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Original Weibull Trending Toolkit

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I thoroughly enjoyed working at the Lockheed-California Company Rye Canyon Research and Development Center, Saugus, California.

One of my independent research and development reports was LR27399, "Correlation of Failure Analysis Data: Pitting Corrosion". I was assigned to work in the Life Sciences Bldg. Here below the Last.fm link is a copy of report LR27399, page 1.

During July 2001, I received comments from Robert Heidersbach about my work on statistics of corrosion pit depths. He was then Professor and Chair, Materials Engineering, at Cal Poly. He was also Technical Editor, Corrosion-the-Online Corrosion Journal, http://www.corrosionsource.com/corrosioneering/index.html.

Because of encouragement extended by Prof. Heidersbach, I decided to post a report online. It is titled "Correlation of Failure Analysis Data: Pitting Corrosion".

This note was posted on October 20, 2001.

On September 29, 2004, he forwarded a note about the course. The note listed the address:
Bob Heidersbach
Dr. Rust, Inc.
Cape Canaveral, Florida
drrustinc@earthlink.net

In this website, I use methods described in 1975 report LR27399 to present an application of my Weibull Trending Toolkit(WTT). Files updated in July 2003 are: wtt01.html, wtt02.html, and wtt03.html

Updated references are:
wtt01.html
wtt02.html
wtt03.html

Weibull Trending Toolkit

Dedicated to dear friends Kitty (Gusta) and Walter Trapp. Walter died February 19, 2002.

Tribute to Waloddi Weibull

During June 1996, I asked Walter J. Trapp to help me in writing to Mrs. Inga Britta (Ibbi) Weibull. I remembered Walter telling me about Waloddi Weibull having received an award from King Gustav of Sweden, and I wished to include an image of the event in this tribute.

Waloddi Weibull devoted his entire professional life to studying ways to increase our understanding of material sciences. He was a soldier-engineer who gave his utmost to improve our use of materials. I sent a note of thanks to Mrs. Ibbi Weibull and to Göran Weibull in remembrance of husband and father, Waloddi Weibull.

Waloddi Weibull 1887-1979
Photo by: Sam C. Saunders, Pullman Washington, USA

The above photograph is a copy from the first page of a document from the Weibull Symposium, Stockholm, 1984. The reference: "IUTAM Symposium, to the memory of Waloddi Weibull. Probabilistic Methods in the Mechanics of Solids and Structures, Stockholm, June 19-21, 1984. Organized by: The Aeronautical Research Institute of Sweden, FFA, in cooperation with The Swedish National Committee for Mechanics."

On 18 Sept. 1996, I received the following letter from Mrs. Ibbi Weibull and Göran Weibull:

Genarp, Sweden 13 Sept. 1996

Dear Dr. Bowie,

We, that is Mrs. Weibull and Göran W. Weibull, have received and read your kind letter 0f 20 August 1996. We are happy to contribute to your idea of giving better information into Internet about Waloddi Weibull. His full name is Ernst Hjalmar Waloddi Weibull. The name Waloddi was shortened to Doddi in the family and by close friends.

After some research we have found an appropriate text in a report from IUTAM Symposium to the memory of Waloddi Weibull, Stockholm, 19-21 June 1984, written by Dr. Robert A. Heller. A copy of the first page of the report and Dr. Heller's speech are enclosed. Perhaps you can use the photograph from the first page.

We know Robert Heller very well and have found his speech very enjoyable. The information about Waloddi is absolutely correct. Actually, Mrs. Weibull has written a letter to him and asked for permission to use it.

If the text is too long, perhaps you can make an excerpt. If you have any questions don't hesitate to get in touch. You will find addresses at the end of the letter.

You put two questions in your letter, and these are the answers:

  • Hans Waloddi was the eldest son and
  • I, Göran Waloddi, child number 5, started as an officer of the Royal Wendes Artillery Regiment and later transferred to The research Institute of National Defense as a researcher mainly concerned with weapons effects.

