Weibull
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Weibull
World from A to Z:
Benchmarks and Standards,
Best Practice, Biographies, Classes/Seminars, Consulting,
Good Software from Fulton Findings, Handbooks and References, Languages and International Use, Product Support, Skunky
Software Alert, Software Tutorial . . . OR
CHOOSE FROM BELOW. . .
SOFTWARE DESCRIPTIONS:
SuperSMITH(TM) Software Suite, SuperSMITH(TM) Weibull, SuperSMITH(TM) Visual, SuperSMITH(TM) YBath(TM)
PUBLICATION DESCRIPTIONS:
The New Weibull Handbook(c), PlayTIME(TM) with SuperSMITH(TM), New Weibull Methods + Video


Accelerated Test / Parameter
as Function of Engineering Variable (PFEV) / Degradation / Covariate Data
Analysis
There
are lots of names for this kind of posttest results analysis. They all refer
to a changing solution model parameter as test conditions change. The resulting
model for lifetime is often termed an `S/N` relationship (Stress vs. N time
units of life capability). Accelerated testing generally consists of increasing
some or all the significant stresses that control the length of product life.
This is done for the purpose of producing the same endoflife results as
normal operating level stresses, but with shorter overall test times and lower
cost. It is often difficult to increase stresses without also changing the
physics of failure invalidating this kind of test for the stated purpose,
unless test levels are held within an acceptable range. Even after a successful
accelerated test (no significant failure mechanism change) the life data from
higher loading must be correlated to life at normal load. Dr. Wayne Nelson, a
leading authority on accelerated testing, refers to many such techniques in his
Accelerated Testing book. One source for accelerated testing
analysis is SuperSMITH(TM) Weibull software. S/N curves for the
product can be easily estimated based upon such test results. Then the lifetime
found at higher stress in the laboratory can be converted to estimate actual
service lifetime using this model. SuperSMITH allows
up to 16 sets of data each with possible different conditions.
There are two data analysis types in the
Accelerated Test part of SuperSMITH:
A) Standard PFEV  This is where each data
set represents a different stress (or a different group of stress factors)
where stress factors are held constant for the length of the test.
B) StepLoad or StepUtilization  This is
where the stress level is changed according to a schedule as the item is being
tested. As you might think, stepstress solution is a bit more challenging and
a special case of the general methods in Dr. Nelson`s book used in the software
considers Miner`s rule (incorporation of `equivalent damage`).
There are two data analysis types in the
Accelerated Test part of SuperSMITH:
STANDARD
PFEV: Variability models include Weibull, lognormal, normal, and Gumbel extreme
value (lower and upper). Focus is on producing a 2parameter solution which
changes as a function of stress or as a function of some other covariate, the
covariate being something changing in between sets of data. Maximum quantity of
active data sets in the software is 16. SuperSMITH
gives the user a choice whether to solve the relationship separately for each
of the 2 model parameters, slope and life capability . . . OR . . . to solve for
a common slope parameter (best choice for all data sets) and then solve for the
life capability S/N curve by itself. Solution likelihood for all sets taken
together is maximized to get the answer, also called maximum likelihood
estimate (mle). The program does not select the PFEV
equation form (Fit Type). That is the responsibility of the user. Equation
forms for the PFEV Fit Type are:
1) Linear  not often used but available
2) Exponential  not often used but available
3) Power  very often used for mechanical
stresses like tensile and torsion and bending (sometimes called Inverse Power)
4) Arrhenius  very often used for stresses
related to temperature like voltage in electrical applications
After solution, the user can view the
solution for a specific value of engineering variable by plotting a `Marker
Line` result on the same plot as the data. Also, the user can view the
resulting S/N curve with automatic use of the SuperSMITH
Visual program.
STEPLOAD OR STEPUTILIZATION: We are
again looking for the result of an S/N curve but with test conditions, e.g.
stresses, changing during the running of the test. Each data set can have a
different `stepstress` schedule. The resulting simple function is a
3parameter model:
For
Weibull, the 3parameter model (Beta, v, p) is:
Beta
(slope) = taken as same value for all stresses within useful range
Eta
= (v/X) ^ p ... where v is stress reference value, X is equivalent applied
single stress value for entire life, p is exponent.
For
lognormal, the 3parameter model (SigF, v, p) is:
SigF (antilog of std. dev. of log data, inversely related to
slope) = taken as same value for all stresses within useful range
Med
(median) = (v/X) ^ p ... where v is stress reference value, X is equivalent
applied single stress value for entire life, p is exponent.
Maximum likelihood is again used with the
special case of Miner`s rule for the solution. After solution, the user can view
the solution for a specific value of engineering variable by plotting a `Marker
Line` result on the same plot as the data. Also, the user can view the
resulting S/N curve with automatic use of the SuperSMITH
Visual program.
