The New Weibull Handbook

Weibull analysis is the world's most popular method of analyzing and predicting failures and malfunctions of all types.  About 85%-95% of all life data are adequately described with Weibull probability plots.  Whereas about 85%-95% of all repair times are adequately described by log normal probability plots.  The New Weibull Handbook provides practical tools for analyzing life/repair data. 

The Weibull method identifies the category of failure: infant mortality, random or wear out.  Weibull analysis provides the quantitative information needed for making RCM decisions which are often made from a qualitative approach.  Weibull failure predictions are accurate even with very small samples of data.   Weibull analysis calculates optimal parts replacement intervals for minimizing cost.  Weibull analysis is needed for making risk based inspection decisions to take action or defer action on potential failures.   IEC 61649:2008 Second Edition used The New Weibull Handbook as the source document for the 2008 revision.

Crow-AMSAA charts, a different use of Weibull analysis, predict future failures, analyze R&D testing, track fleets of repairable systems, and provide the most accurate trending of significant events for management. Both techniques may show either events or cost analysis.  Crow-AMSAA numbers tell if failure rates are increasing, decreasing, or staying the same with time.  Crow-AMSAA plots are also useful for forecasting safety issues concerning future safety incidents, spills, and other controllable events.   The Crow-AMSAA plots are useful tools for analyzing mixed failure modes and predicting future failures.  Details for Crow-AMSAA plots are described in IEC 61164: 2004 Second Edition.

If you already own the 4th edition, why purchase the 5th edition?  Weibull analysis is becoming more sophisticated.  Old ideas are being refined.  New tools are introduced.  Early numbers are being improved with new techniques.  Best practices are improved and modified for more accurate analysis.  More experts are providing thoughtful details to the technology through improved usage of computer analysis and simulations.  Everything old is new and improved again!

You can download PDF files of the Cover, Preface, and Table of Contents from The New Weibull Handbook.  And Chapter 1 from The New Weibull Handbook.  This book is used for Weibull Analysis Seminars conducted by Dr. Abernethy and Wes Fulton.

The subtitle for The New Weibull Handbook 5th edition is: Reliability & Statistical Analysis for Predicting Life, Safety, Survivability, Risk, Cost and Warranty Claims.  The 5th edition is identified by: ISBN 0-9653062-3-2 for the 301 pages of fresh information.  The book weighs 1.7 lbs = 0.8 kg and has clear plastic flexible covers.  If you own earlier copies of The New Weibull Handbook should you upgrade to the 5th edition?
                YES because of the new research findings in most chapters of the book. 
At this web site, you can review SuperSMITH Weibull software for performing the Weibull analysis and SuperSMITH Visual software for performing the Crow-AMSAA reliability growth plots which are described in The New Weibull Handbook.

Dr. Robert B. Abernethy is the author and publisher of The New Weibull Handbook, 5th edition released December 2006 with minor updates in February 2007, August 2008, May 2009 and April 2010. (Pronounce the name Weibull as "Y-Bull".)  Dr. Abernethy also offers EagleEYE(SM) service to quickly review your data, using concepts detailed in the handbook, and provide comments on what he observes in your data sets.  A book review from the Royal Statistical Society is shown below for the earlier second edition, and a copy of the review can be downloaded as a PDF file.


The New Weibull Handbook, is distributed by Barringer & Associates for US$98 plus shipping and handling (US$30 for FedEx shipping and handling while shipping to most locations outside the USA is US$50 and up depending upon distance). For pricing and shipping details along with bundled packages of books and software click here. Order The New Weibull Handbook by purchase order (payment terms are net 10 days), American Express, Visa, or MasterCard.  You may prepay by sending a check to the address shown on the home page of this web site.

The New Weibull Handbook, Fifth Edition, has been written to update this text with the latest technology developed by the author, Wes Fulton, Paul Barringer and others for life data and warranty analysis. The figures are updated with higher resolution and better fonts. Some of the new topics included follow:

New Additions Include:        

n  More accurate goodness of fit measures using the coefficient of determination, the likelihood ratio and Anderson-Darling methods are presented. A new appendix compares their "power," the probability of making the selecting the correct distribution.

n  Grouped or interval data methods including the inspection option, the probit method and the interval MLE, are compared with simulation to determine best practices.

n  Life cycle costs is added, written by Paul Barringer, using Weibull analysis including simulation.

n  Warranty Analysis contributed by Joe Weuben of Honda using warranty claims matrixes.

n  Weibull libraries with automatic filing contributed by Randy Pirtle of Honeywell.

n  Revised Best Practices

  Rewritten Sections Include:          

n  --Improved Crow-AMSAA analysis based on accuracy comparisons between regression and MLE and also, critical correlation coefficients for measuring the goodness of fit of the plotted data. The analysis may be done on failure events, warranty claims, or cost using the latest IEC standards.