Enclosed is the photo with King Carl XVI Gustav of Sweden, Waloddi Weibull, and in the middle Gunar Hambræus, then President of the Royal Swedish Academy of Engineering. When Waloddi stood in front of the King he said: "Seventy-one years ago I stood in front of Your Majesty's grandfather's grandfather (King Oscar II) and got my officer's commission." The King then said: "That is fantastic!"


Another photo is enclosed. It is from 1972 when he got the ASME Medal. Waloddi is on the left, in the middle Dr. Richard Folsom, and to the right Neil Armstrong, who got the Spirit of St. Louis Medal.

With best wishes,

Ibbi Weibull
Björnstorps torg
S - 240 13 Genarp
SWEDEN

Göran W. Weibull
Bäckamöllan
S - 277 55 BRÖSARP
SWEDEN

There follows an exerpt from Dr. Robert A. Heller's speech to the Weibull Symposium, Stockholm, 19-21 June 1984. I beg Dr. Heller's understanding in presenting the exerpts in advance of receiving word of his approval from Mrs. Ibbi Weibull.

THE WEIBULL DISTRIBUTION DID NOT APPLY TO ITS FOUNDER

Robert A. Heller, Roanoke, Virginia, USA

Though it is an honor to have been asked by the Chair to talk about Professor Weibull, I am saddened that my substitution is occasioned by the untimely passing of another great engineer, Professor Folke Odquist, who was to give us his impressions of his old friend and colleague.

The information I have gathered about Professor Weibull comes from several sources: from his friends; Professor Odquist, Walter Trapp of the US Air Force, Professor Sigge Eggwertz of FFA, from his family; Mrs. Ibbi Weibull, his wife, and Mr. Göran Weibull, his son, and my own personal recollections.

Waloddi Weibull was born on June 18, 1887. This Symposium started on his 97th birthday. His family originally came from Schleswig-Holstein, at that time (in the seventeenth century) closely connected with Denmark. There were a number of famous scientists and historians in the family. His own career as an engineer and scientist is certainly an unusual one.

He became a midshipman in the Royal Swedish Coast Guard in 1904 and was promoted to sublieutenant in 1907, to Captain in 1916 and to Major in 1940. By then he had finished the military schools and simultaneously taken courses at the Royal Institute of Technology and at Stockholm University, finally graduating as Fil.Lic. in 1924. Weibull left active military service in 1917 and acted in German and Swedish industries as an inventor (ball bearings, electric hammers) and as a consulting engineer.

He published his first scientific paper on the propagation of explosive wave in 1914. He took part in expeditions to the Mediterranean, to the Carribean, and to the Atlantic and Pacific Oceans on the research "Albatross" where he used his newly developed technique of explosive charges to determine the type of ocean bottom sediments and their thickness. The same method is used today in offshore oil explorations.

Weibull became a full professor at the Royal Institute of Technology in 1924, and was awarded the degree Ph.D.h.c. at the University of Uppsala in 1932. In 1941 a donation from the Swedish arms factory (A. B. Bofors) gave him a personal research professorship in Technical Physics at the Royal Institute of Technology, Stockholm.

Professor Weibull's ideas about the statistical distributions of material strength came to the attention of engineers in the late 1930's with the publications of two important papers: "Investigations into strength properties of brittle materials" and "The phenomenon of rupture in solids."

His techniques later found wide application in many fields. With great physical insight he proposed the probability distribution which bears his name. Now, in the literature on reliability, statistics, fatigue, fracture and many other fields, one finds reference to the "Weibull Distribution", and the statistic methods Weibull proposed are in everyday use. Subsequently, Dr. Weibull extended his studies to many aspects of fatigue, fracture and the analysis of probability distributions.