Benchmarks and Standards
SuperSMITH (TM) is the leading Weibull analysis
software. Ours is the accepted metric analysis standard for the automotive
industry, the medical industry, the power generation industry, the hydrocarbon
processing industry, the railroad industry, the aerospace industry, the
computer industry, the communications industry and many other industries and
organizations including the U.S. military and the Federal Aviation
Administration. Classic case studies out of standard textbooks provide ideal
benchmarks for our software calibration. Our thousands of customers demand this
high standard. Such case studies might typically include analysis of aircraft
components after inflight shutdowns, comparison of new and old medical remedies,
and performance of electrical insulation in power transmission. SuperSMITH (TM)
Weibull software includes several
benchmarks ready to use for comparison and validation. The supplied data values
are easily copied for use in other software. Full instructions are given for
interpretation. Find out if you are using the best software. Can the software
you use measure up? Try the benchmark data and see.
The
latest edition of The New Weibull Handbook by Dr. Robert Abernethy contains
standard procedures for performing Weibull analyses. Bestpractice methods are
specified for different data analysis situations. Does your reliability effort
produce the most costefficient results and the most accurate results? Maybe
you should be using standard procedures to minimize the work required for the
maximum output. Join the thousands of companies that have chosen The New Weibull Handbook as the standard metric analysis method for their reliability
programs.
Best Practice
Does
your software give you the most for your time and effort? Is it performing at
the highest industry expectations? A conscientious analyst can be selective
with all of the analytical methods available for the computer. There are many
complex equations thrown into software (copied directly from a textbook) that
are practically unusable, or worse, misleading. This technical clutter can be
confusing or maybe even misleading. We recommend picking out a few good tools
to keep handy that have proven worthwhile. The
New Weibull Handbook written by Dr. Bob Abernethy
is the world standard reference for Weibull analysis and provides the select
few bestpractice methods. This handbook cuts through the clutter with a
handful of solid techniques. SuperSMITH
(TM) is the only software that is 100% capable of these bestpractice
techniques. It is the only Weibull software widely recognized as the world
standard.
Binomial and Poisson
Yes/no,
on/off, good/bad, pass/fail all can be binomial situations. The simple classic
formula for the binomial distribution was discovered in 1663 by John Newton (Is
he any relation to Sir Isaac?). If you know the proportion of the time that
each of the two outcomes are expected and you know how many samplings
are to be made, you are home free. This most basic of all distributions is used
extensively in quality control applications and in gambling. Another basic
distribution is the Poisson distribution for rare events in a continuum. The
Poisson is often used as an approximation for binomial when the values are
within appropriate limits. Read more about these related methods in The New Weibull Handbook by Dr. Bob Abernethy.
Bvalue/Blife/Llife
Bvalue
is the shorthand for percentile in the world of Weibull. The bearing
industry uses it as a barometer for rated length of service. For example, B10
life represents the length of service time allowable with approximately 10
percent expected to fail. B5 life for the same part would be some reduced
service time with only 5 percent expected to fail. These values are provided in
SuperSMITH(TM) Weibull, by entering the data and looking
at the graph. It's easy to get precise readings with the predict button
in the software.
Biographies
Dr. Robert Abernethy is known worldwide for his Weibull
workshops presented in Australia, China, Japan, Sweden, Israel, Great Britain, Canada and the USA. Retired from Pratt & Whitney
Aircraft, he has numerous awards from SAE, ASME, AIAA, and ISA for his
development of advanced Weibull technology during the last thirty years
including the Weibayes method, failure forecasting and the Weibull
substantiation test designs. He is a fellow of ASQ, SAE and the Royal
Statistical Society, and an associate fellow of AIAA. He received the ASME 1988
Gold Medal the SAE 2001 McFarland award for contributions to Weibull education.
He founded and chaired SAE's G11 Committee on Reliability and Maintainability.
The patent on the J58 engine that powers the world's fastest airplane, the
SR71 Blackbird, is in his name, as well as the patent on the afterburner
control on the F100 engine in the F15 and F16 fighters. He was a Navy Scholar
as well as a Fulbright Scholar to Great Britain. He is the principal author of
the original USAF Weibull Analysis Handbook and the sole author of The New Weibull Handbook. He has presented his course, the Weibull/Lognormal Analysis
Workshop, all over the world and continues to teach and provide consultation on
Weibull related methods.
Wes Fulton is founder/CEO of Fulton Findings(TM) and
the creator of all of the Fulton Findings 'SMITH software
including WeibullSMITH, Visual*SMITH, MonteCarloSMITH, BiWeibullSMITH, SuperSMITH(TM) Weibull, SuperSMITH
Visual and the SuperSMITH package. He has 16 years of
experience as program engineer for Garrett AiResearch
(product line ownership changed several times, first to AlliedSignal and then
later to Moog). He supervised development and production engineering of
aircraft flight control projects, especially maneuvering flybywire actuation
systems. He supervised the successful Indigenous Defensive Fighter (IDF) wing
leading edge flap actuation system from development through completion of
production and also developed the IDF turbine engine flowcompensated fuel
bypass. He was program engineer for the F16 leading edge flap production
program and the X31A leading edge flap program. He copatented the multifuseable shaft (a highperformance drive train device) and
is a member of ASME, IEEE, and SAE. He originated the Fulton Factor used in set
comparison, invented the concept of equivalent probability and confidence known
as assurance, and developed probabilistic S/N curve analysis. He teaches
seminars in Weibull analysis for organizations such as SAE and ASME.