n  Reduced Bias Estimation for small sample sizes for "Now Risk" producing better tests for batch problems.

n  Small samples reduced bias adjustments (RBA) for maximum likelihood estimates for the Weibull, normal and log normal distributions providing significant improvements in accuracy. Maximum likelihood estimates can now be made for small samples as accurately as median rank regression.

n  Dr. Wayne Nelson's new methodology: graphical repair analysis.

n  There are many methods and types of analysis described in The New Weibull Handbook. How can the novice analyst decide which is the most appropriate procedure for his problem? Best practices are indicated throughout the text.

n  The logic diagram developed by Bob Rock of PACCAR, has been improved to provide step-by-step guidance to select the best practice methods for all types of data sets.

n  New case studies have been added.


ABOUT DR. ABERNETHY-
Dr. Abernethy is THE leading world authority on the principles and application of Weibull analysis for solving failure problems in a number of different fields. Dr. Abernethy was a practicing Mechanical Engineer prior to earning his Ph.D. in Statistics which eventually involved him in Weibull statistics as the tool of choice for reliability engineers.. Dr. Abernethy (affectionately know around the world as Dr. Bob) is the retired Chief Statistician for Pratt & Whitney Aircraft. At Pratt & Whitney Aircraft, he gained practical use of Weibull techniques for solving reliability problems.

Dr. Bob was the manager of reliability, safety, maintainability and statistical analysis of Pratt & Whitney's military engine division. He holds the patent on the J58 engine cycle used in the SR-71 "Blackbird" supersonic spy plane that still holds all seventeen world speed records. He also has the patent on the afterburner control system used in the F15 and F16 aircraft. He was the principal author and project manager for the US Air Force Weibull Analysis Handbook, the original edition of The New Weibull Handbook. Since his early retirement from Pratt & Whitney in 1987, he has conducted extensive research to develop new and improved Weibull methods as described in the 2nd edition of the Handbook. Dr. Bob's experiences as a consultant include medical devices, automotive, electrical/electronic equipment, and nuclear reactor components as well as aerospace. His client list includes most major companies around the world. He is noted lecturer for the major scientific and engineering societies in Weibull analysis and routinely teaches training courses for the societies--although most of his training work is done on specific assignments for individual companies on a contract basis.
For advanced technical questions about Dr. Bob's book or queries about his consulting or training schedules you can reach him by e-mail at Dr. Bob. His seminar schedules are posted on the web.

Dr. Abernethy also offers EagleEYE(SM) service to quickly review your data, using concepts detailed in the handbook, and provide comments on what he observes in your data sets.

The New Weibull Handbook is the reference text for theory and methodology for the SuperSMITH software written by Fulton Findings for solving reliability on a personal computer. The SuperSMITH software packages include SuperSMITH Weibull and SuperSMITH Visual as Windows programs. More details on software prices and features are available from the SuperSMITH web page.

A tutorial book call PlayTIME with SuperSMITH is available. The tutorial has step-by-step instructions for solving over thirty problems illustrating all the features and options in the software. This tutorial with The New Weibull Handbook and the Windows based software from Fulton Findings provides a complete home study package for engineers and scientist. The tutorial includes a diskette with the PlayTIME data-sets to avoid the drudgery of hand input except for a few examples to illustrate input methods.  A complete set of coaching tools is available for home study of Weibull Analysis.

The New Weibull Handbook undergoes continuous improvement. Each printing is substantially improved based on the latest findings of Dr. Bob's research.

The original Weibull Analysis Handbook published in 1983 set the standard for the analysis of reliability data. The New Weibull Handbook undergoes continuous improvement. Each printing is substantially improved based on the latest findings of Dr. Bob's research Where several methods are available, best practice is indicated. The first edition of The New Weibull Handbook was published in 1993. It had two printings and represented a substantial upgrade from the original Weibull Analysis Handbook.


The following book review was described in the Journal of the Royal Statistical Society/ A (1997) 160, Part 2. pp 367-380.

