Weibull Database

Weibull databases require considerable use of engineering judgment for meaningful application of the facts stored in database format. Do not apply the data blindly without understanding the specific situation, as this database is solely intended for educational purposes.

Data, described in this database, are very general. The facts are broad as is usually found in engineering references. Typical values are given for a specific case which may not be applicable for each condition envisioned by the end user of the database as exceptions always exist. Therefore you are the sole responsible individual for use of this table--Barringer & Associates, Inc. assumes no liability for your use/misuse of these tables in any manner either obvious or implied.

Item	Beta Values			Eta Values
	(Weibull Shape Factor)			(Weibull Characteristic Life--hours)
	Low	Typical	High	Low	Typical	High
Components				My engineering judgment does not support the range of a few values shown in published databases
Ball bearing	0.7	1.3	3.5	14,000	40,000	250,000
Roller bearings	0.7	1.3	3.5	9,000	50,000	125,000
Sleeve bearing	0.7	1	3	10,000	50,000	143,000
Belts, drive	0.5	1.2	2.8	9,000	30,000	91,000
Bellows, hydraulic	0.5	1.3	3	14,000	50,000	100,000
Bolts	0.5	3	10	125,000	300,000	100,000,000
Clutches, friction	0.5	1.4	3	67,000	100,000	500,000
Clutches, magnetic	0.8	1	1.6	100,000	150,000	333,000
Couplings	0.8	2	6	25,000	75,000	333,000
Couplings, gear	0.8	2.5	4	25,000	75,000	1,250,000
Cylinders, hydraulic	1	2	3.8	9,000,000	900,000	200,000,000
Diaphragm, metal	0.5	3	6	50,000	65,000	500,000
Diaphragm, rubber	0.5	1.1	1.4	50,000	60,000	300,000
Gaskets, hydraulics	0.5	1.1	1.4	700,000	75,000	3,300,000
Filter, oil	0.5	1.1	1.4	20,000	25,000	125,000
Gears	0.5	2	6	33,000	75,000	500,000
Impellers, pumps	0.5	2.5	6	125,000	150,000	1,400,000
Joints, mechanical	0.5	1.2	6	1,400,000	150,000	10,000,000
Knife edges, fulcrum	0.5	1	6	1,700,000	2,000,000	16,700,000
Liner, recip. comp. cyl.	0.5	1.8	3	20,000	50,000	300,000
Nuts	0.5	1.1	1.4	14,000	50,000	500,000
"O"-rings, elastomeric	0.5	1.1	1.4	5,000	20,000	33,000
Packings, recip. comp. rod	0.5	1.1	1.4	5,000	20,000	33,000
Pins	0.5	1.4	5	17,000	50,000	170,000
Pivots	0.5	1.4	5	300,000	400,000	1,400,000
Pistons, engines	0.5	1.4	3	20,000	75,000	170,000
Pumps, lubricators	0.5	1.1	1.4	13,000	50,000	125,000
Seals, mechanical	0.8	1.4	4	3,000	25,000	50,000
Shafts, cent. pumps	0.8	1.2	3	50,000	50,000	300,000
Springs	0.5	1.1	3	14,000	25,000	5,000,000
Vibration mounts	0.5	1.1	2.2	17,000	50,000	200,000
Wear rings, cent. pumps	0.5	1.1	4	10,000	50,000	90,000
Valves, recip comp.	0.5	1.4	4	3,000	40,000	80,000
Machinery Equipment
Circuit breakers	0.5	1.5	3	67,000	100,000	1,400,000
Compressors, centrifugal	0.5	1.9	3	20,000	60,000	120,000
Compressor blades	0.5	2.5	3	400,000	800,000	1,500,000
Compressor vanes	0.5	3	4	500,000	1,000,000	2,000,000
Diaphgram couplings	0.5	2	4	125,000	300,000	600,000
Gas turb. comp. blades/vanes	1.2	2.5	6.6	10,000	250,000	300,000
Gas turb. blades/vanes	0.9	1.6	2.7	10,000	125,000	160,000
Motors, AC	0.5	1.2	3	1,000	100,000	200,000
Motors, DC	0.5	1.2	3	100	50,000	100,000
Pumps, centrifugal	0.5	1.2	3	1,000	35,000	125,000
Steam turbines	0.5	1.7	3	11,000	65,000	170,000
Steam turbine blades	0.5	2.5	3	400,000	800,000	1,500,000
Steam turbine vanes	0.5	3	3	500,000	900,000	1,800,000
Transformers	0.5	1.1	3	14,000	200,000	14,200,000
Instrumentation
Controllers, pneumatic	0.5	1.1	2	1,000	25,000	1,000,000
Controllers, solid state	0.5	0.7	1.1	20,000	100,000	200,000
Control valves	0.5	1	2	14,000	100,000	333,000
Motorized valves	0.5	1.1	3	17,000	25,000	1,000,000
Solenoid valves	0.5	1.1	3	50,000	75,000	1,000,000
Transducers	0.5	1	3	11,000	20,000	90,000
Transmitters	0.5	1	2	100,000	150,000	1,100,000
Temperature indicators	0.5	1	2	140,000	150,000	3,300,000
Pressure indicators	0.5	1.2	3	110,000	125,000	3,300,000
Flow instrumentation	0.5	1	3	100,000	125,000	10,000,000
Level instrumentation	0.5	1	3	14,000	25,000	500,000
Electro-mechanical parts	0.5	1	3	13,000	25,000	1,000,000
Static Equipment
Boilers, condensers	0.5	1.2	3	11,000	50,000	3,300,000
Pressure vessels	0.5	1.5	6	1,250,000	2,000,000	33,000,000
Filters, strainers	0.5	1	3	5,000,000	5,000,000	200,000,000
Check valves	0.5	1	3	100,000	100,000	1,250,000
Relief valves	0.5	1	3	100,000	100,000	1,000,000
Service Liquids
Coolants	0.5	1.1	2	11,000	15,000	33,000
Lubricants, screw compr.	0.5	1.1	3	11,000	15,000	40,000
Lube oils, mineral	0.5	1.1	3	3,000	10,000	25,000
Lube oils, synthetic	0.5	1.1	3	33,000	50,000	250,000
Greases	0.5	1.1	3	7,000	10,000	33,000