E. J. Gumbel
in the 1920's was the first to seriously investigate extreme values, such as
the 100year flood level. He found that there were only six separate extreme
value distributions (proven by Gnedenko) and went on
to complete a book, Statistics of
Extremes, published in 1958. It
is now the standard reference. The TypeIIIsmallest extreme value distribution
is the Weibull distribution. Waloddi Weibull
independently invented and used this distribution, and later acknowledged E. J.
Gumbel's contributions to extreme value research by using his plotting paper.
Waloddi Weibull was a Swedish engineer and mathematician. He invented the
distribution that now carries his name in 1937 and delivered his first American
paper on the subject in 1951. He also wrote a treatise on fatigue testing, Fatigue Testing and Analysis of Results, which centered on the uses of this
distribution. History has shown that his techniques are extremely useful. They
have become the leading methods in the world for analyzing lifetime data. Click
here
to see a very detailed biography of Waloddi Weibull.
Classes/Seminars
NOTE:
See the contents page for schedules and locations of public sessions.
Dr. Robert Abernethy (Dr. Bob) developed the Weibull/LogNormal Analysis course in the early 1980`s, teaching
the applications and techniques of Weibull analysis. Dr. Bob has taught this
course hundreds of times for engineering/trade society conventions and onsite
for business and government with continuous improvements for new research. Wes Fulton
has been presenting Dr. Bob`s Weibull Workshop since 1990 and has also presented
hundreds of times now. Carl Tarum joined in as copresenter with Wes in 2005.
Now Carl presents on his own. The workshops can be the best introduction to
Weibull for the novice as well as a solid refresher course for the experienced.
It comes in 2day, 3day and 4day formats. Sample topics are:
Day
1: Overview, 23minute
Video, First Weibull, Good Weibulls, Bad Weibulls, Predicting Failures with/without Renewals, Case
Studies, Customer Usage, Maintenance Planning, Goodness of Fit with Critical
Correlation Coefficients, Weibull Experiments, Classwork Problems and
Solutions.
Day
2: WeiBayes,
Improving Accuracy, Smaller Samples, Substantiation Tests, Problem Resolution,
Zerofailure Testing, Zeroonefailure Testing, Sudden Death Testing, Warranty
Analysis, Maximum Likelihood, Rank Regression vs. Maximum Likelihood, Extremely
Small Samples, Inspection Data, Suspensions/Samplesize Effects on Uncertainty,
Experiment Analysis, Leastcost Replacement, Handson Computer Use, Analysis of
Studentsupplied Data.
Day
3: Confidence Intervals,
Design Comparison, Monte Carlo Solutions, Binomial, Poisson, Exponential,
DuaneAMSAA Reliability Growth, KaplanMeier Survivability, System Analysis,
More Handson Computer Use.
Day
4: History of Monte
Carlo, Examples, Random Numbers, System Simulation with Renewal, Case Studies,
Handson Computer Simulation, Reliability and Maintainability with Raptor and Monten, Free Copies of Simulation Software.
Note: A
separate two day refresher course includes review of risk analysis
through to the latest Weibull technology recently implemented in software.
Lecturers:
Either Dr. Bob Abernethy or Wes Fulton will lead the seminar. On occasion, both
will participate.
Please
contact Dr. Bob or Wes Fulton as
indicated in the Email Addresses, Sites and
Telephone #'s section.
Confidence  Useful confidence
methods include:
Johnson's
BetaBinomial
Nelson's
Fisher Matrix
Lawless's Likelihood Ratio
Greenwood's
Variance for KaplanMeier
Binomial
for Probit
Abernethy/Fulton
Likelihood Ratio Contours
Monte
Carlo Simulation
Before
putting your faith in published analysis results, be sure to find out how
confidence is calculated. According to The
New Weibull Handbook by Dr. Bob Abernethy
the best practice for small samples (around 10 or less) is MONTE CARLO SIMULATION
based upon a pivotal statistic (pv method) as it is
automated in SuperSMITH(TM) Weibull. The best practice for larger
samples using the maximum likelihood fit method especially with a quantity of
suspensions is LIKELIHOOD RATIO confidence. Likelihood ratio was first
made available for PC's in SuperSMITH
Weibull. Best practice for larger samples using the least squares fit method
and few suspensions is Fisher matrix. Fisher matrix was first made available
for PC's in SuperSMITH. Binomial bounds are best for probit
analysis. Greenwood's bounds are best for KaplanMeier (also available first in
SuperSMITH. Many of these techniques are not
available elsewhere as of this writing.
Consulting
Carl Tarum and Wes
Fulton are available as schedule
allows for consulting on life data, reliability and
maintenance concerns. Dr. Abernethy, the principle author of the original U.S.
Air Force Weibull Handbook, has over 40 years of experience as one of the
leading Weibull experts in the world. Wes Fulton, who released the first useful
PC Weibull plotting software over 10 years ago, is a pioneer in the development
of userfriendly technical software and he is the CEO of Fulton Findings ^{TM}.
Both are degreed engineers with many years of experience in actual application
of these techniques, and both now teach Dr. Abernethy's threeday course on
Weibull. They can be reached at the numbers given in Email Addresses, Sites and Telephone #'s. NOTE: Dr. Bob prefers that Wes consult
for northern clients in winter, except whenever the client is in Sweden. See a
pattern?