 

Permission was given on October 1, 2001 via Email to Dr. Robert B. Abernethy to publish this review on the Internet by Martin Owen (m.owen@rss.org.uk), Executive Editor of the Royal Statistical Society, 12 Errol Street, London, EC1Y 8LX, UK http://www.rss.org.uk and by Malcom A.J. Allison (Malcolm.Allison@blacksci.co.uk), Permission Assistant, Blackwell Publishing, Osney Mead, Oxford OX2 0EL, UK http://www.blackwellpublishing.com .  The original copyright was 1997 by the Royal Statistical Society. [Hyperlinks have been added to the review for use as Internet pages at http://www.barringer1.com ]                         Return to top

 

Book Review

 

“1. The New Weibull Handbook, 2nd edn. By R. B. Abernethy. ISBN 0 9653062 0 8.  Abernethy, North Palm Beach, 1996. $88.00.  [Please note, The New Weibull Handbook is now at the 4th edition using ISBN 0-9653062-1-6.  The price is US$98 + shipping and handling]

 

            The handbook is used as a manual for training by the author who took early retirement in 1987 to undertake full-time lecturing in Weibull analysis.  The print is in a large fount and the equations are in even larger fount so that those of us whose sight is poor will have no excuse for not absorbing the message.  There is no doubting the author’s enthusiasm for the Weibull distribution and indeed, as I read on, I found myself influenced increasingly by the author’s persuasiveness.  Some of the claims made for its predictive ability for small samples may seem extravagant but, in this respect, I think that we must bow to the wealth of experience gained by Dr. Abernethy over many years.  There is a bewildering variety of software from Fulton Findings to accompany the handbook, namely WeibullSMITH™, VisualSMITH™, BiWeibullSMITH™ and MonteCarloSMITH™, none of which were presented with the manual for review.  True, other life distributions are mentioned such as the log-normal but, in the context of the handbook, they are subservient to the Weibull.

            Probability plots are strongly emphasized and sufficient introductory theory is relegated to appendixes.  The plotting position recommended, particularly for skew distributions, is the median plotting position.  Not having pursued the merits of one plotting position versus another I fail to understand the logic given for this but the author does quote a remark made by Wayne Nelson that such arguments are just as fruitless as arguing religions since they all point to heaven.

            Both nonparametric and parametric methods are explained and well illustrated.  These include the Kaplan-Meier, maximum likelihood and likelihood ration approaches.  Confidence intervals for parameters and for quantiles such as the B10 life are calculated but the author is not in favour of their use in presentations to management because they are so little understood (in this respect he quotes a ‘Forthsooth’ from RSS News in 1992).  I agree with his opinion on this but I take strong exception to his answer to one of the question from readers where he states that ‘even most statisticians do no understand the confidence concept’.  However, it may be true that many who profess to be statisticians do not understand the concept.

            Particularly in the field of reliability there is much confusion and lack of understanding of classical statistics as enshrined in military standards.  Engineers without previous exposure to statistics more readily take to the Bayesian approach.  To a certain extent this is catered for by WeiBayes in the handbook, but it is not a full Bayesian approach since a single value is established for the shape parameter on the basis of past experience.  There is no natural conjugacy for the Weibull distribution but there is gamma conjugacy for a scale parameter conditional on discrete prior values for the shape parameter (Martz and Waller, 1982).  This should not be at all difficult for engineers to assimilate, especially when displays of priors and posteriors are easy to produce.

            The difficulties in estimation for the Weibull distribution with a threshold parameter t0 are not sufficiently emphasized.  The technique of subtracting values from failure times and suspension times until the Weibull plot ‘straightens’ is easier said than done since substantially different values for t0 can make very little difference to a straightened plot.  Another manifestation of this difficulty is that the likelihood function is quite flat over wide ranges of t0.

            There is a section on reliability growth and the Duane model written by D. P. Weber, a reliability consultant.  My only criticism of this section is in his use of the term instantaneous failure rate.  There is thus no distinction between its use here and its previous use for non-repairable items.  Many researchers now use the rate of occurrence of failures for the repairable case.

            I detected few errors in the handbook.  On p.2-10 the author states that as time progresses the reliability of components surviving infant mortality increases.  To be precise reliability should be replaced by conditional reliability.  On p. 2-22 the Weibull closure, or self-locking property, is the reciprocal of the correct answer and in Appendix G-23 the second moment about the origin is incorrect and is also incorrectly signified by m2 rather than by m2.  There are a few inconsistencies such as the use of both s2 and s2 to denote a theoretical variance and the author talks about inverse ranks when he means reverse ranks.

            In summary the handbook, together with the previously mentioned software (or other), will be an invaluable aid to reliability engineers.  Statisticians would probably prefer a more concise theoretical treatment with more sophisticated applications such as Weibull regression models.  As a statistician who is interested in the application of statistical methods in industry I found the many diverse applications and case-studies extremely interesting.

Reference

Martz, H. J. and Waller, R. A. (1982) Bayesian Reliability Analysis. New York: Willey

 

Alan Winterbottom

City University

London                                  Return to top


The 5th edition of The New Weibull Handbook is now available with the latest findings from the Weibull community of experts around the world.  You can download the cover, preface, and table of contents as a PDF file, and Chapter 1 is also available as a PDF file.
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Last revised September 15, 2010