section contains Chapter 7 on Planning Of Test Programmes
and Chapter 8 on Presentation Of Results [Weibull
probability plots appear in this section]
3.179MB PDF
file (27 pages)
The
seventh section contains Chapter 9 on Analysis Of Results [Dr. Weibull shows how to
transform two-dimension S-Se into a one-dimensional function, and
he mentions Benard’s median rank, discusses
graphical methods for plots, etc.]
3.642MB PDF
file (33 pages)
The
eight section contains the Bibliography
3.758MB PDF
file (28 pages)
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12.
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Waloddi Weibull author,
August 1962
The
Effect Of Size And Stress History On Fatigue Crack Initiation And Propagation
Abstract-
The
first part of investigation deals with the effect of size and preloading on
the duration Ni of the crack initiation period. Geometrically similar sheet specimens of
two different aluminum alloys were subjected to various load cycles. It was found that each size had its
individual S-Ni curve, considerable differing from those of other
sizes. A reduction to one and the same
size by means of the Neuber stress concentration
factor KN was only partially successful. A static preload was found to increase the
value of Ni from 11 kc to 205 kc.
The
second part of the investigation deals with the propagation period. Equations relating crack length to number
of cycles are derived for two alternatives: constant stress cycles and
constant load cycle applied to a sheet specimen. The formulas are verified by tests
including various combinations of material, size, and stress amplitude.
In
the first alternative, it was found that the rate of crack growth is,
independently of the crack length, constant after a transition period has
been passed. The duration of this
period is dependent on the duration of the preceding initiation period. For small values of Ni it does
not even exist.
In
the second alternative a convenient method for interpreting the results was
obtained by plotting crack length vs. number of cycles. It was found that the propagation period
starts with a transition period, followed by one, two, or even three stable
propagation periods, the number depending on the magnitude of the applied
load. As examination of the broken
specimens showed that these periods correspond to different fatigue
mechanisms.
It
is concluded that total fatigue life cannot be predicted without considering
separately the parts of which it is composed.
Consequently, it cannot be expected tat the shape of the conventional
S-N curve that relates total life to applied load can be corrected to relevant
testing conditions.
Forward-
This
report was prepared by Prof. Dr. Waloddi Weibull, Bockamöllan, Sweden under USAF Contract No. AF
61(052)-522. The contract was
initiated under Project No. 7351, “Metallic Materials”, Task No. 735106,
“Behavior of Metals.” The contract was administered by the European Office,
Office of Aerospace Research. The work
was monitored by the Directorate of Materials and Processes, Aeronautical
Systems Division, under the direction of Mr. W. J. Trapp.
This
report covers work conducted during the period September 1960 to September
1961.
Report Number:
ASD-TDR-62-785
Originating Activity:
Bockamöllan, Sweden
Referenced as:
AD-287962 / xag
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 370K PDF file
(23 pages)
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13.
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Waloddi Weibull author,
February 1963
Outline Of An Algebra Of Stochastic
Quantities
Abstract-
The
aim of the work reported has been to develop methods of solving random
equations, that is, equations involving variates (random variables). The main difficulty of this task arises
from the fact that no variate, if not degenerate, is invertible, or,
algebraically expressed, even if the set V of variates is a commutative monoid under both addition and multiplication, it does
not constitute a field.
For
this purpose a set S of elements, called stochastic quantities (for brevity,
stochastics), of which V is a subset, has been constructed with the property
that it constitutes a field. This
implies that there exists for every element of it an inverse element relative
to both the additive and multiplicative laws of composition, and thus it will
be possible to compute with the stochastics just as easily as is done with
the rational numbers with respect to the four fundamental operations +,
-, •, :.
Considering
a variate as a finite or infinite set of ordered pairs, denoted by f(x) [x],
where the first projection f(x) is a real-valued, non-negative function,
defined for a continuous set of values of x or for an at most denumerable set
of points xi and interpreted as a mass density or as discrete
parts of a unit mass, respectively; and the second projection [x] is anyone
of the values that the variate can take, the notation of a stochastic is
f(x)• j [x],
where f(x) is a real valued, positive or negative, function and the symbol j[x]
is defined, for n = 1, by j [x] = (1/dz)[x] – (1/dz)[x+dz]. Thus j may be interpreted as a duplex mass, composed of two
infinitely large masses (1/dz) and –(1/dz) located
at an infinitesimal distance dz from each
other. For n = 2 we have j [x] =(1/dz )[x] – (2/dz)[x+dz] + (1/dz)[x+2•dz] and jmay be interpreted as a triplex mass, composed of three
infinitely large masses at an infinitesimal distance dz
from each other, and so on for arbitrary values of n. Since, by definition, j [x] = 1[x], the general expression includes the variates as
a special case obtained by setting n = 0.
From
the definition above it follows, if f(x) is a continuous function, that f(x)
• j[x]
is equal to the ordinary derivative dn(fx))/dxn. Thus, j
can be regarded not only as a multiplex mass but also as an operator. In the same way, j , defined as the inverse of j ,
can be interpreted both as a mass distribution and as a repeated integration,
further, the operator dn/dxn = jn
may be defined, as is demonstrated, also for the general case that nx is an arbitrary real number.
Since
some problems leading to random equations have been presented, general
properties of variates and multiplex stochastics are indicated. Based on the know laws of composition of
variates, corresponding laws and some general theorems valid for multiplex
stochastics have been deduced. Owing
to the dual nature of the symbol jn,
simplified methods for composition and inversion of variates can be developed
as is demonstrated. Finally,
classification and some solutions of random equations and criteria for the
existence of real roots are indicated.
Forward-
This
report was prepared by Prof. Dr. Waloddi Weibull,
La Rosiza, Lausanne, Switzerland under USAF
Contract No. AF 61(052)-522. The
contract was initiated under Project No. 7351, “Metallic Materials”, Task No.