Cost Reduction
Are you
talking only the language of engineers and statisticians? Or can you speak the
universal language of business, so the people holding the checkbook understand?
When it comes time to renew the annual budget or buy capital equipment for
manufacture, then it helps to speak as clearly as possible. You can benefit by
thinking and communicating in terms of money. If you do, you will be noticed
and your priorities might go directly to the top of the agenda. How? Paul Barringer of
Barringer and Associates knows how. From what we have seen, he communicates
pretty well for an engineer. One of the techniques promoted by Dr. Bob Abernethy
and Mr. Barringer is determination of the lowestcost planned replacement
interval. The optimum replacement interval, or best allowed time of service
before equipment is retired and new equipment is substituted, is the one with
the smallest cost per unit time. Another way to reduce cost is by using sudden
death WeiBayes testing as described in The New Weibull Handbook. These techniques are automated in SuperSMITH(TM) Weibull
software and provide an excellent icebreaker for an executive boardroom
discussion. But whatever you do in a boardroom, do not confess any technical
ability. We do not want anybody getting hurt.
Critical Correlation
Coefficient (CCC) and Distribution Analysis
Dr. Bob Abernethy has developed critical values of the
correlation coefficient for the Weibull distribution based upon simulations
performed by Carl Tarum using Monte Carlo simulation. Goodness of fit tests have been greatly
simplified and have become easier to understand. Use of the CCC is best
practice for determining the most appropriate distribution for a set of data from
statistics. Certainly CCC must also be used in conjunction with results from
investigation into root cause of failure to complete the analysis. These values
are automatically included in SuperSMITH(TM)
Weibull distribution analysis and in the reporting.
Design (Data Set) Comparison
Comparing
designs is easy with SuperSMITH(TM)
Weibull. It automates the use of likelihood ratio and provides the amount of
difference between different sets of data. Comparison is not limited to two
sets. This technique is useful for comparing new design to old design, supplier
A against supplier B, and application C vs. application D vs. application E,
etc. You can also use techniques such as likelihood contour comparison and
graphical comparison as requirements dictate. Let The New Weibull Handbook be your guide to selecting the appropriate design comparison
method.
Handbooks and References
*
Abernethy, Robert B., The New Weibull Handbook (NWH), selfpublished,
1997. This is the world standard reference for Weibull analysis techniques. The
NWH replaces the original Air Force Weibull Handbook also written by Dr. Bob
Abernethy, one of the leading authorities on Weibull analysis. It contains step
by step instructions for performing a Weibull analysis and related techniques
such as forecasting failure quantity expected, WeiBayes
comparison, substantiation test planning, least cost replacement interval, and
related techniques, with several case studies for each method included. You can
order this from Dr. Bob Abernethy or Wes Fulton or Paul Barringer as indicated
in Email Addresses, Sites and Telephone #'s. Price and availability is given on the Main Page.
*
Abernethy, Robert B., New Weibull Methods + Video, selfpublished, 2003. Seven
case studies in a Powerpoint presentation, explained
in detail with an included Word document, plus a 22 minute video showing 3 more
case studies. You can order this from Dr. Bob Abernethy or Wes Fulton or Paul
Barringer as indicated in Email Addresses,
Sites and Telephone #'s. Price
and availability is given on the Main Page.
*
Fulton, Wes, PlayTIME(TM) with SuperSMITH(TM),
selfpublished, 2003. This is the computer tutorial for the Fulton Findings(TM)
software. You can order this from Dr. Bob Abernethy or Wes Fulton or Paul
Barringer as indicated in Email Addresses,
Sites and Telephone #'s. Price
and availability is given on the Main Page.
*
Gumbel, E. J., Statistics of Extremes, Columbia University Press, New
York, 1958.
* Liu,
ChiChao, A Comparison Between the Weibull and Lognormal Models Used to Analyse Reliability Data, University of Nottingham
Doctoral Thesis, 1997.
*
Nelson, Wayne, Accelerated Testing, John Wiley & Sons, New York,
1990. The world standard reference on accelerated testing. This is an excellent
sourcebook for life data analysis. There are many new techniques in this volume
to complement his other standard references on life data analysis. Contact Dr.
Wayne Nelson as indicated in Email Addresses,
Sites and Telephone #'s if you
are interested.
*
Weibull, Waloddi, Fatigue Testing and Analysis of
Results, Pergammon, New York, 1961.
Languages and International
Use
Version
2.0 and above of all Fulton Findings^{TM}
Windows software includes simple language translation capability. Please
contact Wes Fulton as
indicated in Email Addresses, Sites and
Telephone #'s, if you want to
have the program translated into another language. New language capabilities
will be added to the distributed software, as they become available. A
character or a brief character combination can be selected to specify currency.
Also, Version 2.0 and above recognizes the selection of decimal symbol (either
period or comma) made in the Control Panel setup in Windows. These new features
were added by request from our customers overseas. Languages have been added
and now include . . .