You'll recognize the form of the above table from Appendix A of the reference: Bloch, Heinz P. and Fred K. Geitner, 1994, Practical Machinery Management for Process Plants, Volume 2: Machinery Failure Analysis and Troubleshooting, 2nd Edition, Gulf Publishing Company, Houston, TX. If you're interested in machinery life, you'll find this book (and others written by Block and Geiter) worthy of adding to your library for good maintenance practices and good solid advice on plant equipment.

Bloch and Geitner's Appendix A is given in failures per million hours. Information from Appendix A has been interpreted and converted into ages-to-failure as shown under the low/high values by Barringer & Associates, Inc. along with estimates of typical Weibull values. Bloch and Geitner also give additional failure rates in their 1994 book: An Introduction To Machinery Reliability Assesment, 2nd Edition, Table 4.3. This book is also published by Gulf Publishing Company in Houston, TX.

Bloch and Geitner also list Weibull shape factors in Table 7-2 of the above reference. You will find many of their values are different than listed above (remember you can always think of different applications and situations which result in different Weibull values for shape factors and characteristic life!!--be carefull when you use the data!!). The issue is not which Weibull value is right or wrong--the issue is to understand your conditions so you select the correct value for your operations based on your experience and your operating conditions. Frequently we find the same equipment in use in similar applications within large companies will display significantly different Weibull values because of the way it is installed, maintained, and operated--so don't be surprised by different Weibull values.

You can communicate with: Heinz P. Bloch, P.E. in West Des Moines, IA by e-mail at     hpbloch@mchsi.com and Fred K. Geitner, P.Eng. in Brights Grove, Ontario, CANADA by e-mail at     fgeitner@compuserve.com.

Other information for this database was developed from details supplied verbally by David P. Weber. Dave is a gas turbine reliability expert and author of papers in fuzzy logic for solving reliability problems. He has an extensive Weibull database information on gas turbines and other equipment. You can contact Dave at Phone: 513-697-0852 or FAX: 513-697-0860 and     e-mail.   Also consider use of Dave Weber's Weibul db software. Weibull db uses data from the above database and displays probability plots, hazard plots, and Monte Carlo variations of the above information in an Excel spreadsheet--cost for the software is US$70 plus shipping and handling.

This database is intended for educational purposes only. Barringer & Associates, Inc. clearly is not responsible (neither obvious liability or implied liability) for how you use this database. If you are not personally responsible for knowledgeable use of the details in this database, then don't use it.