735106, “Behavior of Metals”. The
contract was administered by the European Office, Office of Aerospace
Research. The work was monitored by
the Directorate of Materials and Processes, Aeronautical Systems Division,
under the direction of Mr. W. J. Trapp.
The
report covers work conducted during the period February 1960 to August 1962.
[Formulas presented in this ASD-TRD-63-63, also referenced as AD-298991, were
used in the March 1969 report AF61(052)-522 as worked out examples, also
referenced as AD-816012.]
Report Number:
ASD-TDR-63-63
Originating Activity:
La Rosiaz
Lausanne, Switzerland
Referenced as:
AD-0298991
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 3 Meg PDF file of AD-0298991 (57
pages)
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14.
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Waloddi Weibull coauthor—December 1963
”First Seminar On Fatigue And Fatigue Design”, by A. M. Freudenthal, W. Weibull, and A. O. Payne, Sponsoring
Agencies: Office of Naval Research, Air Force Materials Laboratory, Advanced Research
Projects Agency, Contract No. NONR 266(91), Project NO. NR 064-470, Technical
Report No. 2, Columbia University Department Of Civil Engineering And
Engineering Mechanics, December 1963
The report is broken into six sections for ease of download:
1. Fatigue Mechanisms and Fatigue Damage Accumulation by A. M. Freudenthal, Cover page through page 23, 1.3 Meg PDF file. Provides an introduction and the state of
fatigue in 1963.
2.
Fatigue Crack Propagation In
Sheet Specimens by Waloddi Weibull, page 24 through page 52, 1 Meg PDF file.
Discusses a failure model for fatigue crack propagation which is independent
of the crack length.
3.
Fatigue Design And Reliability
by A. M. Freundenthal, page 53 through page 67, 0.5 Meg PDF file.
Discusses load-strength interference and structural reliability under conditions
of fatigue with a probabilistic approach to safety analysis.
4.
Analysis Of Fatigue Test
Results by Waloddi Weibull, page 68 through page 89, 0.7 Meg PDF file.
Discusses probit tests for life and stress levels and the three parameter
Weibull equation to model fatigue life or fatigue strength.
5.
Fatigue Of Structures by A.
O. Payne, pages 90 through page 137, 2 Meg PDF file.
Discusses fatigue failures for aircraft, welds and welded construction
fatigue, fatigue of welded pressure vessels, riveted aluminum fatigue,
notched material fatigue, effects on preloads on fatigue life [Mustang wings
refer to the P-51 airplane], safe life structures modeled by the log normal
distribution, submarine hulls fatigue life, tanker trucks fatigue life,
6.
Appendix, pages 138 through
page 172, 1.1 Meg
PDF file.
Contains the graphs and tables associated with the Fatigue of Structures
paper. Appendix I discusses Methods of
Improving the Fatigue Resistance of Welds.
Appendix II discusses Design of Program Load Test For Aircraft Wing,
Tables, and Figures.
Report Number:
TR-2
Referenced as:
AD-619075 / xag
– also see AD-611414
Thanks to Sam Chan of The Boeing Company for finding this document.
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15.
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Waloddi Weibull author—March 1967
“Estimation Of Distribution
Parameters By A Combination Of The Best Linear Order Statistic Method And
Maximum Likelihood”.
Abstract-
This
report consists of three parts, the first one dealing with the unbiased,
minimum-variance estimation of location scale parameters, assuming the shape
parameter to be known, the second one presenting formulae for computing the
likelihood of a given sample, the third one specifying the estimation
procedure. The first part develops
general formulae for computing the coefficients of linear estimators,
composed of all or part of the elements of a random sample. These formulae are specialized for the
cases of exponential distributions and also for estimations, using two of the
order statistics only. Formulae for expected
values, variances and covariances of standardized
Weibull order statistics are deduced and applied to a system of equations,
which determines the linear coefficients.
For the solution of such systems, a program has been written and
applied to a IBM 7090 computers, which delivers the results extremely fast,
thus eliminating the need of extensive tables. Tables of expected values and covariance
matrices are presented for sample sizes n = 5, 10, 15, 20 and a = 0.1, 0.3, 0.5, 0.7, 0.9, 1.0, useful
when no computer is available. The
second part presents formulas for computing the likelihood of a given sample
for the most general situation, that is, for arbitrarily censored, truncated
or grouped samples, and, for the special case of life testing, when the
sample may be composed of one subset of items, which have failed after observed
time units, a second subset of items, which have accumulated observed time
units, without failure, and a third subset of items, which have failed during
one or more inspection periods, without knowing their exact life times. The third part defines the procedure of
combining the preceding formulas for best estimation, when none of the
parameters is known.
[Formulas presented in this
AFML-TR-67-105, also referenced as AD-816206, were used for in report
AFML-TR-69-143, also referenced as AD-689407.]
USAF report AFML-TR-67-105 / AF 61(052)-522 —1967
This report is broken into two parts for easier download.
The
first is a narrative of the BLUES (best linear unbiased estimate)
581KB PDF
file (16 pages)
The
second contains tables
597KB PDF
file (15 pages)
AD-816206 / XAG
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16.
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Waloddi Weibull author, June 1967
“The Order Statistics yi = log(zim), Their Properties And Use For
Parameter Estimation (z = standardized Weibull variate)”
USAF AFML-TR=67-161; indexed as report AD-818104
Abstract-
Pertinent
formulas for the confidence limits, expected values, variance and covariances of the order statistics yi
= log(zim) have been
developed and used for application of the generalized least-squares method,
resulting in unbiased, minimum-variance estimates of the distribution
parameters. Approximation formulae,
based on simplified covariance matrices, have been proposed and
examined, Extensive tables of the
required statistics, computed by use of an IBM 7090 computer, are presented.