American / English  `English`
Dutch  `Nederlands`
French  `Francais`
German  `Deutsch`
Hungarian  `Magyar`
Italian  `Italiano`
Java (Indonesian)  `Basa Jawa`
Polish  `Polsku`
Portuguese
(Brazilian)  `Portugues`
Spanish  `Espanol`
Swahili  `Kiswahili`
Swedish  `Svenska`
Turkish  `Turk`
From
the `Setup` section, select the Language / Currency / Decimal / Time / Date
icon (showing two people talking) and then select L (for Language) from that
menu to get the language menu.
Likelihood Ratio Techniques
The
likelihood ratio method for confidence was made accessible by Fulton Findings ^{TM}
in 1990 and is still not available elsewhere for easy use on a PC as of
this writing. Since that time, the likelihood ratio technique has been expanded
in Fulton Findings software to compare designs for significant difference based
upon exclusive research conducted by Wes Fulton and Dr. Bob Abernethy. SuperSMITH(TM) Weibull
appears to be the only easily accessible and widely used personal computer
software using it for confidence. Many other uses of this technique are
projected. With proper compensation for small sample bias, it is the best
practice available for comparison of groups of data.
Method of Analysis
Several
data formats and associated methods of analysis are available. They include
rank regression, maximum likelihood, probit,
KaplanMeier, etc. Each technique has benefits for certain data formats. For
example, inspections produce data different than tests where precise failure
times are known. This is similar to coarse readout data from imprecise
instrumentation. Grouped data can be handled effectively with either probit or KaplanMeier. Rank regression has benefits for
smaller sample size and maximum likelihood is suggested for data with many
suspended values. There are other issues associated with plotting methods and
interval data. The New Weibull Handbook is the best source of information
regarding these different methods and their application. SuperSMITH(TM) Weibull
provides all of these techniques that are best practice based upon the
particular data format.
Mixed Distributions
Sometimes
the data collection is less than perfect. Different failure mechanisms can be
mixed together. The mixed distribution model is covered in The New Weibull Handbook ^{TM} (NWH). One technique is to analyze for
competing risk. SuperSMITH(TM) Weibull (SSW) searches for a competing
risk solution from two possible mechanisms (two Weibulls
or two Normals or two Lognormals, etc.) by evaluating
ordered combinations. Pvalue technology is found to indicate the power of the
mixed distribution model. If the power is very low, SSW indicates a small
probability of mixture. Otherwise the pvalue is given along with the four
parameter solution. This level of competing risk mixture analysis is not
available elsewhere. YBath(TM) software programmed by Carl Tarum
and now owned by Fulton Findings(TM) provides additional analysis of more
complex situations including partial populations and competing risk.
Beware
of amateur software from other sources with unsubstantiated mixture analysis
methods. Bad software provides solutions even without reasonable supporting
evidence. You must always take care with mixture analysis, since false
indication of mixture for nonmixed data is common. This can be easily tested.
Feed the suspect software several random samples from a single distribution and
determine the frequency you obtain mixture solutions. If a high proportion of
mixture solutions (high pvalues if given) are provided for the single
distribution samples, then the software is not very good. The best procedure is
to perform careful analysis of mechanism root cause to avoid mixing altogether.
Refer to NWH for more details.
Monte Carlo Simulation and
Confidence
Monte
Carlo (mc) is a special technique for simulation made possible with fast
computers. It is used as a prediction tool and can provide a reference for
analytical techniques. The pivotal (pv) confidence
method is based upon generating and processing large quantities of random
variates. SuperSMITH(TM) Weibull software uses the power of Monte Carlo to
generate correlation PValue and confidence limits for Blives and parameters
such as Beta and Eta. Distribution of the correlation coefficient and t0 (third
parameter in Weibull) for research purposes can be investigated with MonteCarloSMITH^{ TM}. SuperSMITH(TM) Weibull pv confidence should be used for small samples (around 10
or less) instead of analytical techniques. The 4^{th} day in Dr.
Abernethy's 4day Weibull Engineering
Workshop is devoted to mc
simulation. For more information, please contact Dr. Bob Abernethy or Wes
Fulton as indicated in Email Addresses, Sites
and Telephone #'s.
Probabilistic Design
Probabilistic
analysis is just what the doctor ordered for new designs. The previous method
of using safety margins and safety factors is not good enough any more. Reducing the chance of failure is the real
challenge. That means you need to measure the probability of the applied stress
being larger than the strength for each load application. If you can estimate
the distribution of stress and the distribution of load, then SuperSMITH(TM) Weibull can estimate the probability of
failure within your needed accuracy. This very flexible and powerful technique
can also be applied to life distribution vs. usage distribution with similar
results.
Product Support
For
software questions contact Wes Fulton at Fulton Findings and for Weibull
analysis questions contact Dr. Bob Abernethy as indicated in Email Addresses, Sites and Telephone #'s section. All software and handbooks are
guaranteed for customer satisfaction. Most questions are resolved with one
call. Any suggestions for software or handbook enhancement are welcome.