In 1953 he retired from the Royal Institute of Technology and became a professor emeritus. For most people retirement is the end of a professional career, but not for Weibull. His activities just started. He became a consultant to the Fatigue Branch of the U.S. Air Force Materials Laboratory, then under the direction of Mr. Walter Trapp. For 14 years he conducted research and wrote many papers and technical reports which provide valuable information and data on material properties and on the analysis of probability distributions and other related topics. This and other work is summarized in a book, co-authored with his son Goran and published by the Swedish National Defense Research Institute. Professor Weibull continued to be active as a consultant. He conducted work on turbine fatigue and studied new methods of estimating the parameters of the Weibull Distribution. His work on the planning and interpretation of fatigue data is monumental and resulted in his book "Fatigue Testing and Analysis of Results" in 1961.

In 1963, at the invitation of the late Professor Alfred Freudenthal, he became a visiting Professor at Columbia University's Institute for the Study of Fatigue and Reliability. Many of us at this Symposuim have been associated with the Institute at that time and got to know Dr. Weibull personally. Hal Liebowitz was one of our sponsors. Alf Payne, Agnes Heller, Jann Yang, Lars Jarfall and I learned a lot from him, from Emil Gumbel, who was also a member, and from Fred Freudenthal, the three founders of Probabilistic Mechanics of Structure and Materials. It was interesting to watch the friendly rivalry between Gumbel, the theoretician and the two engineers, Weibull and Freudenthal.

The Extreme Value family of distributions, to which both the Gumbel and Weibull type belong, is most applicable to materials, structure and biological systems because it has an increasing failure rate and can describe "wear out" processes. Well, these two men, both in their late seventies at the time, showed that these distributions did not apply to them. They did not wear out but were full of life and energy. Gumbel went skiing every weekend and when Agnes and I took Dr. and Mrs. Weibull to the Roosevelt Home in Hyde Park on a cold winter day, he refused my offered arm to help him on the icy walkways saying: "A little ice and snow never bothered a Swede."

In the course of his long and productive career, Professor Weibull has received many honors: the Polhem Medal in 1940, an honorary doctorate from the University of Uppsala in 1932, and in 1972, the American Society of Mechanical Engineers awarded him the ASME medal with the inscription: "A pioneer in the study of fracture, fatigue and reliability who has contributed to the literature for over thirty years. His statistical treatment of strength and life has found wide-spread application in engineering design."

The other recipient of a medal at the sme meeting, Astonaut Neil Armstrong, the first man on the moon, probably did not know that his successful voyage was partly due to the pioneering work of Waloddi Weibull.

Professor Weibull's proudest moment came in 1978 when he received the Great Gold Medal from the Royal Swedish Academy of Engineering Sciences which was personally presented to him by King Carl XVI Gustav of Sweden.

He was devoted to his family and was proud of his nine children and numerous grand- and great-grandchildren. Dr. Weibull was a member of many distinguished Swedish Academies and Societies and worked to the last day of his remarkable life. He died on October 12, 1979, in Annecy, France.

Here is a way to test your interest level. Accomplish the following busy work.

  • Save executable file wtt01.exe in directory wtt01.
  • Enter http://weibull.trending.toolkit.tripod.com/6061.txt. Save as a text file in directory wtt01.
  • Rename 6061.txt to be 6061.dat.
  • Repeat for data file 7075.dat.
  • Check to see if you have Vbrun300.dll in your Windows/System directory.
    If not search the Web for Vbrun300.dll and install it.
Run wtt01.exe, see two buttons: Match Sample Statistics and Plot Control Chart.
Click the Match button and enter 6061. Study the results. Click the Plot button
and enter 800. Repeat for 6300 and 7075. Use 80 or 100 for 7075 graph upper limit.

Write to me if you have comments or need help. I refer to notes on use of wtt01.exe as Course I Three QBasic programs mentioned in the notes are stored here as makefile.txt, and sort.txt.

Save these two text data files, then Rename them to have file extension .bas.