The first part contains Table Of Contents and Symbols 184KB
PDF file (6 pages)
The second part contains the body of the report in Sections 1-3. 952KB PDF
(26 pages)
The third part contains Tables 1: Values of Percentage Points, and Table 2:
Differences between Benard and Exact Percentage
Points 644KB
PDF file (8 pages)
The fourth part contains Table 3: Values of Percentiles yi,p;
N=1(1)25 533KB
PDF file (6 pages)
The fifth part contains Table 4: Expected Values E(yi),
Percentage Points P-bar-i and Variances 1,122KB
PDF file (17 pages)
The sixth part contains Table 5: Values of Correction Term, Table 6: Accuracy
of Proposed Formulas for Plotting Positions, and Table 7: Coefficients ai, bi of Linear, Unbiased, Minimum Variance Estimators:
N = 2(1)5;10;20 145KB
PDF file (3 pages)
Report Number:
AFML-TR-67-161
Originating Activity:
La Roziaz
Lausanne
Referenced as:
AD-818104
Thanks to Jim Breneman of Pratt & Whitney for finding this document.
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17.
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Waloddi Weibull author, June 1967
“Estimation Of Parameters From Large
Samples Arbitrarily Censored Or Truncated”
Abstract-
Approximation formulas for the
expected values, variances and covariances of the
order statistics yi, which provide a
very good approximation for sample sizes equal to or larger than N=20, are
developed. Their applications to
graphical analysis and parameter estimations by use of desk computing
machines and digital computers are demonstrated. Tables which simplify the computing
procedure are presented.
Report Number-
AFML-TR-67-197
Referenced as-
AD-0657318
Waloddi
Weibull LAUSANNE (SWITZERLAND)
Download this 1.1 Meg file as AD-0657318.
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18.
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Waloddi Weibull author, December 1967
“Moments About Smallest Sample Value”
Abstract-
A new type of moments has been
achieved by substituting in the central moments the smallest value of the
sample for its mean. The new moments
have the same advantage as the central moments of being independent of the
location parameter but for certain value of the shape parameter they have
less variance and thus are preferable for estimating purposes. The asymptotic properties of four
estimators, three of them composed of the new moments and one of them of
central moments have been examined. It
could be concluded that for the shape parameter a ≥ 0.5 the
estimator, which was composed of the first and second order moments of the
new type, was by far the most efficient one.
Small-sample properties of the new-moments estimators have been
appraised by use of extensive Monte-Carlo studies and it could be stated that
the same conclusion applies also to small and moderated sample sizes.
Report Number-
AFML-TR-67-375 Referenced as AD-0664049
Waloddi Weibull LAUSANNE
(SWITZERLAND)
Download this 2.3 Meg file as AD-0664049.
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19.
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Allis/Seimens, 1968
“Instructions For How To Perform A Weibull Analysis By Hand”—1968.
This report is broken into three parts for easier download.
The
first is a narrative file
1.24Meg PDF file (14
pages).
The
second contains tables
760KB PDF file (12
pages).
The
third contains graphs.
598KB PDF (4 pages).
Unfortunately, every other page is missing from the original file!!
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20.
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Waloddi Weibull author, 1969
A List Of USAF reports
192K
PDF file (5 pages)
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21.
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Waloddi Weibull author, 1969
A list of books and papers
264KB
PDF file (7 pages)
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22.
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Waloddi Weibull author, March 1969
”Composition And Decomposition Of Bounded Variates With Special
Reference To The Gamma And The Weibull Distributions”.
USAF report AF61(052)-522; indexed as report AD-816012
Abstract-
The
algebra published in Technical Report No. ASD-TDR-63-63 has been further
developed, and its use has been illustrated by some worked examples. After some modifications of the notations,
the differentiation and integration of stochastics, including the variates as
a special case, have been more thoroughly examined, in particular with
respect to the concept of broken derivatives and integrals. A generalized distribution function
has been set up. By proper
specification of its two shape parameters, it can be brought to reproduce the
density functions of the Exponential, Gamma, Pearson Type III, Chi-square,
Rayleigh, Weibull, and some more distributions of practical importance. This general function has been expanded in
a power series which is transformed in a series, called the integral
series. Based on these formulae, rules
of summation and multiplication of independent variates are presented and
applied to some distributions. Inverse
addenda for various variates have been developed and used for decomposition
of sums of Gamma and Weibull variates.
Forward-
This
report was prepared by Prof. Dr. Wallodi Weibull,
Lausanne, Switzerland, under USAF Contract No. AF 61(052)-522. The contract was initiated under Project
No. 7351, “Metallic Materials”, Task No. 735106, “Behavior of Metals”. The contract was administered by the
European Office, Office of Aerospace Research. The work was monitored by the Air Force
Materials Laboratory, Research and Technology Division, Air Force Systems
Command, Wright-Patterson Air Force Base, Ohio, under the direction of Mr. W.
J. Trapp.
This
report covers work conducted during the period February 1964 to February
1965. The manuscript was released by
the author in November 1966 for publication as an AFML Technical Report.
[Worked out formulas presented in this March 1967 report AF61(052)-522, also
referenced as AD-816012, were derived from the February 1963 report
ASD-TDR-63-63, also referenced as AD-298991.]
The
first part contains the Abstract, Table of Contents, and the Introduction
227KB
PDF file (5 pages)
The
second part contains Notations For Discontinuous Functions, Notations For
Variates And Other Stochastics, Differentiation and Integration Of
Stochastics
582KB
PDF file (12 pages)
The
third part contains A Generalized distribution Function, Expansions In Power
Series and Integral Series, Composition Of Independent Variates,
Decomposition Of Sums Of Independent Variates, and Tables
531KB
PDF file (11 pages)
Thanks to Jim Breneman of Pratt & Whitney for finding this document.