Reliability and Maintenance
Probability
of success is the definition of reliability. A reliable product intelligently
maintained will provide adequate service life and garner high marks for
customer satisfaction. An unreliable product without proper maintenance is a
disaster. Scheduled maintenance can be costly and should only be considered for
wearout failure mechanisms when older parts
are more likely to fail (increasing instantaneous failure rate). Weibull
analysis can indicate whether older parts or newer parts are more likely to
fail. For electronics, generally newer parts are more likely to fail at least
during normal usage (decreasing instantaneous failure rate). This type of
failure mechanism common in electronics is called infant mortality due
to the higher probability of failure at the start of service life. Constant
failure rate indicates the exponential distribution. Maintenance for
infant mortality and exponential failure mechanisms is wasteful. A better
approach is to apply some sort of screening just before actual usage.
Certainly, this is why we feel better after the computer store has burnedin
our new computer for a few hours before we take delivery. SuperSMITH(TM) Weibull
software provides useful estimates of failure mechanism type, the predicted
number of failures to expect, the lowestcost replacement strategy, spares
requirements, and assessments of corrective action effectiveness.
Reliability Growth (CrowAMSAA
based upon J.T. Duane's postulate)
A
technique related to Weibull analysis for evaluating failure occurrence is
called reliability growth modeling. It requires less information than Weibull
requires, but it still can indicate instantaneous failure rate changes. Of 27
different competing reliability growth models, Crow/AMSAA has been found to be
best practice. Dr. Larry Crow took J. T. Duane's postulate for learning curve
modeling and extended the analysis with powerful statistical capabilities while
working with AMSAA. It is included as a part of SuperSMITH(TM) Visual software. There is no need for a separate
program, since this technique simply consists of plotting a straight line on a
loglog plot. Predicting the quantity of failures to expect for spares ordering
and maintainability planning is very easy. The
New Weibull Handbook has a
complete section devoted to Crow/AMSAA.
Risk Analysis (Expected Quantity Forecast)
Estimating the expected quantity of occurrences or failures in the coming months is called risk analysis. Chapter 4 in The New Weibull Handbook covers this type of estimating. It is extremely useful for identifying a batch problem or for determining spares purchase policy. It was developed and used effectively by Dr. Abernethy years ago in response to customer information requirements. Risk analysis is automated in SuperSMITH(TM) Weibull software and is not available elsewhere as of this writing for easy use on a PC.
Skunky Software Alert!
Be
careful. We recommend checking all potential software out with a set of benchmarks
from standard textbooks. Our software meets the benchmarks and often betters
them. We have copied the benchmarks for you and they are easily accessible from
our Windows software. Please contact us if you want to use the benchmarks for
comparison. If possible, try the benchmarks on software you might buy before
actual purchase to see if the software measures up. You may be surprised to
find out how disappointing some software can be. You will not be disappointed
with our software. It is the world standard for performing Weibull analysis.
Software from Fulton Findings
General
descriptions follow. Click here for the latest software version numbers
and revision information.
SuperSMITH(TM) `SS` is a bundled package of programs
from Fulton Findings^{TM} for reliability and
variability solutions on a personal computer at a discount price. It is a
complete selfstudy package with SuperSMITH(TM)
Weibull and SuperSMITH Visual and SuperSMITH YBath(TM) from Fulton
Findings (TM). The `PlayTIME With SuperSMITH
(TM)` tutorial is now available free online as a `.PDF` file. AMAZON sells Dr.
Bob`s standard Weibull handbook, and it is easy to order there. SuperSMITH performs all the techniques in Dr. Bob`s
handbook. SuperSMITH is the standard for performing
Weibull Engineering analysis, and is used by thousands
of companies worldwide. Recently published benchmarks indicate
SuperSMITH as the only trustworthy source for best
practice solutions to these kind of problems.
You
can order SS software as indicated in Email Addresses,
Sites and Telephone #'s. Price
and availability are accessible from the Main
Page.
SuperSMITH Weibull `SSW` software for Windows
performs all of the Weibull techniques in Dr.
Abernethy's New Weibull Handbook. SSW contains results of independent research
with several methods developed by Dr. Abernethy in cooperation with Fulton
Findings. Many of these techniques are not available elsewhere, such as
likelihood ratio confidence, simplified design (set) comparison, KaplanMeier
simulation and solution, critical correlation coefficient, suddendeath WeiBayes, parameter as a function of engineering variable,
etc. SuperSMITH Weibull for Windows uses Weibull,
Normal or LogNormal equations. It replaces the DOS
program WeibullSMITH^{TM} and the Windows
program SuperSMITH(TM) Weibull (SSW), previously the leading Weibull analysis
software programs.
SuperSMITH Visual `SSV` software for Windows
provides general scientific plotting. It includes CrowAMSAA modeling for
reliability growth analysis and it plots probability density functions,
cumulative distribution functions (regular scaling), likelihood contours,
leastcost replacement intervals, failure forecasts, and histograms all from SuperSMITH^{TM} Weibull files. The modified
lowerbias likelihood contour comparison capability in SSW & SSV is not
available elsewhere. The program also includes function plots, data
transforms (global edit), and curve fitting as well as XY plots, bar charts and
pie graphs.