To learn how useful the Weibull Trending Toolkit can be read:

  • Course II, On Pitting Corrosion; http://weibull.trending.toolkit.tripod.com/wtt02.html
  • Course III; On Cracks, Fracture, and Crack Growth: http://weibull.trending.toolkit.tripod.com/wtt03.html

    Use the above results for 6061.dat to apply Risk.bas. Treat the example to be a risk design application with production run size 102.

    CLS
    PRINT "Enter Weibull Shape Parameter k:";
    INPUT k
    PRINT "Enter Weibull Threshold Parameter e:";
    INPUT e
    PRINT "Enter Median Design Value:";
    INPUT Median
    v = e + (Median - e) / (LOG(2)) ^ (1 / k)
    PRINT "Weibull Characteristic Value ="; v
    PRINT "Enter production run size N:";
    INPUT N
    PRINT "Probability of survival at first failure =";
    P = 1 - 1 / 1 / (N + 1)
    PRINT P
    PRINT "Time to first failure =";
    t = e + (v - e) * (-LOG(P)) ^ (1 / k)
    PRINT t
    PRINT "Risk of failure at time"; t; "equals";
    R = k * ((t - e) / (v - e)) ^ (k - 1) / (v - e)
    PRINT R
    PRINT "Probability density at time t =";
    DENSITY = R * P
    PRINT DENSITY
    PRINT "Probability of survival at second failure =";
    P = 1 - 2 / 1 / (N + 1)
    PRINT P
    PRINT "Time to second failure =";
    t = e + (v - e) * (-LOG(P)) ^ (1 / k)
    PRINT t
    PRINT "Risk of failure at time"; t; "equals";
    R = k * ((t - e) / (v - e)) ^ (k - 1) / (v - e)
    PRINT R
    PRINT "Probability density at time t =";
    DENSITY = R * P
    PRINT DENSITY
    PRINT "Probability of survival at median life = 0.5"
    PRINT "Design median life ="; Median
    PRINT "Risk of failure at median life equals";
    R = k * ((Median - e) / (v - e)) ^ (k - 1) / (v - e)
    PRINT R
    PRINT "Probability density at median life =";
    DENSITY = R * .5
    PRINT DENSITY
    PRINT "Probability of survival at failure"; N; "equals";
    P = 1 - N / (N + 1)
    PRINT P
    PRINT "Time to failure"; N; "equals";
    t = e + (v - e) * (-LOG(P)) ^ (1 / k)
    PRINT t
    PRINT "Risk of failure at time"; t; "equals";
    R = k * ((t - e) / (v - e)) ^ (k - 1) / (v - e)
    PRINT R
    PRINT "Probability density at time t =";
    DENSITY = R * P
    PRINT DENSITY
    END
    

    Results of running QBasic program Risk.bas

    It is possible to generate 102 design times to failure and store them in file d6061.dat. Use the following values found by means of wtt01.exe for measured data 6061.dat:

  • k=3.61498
  • e=195.1232
  • Median=398.3941.

    Use program Wdesign.exe to find the following results.

    Weibull Trending Toolkit resources: Carnegie Mellon University: http://lib.stat.cmu.edu/DOS/general WTT
    The Weibull Trending Toolkit (WTT) is described and applied in three self-extracting files, WTT01.EXE(52k), WTT02.EXE(484k) and WTT03.EXE(1M) QBasic programs in WTT may be executed from DOS or Windows.
  • From 1987-92, I, Glenn E. Bowie, created the first two-year Associate Degree Program at Red Wing Technical College. The program name was Vibroacoustics Technology. There were 27 courses in the program. I created and taught 21 of them. In recognition of the quality of the progam, the 1992 graduating class members were granted their Associate Degrees in Vibroacoustics Engineering Technology. The reference is
    Vibroacoustics Engineering Technology.

    Copyright Glenn Bowie, CorTech Training, Red Wing, MN. All rights reserved.