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23.
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Waloddi Weibull author, April 1969
”A Criterion for The Acceptability Of
Assumed Distributions”
Abstract-
The
usual way to solve the fundamental problem of deciding whether an assumed
distribution function is acceptable or not, consists – if at all done – in
estimating the parameters and checking the attained goodness of fit by some
accepted criterion, in most cases the Chi-square test. In this way, the decision depends not only
on the assumed function, so it may happen that an acceptable function may be
rejected on the basis of results from poor estimating or fitting procedures.
The
purpose of this research was to find a criterion which eliminates such
fatalities and depends entirely on the assumed function alone. Such a criterion, based on the
“number-of-runs” has been proposed.
The properties of this statistic and its usefulness as a measure of
departure from the true distribution have been demonstrated. The concept “maximum number of runs”
(MAXNOR) of a given sample and methods for its ascertaining have been
introduced. Its use as a criterion for
deciding whether the assumed function is acceptable or not has been studied
by applying it to data from tests on strength of brittle materials, fatigue
life of aluminum alloys, etc.
Forward-
This
report was prepared by Prof. Dr. Waloddi Weibull,
La Rosiaz, Lausanne, Switzerland, under USAF
Contract No. AF 61(052)-943. The
contract was initiated under Project No. 7351, “Metallic Materials”, Task No.
7351, “Metallic Materials”, Task No. 735106, “Behavior of Metals”. The contract was administered by the
European Office, Office of Aerospace Research. The work was monitored by the Air Force
Materials Laboratory, Air Force Systems Command, Wright-Patterson Air Force
Base, Ohio, under the direction of Mr. W. J. Trapp.
This
report covers work conducted during the period February 1968 to December
1968.
The
manuscript of this report was released by the author January 1969 for
publication as a technical report.
Report Number:
AFML-TR-69-124
Originating Activity:
La Rosiaz
Lausanne, Switzerland
Referenced as:
AD-689406 / xag
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 0.677
Meg PDF file (36 pages)
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24.
|
Waloddi Weibull author, April 1969
”The Efficiencies Of Unbiased, Linear
Estimators For Scale and Location Parameters Composed Of One, Two, Or Three
Order Statistics”
Abstract-
The
result of this investigation is, from a practical point-of-view, important in
so far as it proves that the procedure of estimating scale and location
parameters can be simplified by suppressing a large part of the sample
without much loss in efficiency provided that the proper ordered observations
are used. These order numbers are
presented for estimators composed of one, two, or three observations. It is remarkable that neglecting, for
instance 39 out of 40 observations reduces the efficiency by 35% only. The actual reduction in efficiency, being
in many cases quite small when using two or three observations, can be read
from the tables.
[Formulas
presented in AFML-TR-67-105, also referenced as AD-816206, were used for this
report.]
Forward-
This
report was prepared by Prof. Dr. Waloddi Weibull, Lausanne, Switzerland,
under USAF Contract No. AF 61(052)-943.
The contract was initiated under Project No. 7351, “Metallic
Materials”, Task No. 735106, “Behavior of Metals”. The contract was administered by the
European Office, Office of Aerospace Research. The work was monitored by the Air Force
Materials Laboratory, Air Force Systems Command, Wright-Patterson Air Force
Base, Ohio, under the direction of Mr. W. J. Trapp.
This
report covers work conducted during the period February 1967 to February
1968. The manuscript of this report
was released by the author March 1968 for publication.
Report Number:
AFML-TR-69-134
Originating Activity:
La Rosiaz
Lausanne, Switzerland
Referenced as:
AD-689407 / xag
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 0.416
Meg PDF file (21 pages)
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25.
|
Waloddi Weibull author, April 1969
”Moment Estimators For Weibull
Parameters And Their Asymptotic Efficiencies”
USAF report AFML-TR-69-135; indexed as AD-690162
Abstract-
The
classical method of moments for estimating distribution parameters which
consists in equating as many of the populations as the number of unknows to the corresponding sample moments has been much
appreciated, because it is quite easy to use and does not need any ordering
of the observation. However, in some
cases its efficiency is very poor, so it has to be used with some
precaution. In order to elucidate this
statement, formulas for the asymptotic efficiency of the most used estimators
have been derived for the alternatives of one, two and three unknown
parameters. Numerical values
corresponding to several values of a
and for the cases of one or two unknown parameters have been computed and are
presented.
Forward-
This
report was prepared by Prof. Dr. Waloddi Weibull, Lausanne, Switzerland,
under USAF Contract No. AF 61(052)-522.
The contract was initiated under Project No. 7351, “Metallic
Materials,” Task No. 735106, “Behavior of Metals”. The contract was administered by the
European Office, Office of Aerospace Research. The work was monitored by the Air Force
Materials Laboratory, Air Force Systems Command, Wright-Patterson Air Force
Base, Ohio, under the Direction of Mr. W. J. Trapp.
This
report covers work conducted during the period 1964. The revised manuscript was released by the
author August 1968,
This report is 535KB
PDF file (15 pages)
Thanks to Jim Breneman of Pratt & Whitney for finding this document
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26.
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Waloddi Weibull author, April 1969
”A General Method For Estimating
Distribution Parameters”
Abstract-
The
method presented is applicable to complete, censored, or truncated samples and
to grouped data drawn from any population having a continuous distribution
function, simple or composed, involving an arbitrary number of unknown
parameters. The estimates are
consistent and asymptotically efficient (in some cases for any sample size)
and easily determined by use of a versatile computer program. The efficiency can be stated for any
individual case, even when only a part of the sample is used for the
estimation. Two criteria of
goodness-of-fit, which complete each other, makes it possible to decide
whether the fit attained is acceptable or not.