SuperSMITH(TM) YBath(TM)
`SSY` for Windows is the most advanced mixture analysis software available for
bathtub curve modeling with multiple and mixed failure mechanisms in the same
set of data. YBath has capability for solving up to
three different mechanisms convolved in the data. With enough input data
entered YBath will provide the correct mixture
solution. Both rank regression and maximum likelihood techniques are available.
For
more information, please contact Wes Fulton as indicated in Email
Addresses, Sites and Telephone #'s.
ARCHIVED
PROGRAMS . , .
WeibullSMITH (WS) for DOS (no longer available) was
the first commercial PC implementation of Weibull analysis including plotting
and failure forecasting. It was replaced by SuperSMITH(TM) Weibull (SSW)
for Windows and finally SuperSMITH(TM) Weibull (SSW).
All previous capability plus a lot more is now in SSW.
VisualSMITH (VS) for DOS (no longer available) is the
precursor to SuperSMITH(TM) Visual (SSV) and finally SuperSMITH(TM)
Visual (SSV). All capability plus a lot more is now in SSV.
BiWeibullSMITH TM (BW) for DOS (available only from
archives) solves two fit lines for one set of data without partitioning. This
is useful for warranty analysis with both infant mortality and wearout failure mechanisms. The late Alan Townsend of
Allison Engines pioneered this BiWeibull solution
technique. This competing risk analysis capability is not available elsewhere
and has now been moved to SuperSMITH(TM) Weibull. Other software available for mixed population analyis is YBath(TM) from Fulton Findings. Contact us as designated in
Email Addresses, Sites and Telephone #'s section.
MonteCarloSMITH^{TM} (MC) for DOS (no longer available) is a
research tool available for general use. Regular Monte Carlo simulation and
Monte Carlo confidence is available in SuperSMITH(TM) Weibull. What makes MC special is its ability to
create, analyze and store the data from up to 1000 simulations (up to 1000000
for certain comparisons). This process provides Monte Carlo estimates of
confidence for probability model parameters such as the mean, standard
deviation and 95^{th} percentile of a normal distribution for example.
Weibull, Normal and LogNormal equations are provided.
These techniques, absolutely necessary to remove bias for small samples, are not
available elsewhere. The current MC software is already easy to run in Windows, since graphics are not involved.
For
more information, please contact Wes Fulton as indicated in Email
Addresses, Sites and Telephone #'s.
Software from Other Sources
Reliability,
Maintainability, Availability  Please contact Paul Barringer indicated in
Email Addresses, Sites and Telephone #'s for information on
reliability/maintainability/availability modeling tools. These tools are especially
needed for complex facility or system management to minimize costs and maximize
product integrity. MonteCarloSimulationS and
Reliability/Maintainability Modeler are software packages summarized below:
1) MonteCarloSimulationS(TM) is a collection of Excel spreadsheets for use in
simulations. Details are available at http://www.barringer1.com/simul.htm. MonteCarloSimulationS contains a series of simulation
models written in Excel which combines the use of spreadsheets, Weibull
statistical failure data, and random numbers to solve diffiult
problems in reliability, availability, and cost. A sampler of these tools can
be downloaded at no cost from http://www.barringer1.com/mc.htm.
2)
Reliability/Availability Modeler TM is a software modeling package using
process flow diagrams of unit operations, subassemblies of plants, or a
complete plant for building a reliability/availability Monte Carlo simulation
model. The simulation model joins equipment with logic, costs, and Monte Carlo
calculations. Outputs from the simulation model give agestofailure for
finding the overall reliability, availability, and costs for unreliability for
a plant or process. The simulation model and its pallet of tools are under
development with first applications expected beginning of second quarter '97.
The software package will use Gensym's G2
knowledgebased intelligent modeling engine running simulations on a PC in a
Windows NT environment. Details are available at http://www.barringer1.com/modeler.htm.
Suspensions and Censored Data
Units
that have not failed by the failure mechanism under investigation are called
suspensions, or censored units. Suspension times represent values that are less
than the actual life with respect to the failure mechanism of interest. In
other words, the actual length of life is greater than the length of service
recorded. Such data can make the study more accurate and should always be
included to complete the analysis. Methods are available for treating suspended
data as detailed in The New Weibull Handbook.
Test Planning
When is
it better to make something more difficult? Answer: When planning a test, of
course. Test design is based on setting up a tough obstacle course and then
navigating through it. The harder the obstacle course, the better you feel when
you walk (or crawl) across the finish line. Completing a difficult course gives
you more confidence that you could do it again if needed. Using this impeccable
logic and the binomial distribution you can plan your test,
but be prepared for lots of testing! The binomial (pass or fail)
distribution requires lots of test samples. You don't
get much life information from pass/fail tests. However, combining this with
the Weibull distribution to model useful life can drastically lower the amount
of testing needed (and reduce the cost). Good software should include
comprehensive test planning. You may have to make it difficult for your
products when planning a test. So make it easy on yourself and use SuperSMITH(TM)
Weibull, the most comprehensive software for test planning.