Two
applications may be mentioned: the evaluation of data from bending and
torsional tests on brittle materials, a problem up-to-now not quite
satisfactorily solved due to the complicated distribution functions arising;
and the analysis of bimodal fatigue-life distributions.
Forward-
This
report was prepared by Prof. Dr. Waloddi Weibull, Lausanne, Switzerland,
under USAF Contract No. AF 61(052)-943.
The contract was initiated under Project No. 7351, “Metallic
Materials,” Task No. 735106, “Behavior of Metals”. The contract was administered by the
European Office, Office of Aerospace Research. The work was monitored by the Air Force
Materials Laboratory, Air Force Systems Command, Wright-Patterson Air Force
Base, Ohio, under the Direction of Mr. W. J. Trapp.
This
report covers work conducted during the period April 1967 to April 1968. The revised manuscript was released by the
author June 1968 for publication.
Report Number:
AFML-TR-69-136
Originating Activity:
La Rosiaz
Lausanne, Switzerland
Referenced as:
AD-689405 / xag
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 0.591
Meg PDF file (36 pages)
|
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27.
|
Waloddi Weibull author,
February 1971
Outline Of A Theory Of Powerful
Selection Of Distribution Function
Abstract-
The
conventional method of analyzing a given set of test data consist in assuming
a distribution function and estimating its parameters. The only way of deciding whether the
function is acceptable or not and which of two assumed functions is the
better one is by means of a test of goodness-of-fit. For small and moderate sample sizes this
test makes a very unreliable basis for a decision, and the confidence that
can be put in the choice is practically unknown.
In order to eliminate these
deficiencies a new method, called the method of powerful selection, is
proposed. By use of a test statistic,
called the selector, it is possible, without preceding parameter estimators,
to state the acceptability of a function on the basis of a pre-assigned
level-of-significance and the decision power, that is, the chance of making a
true decision between two functions.
The tools of this method are presented and their applications
illustrated by numerical analyses of some fatigue-test series.
It
will not too seldom occur that none of several assumed functions will be
accepted. In this situation the
selectors can be used for diagnosing the rejected functions with regard to
causes such as outlying observations, composed populations, and contaminated
data.
Forward-
This
report was prepared by Prof. Dr. Waloddi Weibull,
La Rosiaz, Lausanne, Switzerland under USAF
Contract No. F61052-69-C-0029. This
contract was initiated under Project No. 7371, “Metallic Materials”, Task No.
735106, “Behavior of Metals”. The
contract was administered by the European Office, Office of Aerospace
Research. The work was monitored by
the Metals and Ceramics Division, Air Force Materials Laboratory, Air Force
Systems Command, Wright-Patterson AFB, Ohio, under the direction of Mr. W. J.
Trapp.
This
report covers work conducted from 1 February 1969 to 28 February 1971. The manuscript of this report was released
by the author February 1971 for publication.
Report Number:
AFML-TR-71-52
Originating Activity:
15 Ch. Fontanettaz
1012 Lausanne, Switzerland
Referenced as:
AD-725037 / xag
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 1.7
Meg PDF file (48 pages)
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28.
|
Waloddi Weibull author, June 1972
The Concept Of Pseudo-Standardized
Variables and Its Use As Elements Of Shape Operators
Abstract-
The
concept of pseudo-standardized variable is explained and the fundamental
properties of this variable are indicated.
Its most important property of being scale and location invariant
makes it useful as elements of shape operators, and its space being equal to
the closed interval (0,1) has practical advantages.
Four
types of shape operators are defined and examined. Twenty-five tables which simplify their
practical applications have been prepared and are presented. Two examples concerning data of rotating
beam fatigue performance illustrate the different numerical procedures.
Forward-
The
research work reported herein was conducted by Prof. Dr. Waloddi
Weibull, Chemin Fontanettaz
15, 1012 Lasusanne, Switzerland under USAF Contract
No. F44620-72-C-0028. This contract,
which was initiated under Project No. 7351, “Metallic Materials”, Task
735106, “Behavior of Metals”, was administered by the European Office, Office
of Aerospace Research. The work was
monitored by the Metals and Ceramics Division, Air Force Materials
Laboratory, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio,
under the direction of Mr. W. J. Trapp, AFML/LL.
This
report covers work conducted during the period 1 February 1971 to May
1972. The manuscript was submitted by
the author for publication in June 1972.
Report Number:
AFML-TR-73-98
Later identified as AD-764361
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 2.5
meg PDF file (36 pages)
|
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29.
|
Announcement of Waloddi Weibull receiving 1972 ASME Medal for
distinguished engineering achievement at the Society’s Winter Annual Meeting
November 26-30, 1972. The announcement
also includes a brief biography.
93KB
PDF file. (2 pages)
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30.
|
Waloddi Weibull author, May 1973
The Rank-Score Test-An Improvement Of
The Rank Sum Test
Abstract-
The hypothesis that two random samples are from identically distributed but
unknown populations can be tested by use of the rank-sum as the test
statistic. It is proposed to
substitute for it the rank-score, which, as pointed out. Supplies more
information about the populations of the samples under examination.
This new statistic is
defined and its main properties are indicated. Tables for its application to
pseudo-standardized samples have been established by use of two computer
programs, thereby enabling tests of the hypothesis that the samples are from
populations with identical distribution function, including its shape
parameter, if any, but possible different scale and location parameters.
The practical use of the new
test has been demonstrated by numerical examples concerning samples of
fatigue test data from a large collection prepared at The Boeing Company.
Forward-
The research work reported
herein was conducted by Prof. Dr. Waloddi Weibull, Chemin Fontanettaz 15, 1012
Lausanne, Switzerland under USAF Contract No. F44620-73-C-0066. This contract was administered by the
European Office of Aerospace Research.
The contract, which was initiated under Project No. 7351, “Metallic
Materials:, Task 735106, “Behavior of Metals”, as administered by the
European Office of Aerospace Research.
The work was monitored by the Metals and Ceramics Division, Air Force
Materials Laboratory, Air Force Systems Command, Wright-Patterson Air Force
Base, Ohio, under the direction of Mr. W. J. Trapp, AFML/LL. This report covers work conducted during
the period 15 March 1973 to 15 April 1973.
The manuscript was submitted by the author for publication in May
1973.
Report Number:
AFML-TR-73-203
Originating Activity:
Professor Waloddi Weibul
15 Ch. Fontanettaz
1012 Lausanne, Switzerland
Referenced as: AD-769451 / xag
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 1.1
Meg PDF file (20 pages)
|
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31.
|
Waloddi Weibull author, May 1973
A New Test Operator, VJ, Based On
Class Frequencies
Abstract-
The test statistic X2 of the Chi-square test may, if applied to a
proper sample, be used for selecting distribution functions. When examining its use for this purpose its
decision power was found to be very small due to a kind of pooling, an
inherent property of its definition.
In order to eliminate this pooling, a new test statistic, denoted by
VJ, was introduced. It is defined by
the number vi of sample elements which fall within each of r
properly defined classes into which the space of the variable x has been divided. In fact X2 may be regarded as a
statistic obtained from VJ by a pooling procedure. For this reason VJ was expected to have a
much larger decision power than X2 as was verified by the example
that the decision power for a specified case being 6.6% for X2 was
raised to 69.1% for VJ.
The
properties of VJ have been thoroughly examined. In particular the class limits yielding the
largest decision power have been determined with the result that, in some cases,
the decision power was found to be somewhat larger than anyone so far
attained.
The
statistic VJ can also be used for stating whether a hypothetical distribution
is acceptable or not and also for selecting the most probable one within a
set of such distributions. Necessary
tables for the practical use have been prepared.
Forward-
The research work reported
herein was conducted by Prof. Dr. Waloddi Weibull, Chemin Fontanettaz 15, 1012
Lausanne, Switzerland under USAF Contract No. F44620-72-C-0028. This contract was administered by the
European Office of Aerospace Research.
The contract, which was initiated under Project No. 7451, “Metallic
Materials:, Task 735106, “Behavior of Metals”, as administered by the
European Office of Aerospace Research.
The work was monitored by the Metals and Ceramics Division, Air Force
Materials Laboratory, Air Force Systems Command, Wright-Patterson Air Force
Base, Ohio, under the direction of Mr. W. J. Trapp, AFML/LL.
This
report covers work conducted during the period 1 February 1971 to 30 April
1972. The manuscript was submitted by
the author for publication in May 1972. [This date may be incorrect as the
Document Control Data – R&D transmittal document shows May 1973]
Report Number:
AFML-TR-73-97
Originating Activity:
Professor Waloddi Weibul
15 Ch. Fontanettaz
1012 Lausanne, Switzerland
Referenced as: AD-762604 / xag
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 1.8
Meg PDF file (20 pages)
|
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32.
|
Waloddi Weibull author, May 1973
The EKS-Square Test Of Goodness Of
Fit—An Improvement Of The Chi-Square Test
Abstract-
When
applying the classical Chi-square test of goodness of fit, it is always
assumed that the test statistic is c2-distributed. Since this is true only for very large
samples, some restrictions on the class frequencies have to be
introduced. It is generally accepted
that none of the expected frequencies should be less than ten, which makes
this test useless for small and moderate samples.
In
order to eliminate these – from a practical viewpoint server – restrictions,
it is proposed to use the exact sampling distribution instead of the
limiting c2-distribution.
When doing so, the test will be called the Eks-square
test.
Programs
have been written for computing these distributions and the improvements
attained have been stated.
The
possibilities of using the modified test statistic as a location, scale, and
shape operator have been examined and illustrated by numerical examples. Several tables have been prepared.
Forward-
The
research work reported herein was conducted by Prof. Dr. Waloddi
Weibull, Chemin Fontanettaz
15, 1012 Lausanne, Switzerland under USAF Contract No. F44620-72-C-0028. This contract was administered by the
European Office of Aerospace Research.
The contract, which was initiated under Project No. 7351, “Metallic
Materials:, Task 735106, “Behavior of Metals”, as administered by the
European Office of Aerospace Research.
The work was monitored by the Metals and Ceramics Division, Air Force
Materials Laboratory, Air Force Systems Command, Wright-Patterson Air Force
Base, Ohio, under the direction of Mr. W. J. Trapp, AFML/LL.
This
report covers work conducted during the period 1 February 1971 to 25 February
1972. The manuscript was submitted by
the author for publication in March 1972. [This date may be incorrect as the
Document Control Data – R&D transmittal document shows May 1973]
Report Number:
AFML-TR-73-94
Originating Activity:
Professor Waloddi Weibul
15 Ch. Fontanettaz
1012 Lausanne, Switzerland
Referenced as: AD-762546 / xag
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 1.8
Meg PDF file (20 pages)
|
|
33.
|
Waloddi Weibull author, August 1973
The Concept Of Score Of A Random
Sample
Abstract-
To
any give random sample there may be assigned a number called its score and
denoted by SC(r,Nos), where r = the
number of classes into which the space of the random variable has been
divided and Nos = the number of order
statistics actually used. It is easily
determined from the sample elements and offers some definite advantages as a
test statistic for selecting the most probable population from which the
given sample has been drawn. Its
decision power tends with increasing r to the largest power attainable for
the given sample size. By means of
some versatile computer programs the sampling distributions for several
combinations of r and Nos have been
determined. Tables have been prepared
from which the probabilities of twelve different hypothetical populations can
be immediately read and their acceptability stated.