Tutorial for Software and
Solutions
PlayTIME (TM) with SuperSMITH
is a tutorial for learning how to perform Weibull analysis, available now in
`.PDF` form for download from this website. It is a complete selfstudy course
when combined with SuperSMITH software and The New
Weibull Handbook(c). This combination is called the SuperSMITH
package. Over 50 case studies are presented in the tutorial representing 50
years of actual problemsolving in the product and service industries. It is
written in an easytofollow style with actual computer exercises. This
tutorial comes as part of Dr. Bob Abernethy`s Weibull Workshop presented by Wes
Fulton and/or Carl Tarum, or it is available separately for selfstudy.
Tzero (3 Parameter)
The
third parameter for Weibull analysis is called tzero. It is a time shift
causing curvature on the Weibull graph for time scaling as originally recorded.
The tzero can also be used for other distributions. The value of tzero is
subtracted from each data value before analyzing. A positive tzero solution
indicates a failurefree period where the probability of failure is negligible.
A negative tzero indicates loss of some reliability before service officially
begins. The critical correlation coefficient (CCC) accounts for the bias in
correlation associated with an additional parameter. SuperSMITH(TM) Weibull
solves for the optimum tzero for a given data set and distribution.
Warranty Data
Warranty
data naturally forms a triangular matrix, also called `layer cake` format. The
data is collected by batches produced on a regular basis. If production is by
months, then reports for the last batch produced cannot have age greater than
one month and reports for the batch a month earlier than that cannot have age
greater than two months and so on. Underneath the production quantity number
for the last month there is only one age interval (one month). The batch
produced just before the last one can have ages of either one month or two
months, so there are two age intervals underneath the production quantity
number for that batch. This trend continues with each month further back into
the past having additional age intervals possible. The first row in the table
below represents production quantity by month, in this case 1000 each month.
Underneath the production quantity are report quantity grouped by age in months
after shipment.
WARRANTY
DATA FORMAT
1000 
1000 
1000 
1000 
1000 
1000 
1 
0 
0 
3 
1 
4 
4 
1 
1 
3 
1 

2 
0 
1 
1 


1 
1 
2 



1 
4 




0 





SuperSMITH(TM) can convert warranty data into Weibull
inspect option #1 (with or without renewal), or Weibull KaplanMeier option #4
(with or without renewal), or Duane/AMSAA reiliability
growth (with or without renewal) . . . depending on which software is used. The
analysis can be truncated before the last month of production or can be
extended past the end of production by selection of less or additional columns
respectively as described in the software. The data above is from The New
Weibull Handbook.
WeiBayes
WeiBayes is a term coined by Dr. Bob Abernethy for
Weibull analysis when the slope parameter is selected beforehand, relating to
Bayesian assumption. Dr. Abernethy refers to this technique alternately as the
oneparameter Weibull, since one of the two standard Weibull parameters is already
selected. Other sources now also refer to this technique pioneered by Dr.
Abernethy and independently by Lois Jackson (Gates Rubber Co.) using the same
terminology. This powerful method based upon maximum likelihood provides
answers to difficult questions concerning product improvement and design
comparison. Use is possible without the requirement of testing to failure,
which can be long and costly. The nofailure situation produces a lower
confidence bound for characteristic life. The presence of failures reduces the
characteristic life value to a point estimate. Dr. Wayne Nelson has extended
the technique producing confidence limits even when failures exist. Case
studies and technique details can be found in The New Weibull Handbook, Chapter
5.
Weibull Analysis for
Variability Control (including Normal, Lognormal, Exponential, Gumbel lower and
Gumbel higher)
Graphical
analysis using several probability distributions is now called Weibull
analysis. The most commonly used is the Weibull
2parameter distribution, but the Weibull 3parameter, the normal distribution,
the lognormal distribution, the exponential distribution, the Gumbel lower (or
"Extreme Value") distribution and the Gumbel higher distribution can
also be used effectively. The Normal and Gumbel distributions can predict
negative life for high reliability requirements, an impossibility. Car must be
used when modeling product life with these distributions. Weibull and Lognormal
never predict negative life when used properly. In addition, Weibull has the
special capability to diagnose failure types such as infant mortality (particulary for electronics), ageindependent (accidents
and natural occurrences), or wearout type mechanisms (bearings, filters,
etc.). Dr. Abernethy's course on Weibull and Lognormal Analysis has become the
standard introduction to this method with handson use of related software.
Engineers, technicians, quality assurance personnel, management
and others responsible for variability control can begin to apply Weibull
techniques in the workplace afterward. Many societies and professional
organizations host these seminars during organizational meetings. Please
contact Wes Fulton or Carl Tarum or one of the organizations,
if you are interested in attending. Contact information is indicated at
the main website page (WeibullNEWS.com).
Zoom (A Closer Look)
Get
closer to reality by investigating the source of your data. There is no
substitute for some oldfashioned detective work to find the root cause of
reported difficulties or measured phenomena. Data analysis methods cannot
improve bad data. When there is an indication of mixed rootcause mechanisms,
the first thing you should do is to group the data according to mechanism.
Weibull analysis is best when analyzing each mechanism separately. You can also
zoom into your statistical analysis by using the Zoom button (showing
magnifying glass) in SuperSMITH(TM) Weibull. There are many features for graphical data
editing, hiding or highlighting, changing Xaxis and
Yaxis ranges and so on in the Zoom portion of the software.