Foreword-
The
research work reported herein was conducted by Prof. Dr. Waloddi
Weibull, Chemin Fontanettaz
15, 1012 Lausanne, Switzerland under USAF Contract No. F44620-72-C-0028. This contract, which was initiated under
Project No. 7351, “Metallic Materials”, Task No. 735106, “Behavior of
Metals”, was administered by the European Office, Office of Aerospace
Research. The work was monitored by
the Metals and Ceramics Division, Air Force Materials Laboratory, Air Force
Systems Command, Wright-Patterson Air Force Base, Ohio, under the direction
of Mr. W. J. Trapp, AFML/LL.
This
report covers work conducted during the period 1 February 1971 to July
1972. The manuscript was submitted by
the author for publication in August 1972. [This date may be incorrect as the
Document Control Data – R&D transmittal document shows June 1973]
Report Number:
AFML-TR-73-95
Originating Activity:
Professor Waloddi Weibull
Ch. Fontanettaz 15
1012 Lausanne, Switzerland
Referenced as:
AD-764777 / xag
Thanks to Sam Chan of The Boeing Company for finding this document.
Download this file as a 1.1
Meg PDF file (36 pages)
|
|
34.
|
Waloddi Weibull author, 1973
Scientific Reports & Lectures
prepared for the U.S. Air Force on contract-1973 (with Waloddi
Weibull’s signature).
341KB
PDF file (5 pages)
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35.
|
Dumonceaux & Antle’s paper,
1973
“Discrimination Between the Log-Normal and the Weibull Distribution”
This paper shows 20 samples are needed to distinguish between Weibull
distributions and log-normal distributions—1973.
294K PDF file (4
pages)
|
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36.
|
Waloddi Weibull works and biography--1975
A translation
into English by Stig Elg
for the Swedish Academy of Engineering Sciences.
397KB
PDF file (5 pages)
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37.
|
Waloddi Weibull Summary of papers on the Weibull
distribution--1977
“References On The Weibull Distribution”, Försvarets
Teletekniska Laboratorium
[Stockholm],
FTL A-report, August 1977
[contains 1019 references to the Weibull distribution].
Thanks to Dr. Glenn Bowie, retired scientist from the Structures and
Materials Laboratory at Lockheed-California, Burbank, CA and his company CorTech Training, Red Wing, MN who loaned his report for
conversion into the PDF files listed in this section. You will find excerpts
from Dr. Bowie’s website at the bottom of this page concerning private
conversations he had with members of the Weibull family.
0.3 MB PDF File
(pages cover-5) introduction
0.8 MB PDF File
(pages 6-20) reference 1-115
1.1 MB PDF File
(pages 21-40) reference 116-286
1.2 MB PDF File
(pages 31-60) reference 287-453
1.1 MB PDF File
(pages 61-80) reference 454-617
1.1 MB PDF File
(pages 81-100) reference 618-785
1.1 MB PDF File
(pages 101-120) reference 786-951
1.0 MB PDF File
(pages 121-141) reference 952-1019 + Table of classified references +
cumulative references versus cumulative time.
Page 141 contains a graph of cumulative references to cumulative
time. Putting this data into a
Crow/AMSAA format, we can forecast that in 2003 we should expect the list of
references citing Weibull’s work will reach 10,000 documents.
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38.
|
Waloddi Weibull author, September 1977
The Probability Of Failure Of A System Subjected To The Joint Effect Of
Cyclic Loading And Randomly Distributed Discrete Load Peaks
Abstract-
If a specimen is subjected to some
kind of cyclic loading with a maximum load level S, which is larger than the
fatigue limit of the specimen, then the strength of the specimen will
gradually decrease until its residual strength R reaches the value S, when
static failure occurs.
This deterioration process may, as
indicated, be described graphically by and R-S-N diagram or analytically by a
set of parameter functions of S and N.
If now a discrete load peak of
known level L is imposed upon the specimen and N fatigue cycles, then the
probability of failure may be directly read from the diagram or computed by
use of the parameter functions.
A generalization of the
R=S=N=diagram is proposed in order to make it applicable to the case, when
the discrete load peaks are replaced by sequences of different cyclic
loadings.
By use of this diagram it has been
proved that Miner’s measure of cumulative fatigue damage M = Σni/Ni depends on the order in
which the different sequences are applied, a defect which has been repeatedly
verified by experiment.
Keywords-
Structural failure probability
Cumulative fatigue damage
Fatigue failure distribution
Structural reliability
Report Number-
AFML-TR-77-169
Originating Activity
Waloddi Weibull LAUSANNE (SWITZERLAND)
Referenced as-
AD-A055243
Download this 0.7 Meg file as AD-A055243
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39.
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Waloddi Weibull author, September 1977
“A New Test Of Normality And Of Exponentiality Called The Q-Test”
Abstract-
A new test statistic, denoted by Q and equal to the quotient of two unbiased
estimates of the standard deviation of a normal distribution is proposed for
testing the hypothesis that a given sample is drawn from a normal population
or, alternatively, from and exponential population. The sampling distributions of Q have been
computed and used for setting the limits of rejection regions corresponding
to 1%, 2%, and 5% levels of significance and also for stating the decision
power of Q used as a shape estimator.
Key words-
Distribution functions
Statistical sampling
Fatigue life distribution
Report Number-
AFML-TR-77-168
Originating Activity
Waloddi Weibull LAUSANNE (SWITZERLAND)
Referenced as-
AD-A055242
Download this 0.6 Meg file as AD-A055242
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40.
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Waloddi Weibull author, April 1978
A Test Of Homogeneity Based On Maximum
Likelihood Estimates
Abstract-
A sample is said to be homogeneous, if all its elements are drawn from the
same population, otherwise heterogeneous.
It is self-evident that there is no sense in estimating the parameters
of an assumed distribution from heterogeneous sample. Considering the fact that samples of
fatigue test data are frequently composed of elements drawn from tow or even
three populations, it is an important rule, frequently violated, to start
statistical analysis of a given sample by stating whether it is homogeneous
or not. A simple test based on the
alternative maximum likelihood estimates of the complete sample and of the
sample more or less truncated is presented.
Keywords-
structural failure probability
cumulative fatigue damage
fatigue failure distribution
structural reliability
Report Number:
AFML-TR-78-27
Originating Activity:
Professor Waloddi Weibull
Avenue d’Albigny, 9 BIS
74000 Annecy
FRANCE
Referenced as:
AD-A058102
Thanks to Jerry Sterling of NASA for finding this document.
Download this file as a 0.4 Meg PDF file
(12 pages)
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41.
|
Waloddi Weibull author, September 1977
The Concept Of Maximum Reliability
Selection Of Unknown Distribution Parameters
Abstract-
The classical method of estimating
an unknown parameter of a given distribution function by means of a unique
function of the observations has been replaced by a procedure which consists
in deciding between several possible values of the parameter by use of a test
statistic, called the selector. Its
merit is appraised by use of a new concept, the reliability of the selector,
which is equal to the probability of selecting the true value of the
parameter. It has been proved that the
maximum likelihood estimation method possesses maximum reliability.
Pertinent formulas have been
developed and applied to the Weibull distribution.
Keywords-
Distribution parameter selection
Structural reliability
Distribution functions
Report number-
AFML-TR-77-170
Referenced as-
AD-A055630
Waloddi Weibull LAUSANNE (SWITZERLAND)
Download this 0.9 Meg file as AD-A055630.
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42.
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Waloddi Weibull author, April 1978
Statistical Analysis Of One Hundred And
Twelve Groups Of Fatigue Performance Data: Testing the Homogeneity Of the
Samples
Abstract-
Three
different tests for the hypothesis that the sample is homogeneous, denoted by
MLE, OMLE and TI, are described, and their applications to 112 completed samples
taken from an extensive list of fatigue performance data collected at the
Boeing Company. The hypothesis of
homogeneity was rejected for 60 of 112 examined samples by MLE, 45 of 107
samples by OMLE and 17 of 96 samples by TI.
The number of samples for which the hypothesis was rejected at least
by one of the tests was 64 of 112. The
rejections are mainly due to the high-time outliers, but in some cased to
low-time outliers, which indicate two-component distribution.
Keywords-
Distribution
functions
Random
sampling techniques
Statistical
population sampling
Two-component
distributions
Sample
homogeneity testing
Report Number:
AFML-TR-78-28
Originating Activity:
Professor Waloddi Weibull
Avenue d’Albigny, 9 BIS
74000 Annecy
FRANCE
Referenced as:
AD-A058098
Thanks to Jerry Sterling of NASA for finding this document.
Download this file as a 0.8 Meg PDF file
(25 pages)
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43.
|
Mischke, C. R., A
Distribution-Independent Plotting Rule for Ordered Failures, 1979.
PDF file size is 976K.
Various plotting rules have been developed for associating a cumulative
density, Fi, or a reliability, Ri
[Ri=1-Fi] with an ordered
life measure, xi. These suffer from various biases when rules
formulated for one distribution family are used with another. The plotting rationale presented:
1) is distribution independent,
2) frees the plotter from tabular information while retaining high precision,
3) easily accommodates to censored data, and
4) suggests the proper regression model.
10 pages.
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44.
|
This
Weeks Citation Classic, September 10, 1981.
This document refers to Waloddi Weibull’s publication in
the ASME Journal of Applied Mechanics, 18:293-7,
1951 with comments from from Weibull’s
son Goren Weibull.
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45.
|
Weibull Symposium: Stockholm, Sweden, June 19-21, 1984 To the Memory of Waloddi
Weibull,
Excerpts from “Probabilistic
Methods in the Mechanics of solids and Structures”, editors: S. Eggwertz and N.C. Lind,
1.95MB PDF file
(24 pages)
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46.
|
Mr.
Chi-Chao Lui, PhD 1997 dissertation from University of Nottingham:
A Comparison Between The Weibull And Lognormal Models Used To Analyse Reliability Data.
Abstract,
Contents, List of Tables, List of Figures, Acknowledgements, Glossary, and
Notations And Abbreviations. (use this to decide if your want the longer
document)
1,251 KB PDF file
(22 pages)
Complete
Dissertation as one file
15,800 KB PDF file (293
pages)
Appendices-
Appendix A
– Derivation of the Weibull related functions-6 pages
Appendix B –
Derivation of the Lognormal related functions-8 pages
Appendix C –
Correlation coefficient for the Weibull distribution-47 pages
Appendix D –
Correlation coefficient for the Lognormal distribution-47 pages
Appendix E – Comparison of results for data from the
Weibull distribution-22 pages
Appendix F – Comparison of results for data from the Lognormal
distribution-23 pages
Dr. Abernethy
interprets and summarizes Mr. Lui’s three most
important conclusions regarding life data as:
1. “Median rank regression is
recommended as the overall best method for life data analysis for data sets
with and without all kinds of suspensions.”
2.
“The two best methods of goodness of fit are the likelihood ratio test
and the p-value of the coefficient of determination (both methods are
available in SuperSMITH Weibull
software).”
3.
“For 20 or less failures, always use the two-parameter Weibull
distribution even if you know the underlying failure mechanism demonstrates a
different distribution---the reason for selecting the two-parameter Weibull
is both a more stable predictor and a more conservative
predictor
(Dr. Abernethy believes the log
normal distribution for small data sets is so optimistic in the lower tail,
he sees less reason to use it because it is too optimistic—meaning too few
failures are predicted. This comment
is derived from personal communications with Dr. Abernethy and he viewed it
as a surprise that he and Chi-Chao Liu saw the problem with a similar
viewpoint.).
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