Additional comments concerning Weibull databases-

Most Weibull beta (slope of the Weibull line which is a shape factor) and eta values (a location parameter know as the characteristic value) are frequently viewed by experienced end users of the data as proprietary information.  Experienced practioneers of Weibull technology do not widely publish or disseminate their expensive data.

Weibull beta values are driven by the physics of failure. Weibull eta values are measures of durability. Eta values can be changed by grades of materials whereas the beta values cannot be “dialed up” but are dependent upon the physics of failure . 

Here is an example, in the gas turbine industry, the beta for properly installed, properly maintained, and properly manufactured bearings has a typical beta = 2.0.  Note the beta for bearings in my database above is 1.3.  Why?

In the chemical industry and refining industry where I often work, they frequently allow water and unusual chemicals to enter bearing housings which results in the flatter slopes to the life distributions.  In a similar manner when refineries allow catalysis particles to enter the lubrication systems we also observe more scatter to the data.  Thus industries where I do most of my consulting effort, do NOT observe beta = 2 for ball bearings.  Of course if you hammer assemble bearings it is easy to observe betas below 1.  Similarly, if you overload the bearings following the Lundberg-Palmgren bearing equation you can get widely different values for beta.  If you load rolling element bearings too lightly, you produce betas greater than one with short etas as the bearing skid rather than roll.  If you have numerous insults to the bearings you can get betas ~1 from the mixed failure modes.  Remember the beta value is determined by the physics of failure. 

There are no “true” values for beta—it depends upon experience and specific cases even with test results from bearing manufacturers.  For example, see data from the Journal of Research of the National Bureau of Standards, Vol 57, No. 5, November 1956, Research Paper 2719 which was data furnished to Lieblein and Zelen by manufacturers for their contract to set the Lundberg-Palmgren exponent, which they choose as 3.0 for ball bearings and 3.333 for roller bearings.  I have summarized their betas for download in the April 2001 Problem of the Month.

Add this fact to the problem with historical data:  The uncertainty in reliability data is in the X-axis of Weibull plots (age-to-failure) and many computer programs have the regression in the wrong direction.  At the university on your laboratory experiments you carefully controlled variability in the X-axis and took your variability in the Y-axis so you regressed Y-onto-X.  You can’t do the regression that way for reliability data!  For reliability data your errors are greatest in the X-axis and thus you must regress X-onto-Y which is a “backward” regression.  One automotive manufacture in the USA has 50 years of data in their Weibull database with the regression performed incorrectly (that is Y-regressed-onto X).  These regression details are explained in The New Weibull Handbook, 5^th edition, written by Dr. Robert Abernethy.  By the way, SuperSMITH Weibull software can analyze the data as Y-onto-X, or by the preferred method which regresses X-onto-Y as it follows all the details of The New Weibull Handbook.

In general, I do not have high expectations for Weibull data obtained through open source literature as much of the data is of little true value.  The real data is in the databases of manufacturing companies, who treat the data as very valuable proprietary information and they will not broadly release the information because of misuse, arguments, and abuse of their expensive test data.

When we have the Weibull Users conference (usually held every two years, but it did not occur this year, 2009, because of the poor economy), we hear manufactures describe beta/eta values for practical applications.  Remember manufactures have to spend money to get test data under carefully controlled test, whereas end users of equipment acquire their data as a product of using the equipment under variable and uncontrolled conditions.  So it’s important to “know” some typical values by failure modes. 

Here’s an example of why you need to know failure modes:  Tests of a large quantity sample from a laboratory found many rubber belts driving equipment had a beta between 1 and 2 which is too low for rubber belts.  Most likely their test data had mixed failure modes consisting of some physical infant mortality modes mixed with some physical wearout failure modes. Failure modes must be physically separated to properly categorize the life into the correct value.  What is the correct beta for rubber belts—the answer is beta is between 2 and 3 for correctly tested rubber belts.  I advised reeducation and retraining of assembly technicians into how to correctly assemble a belt onto the pulleys.  They should make sure to tell the technicians to disallow use of screw drivers to pry belts onto pulleys which will cause infant mortality type failure modes (it’s easier to pry the belt over the lip of the pulley when no one else is looking but that incorrect assembly method “breaks the back” of the belt and produces an infant mortality failure mode).  When infant mortality data is mixed with longer lives of properly assembled belts which fail by wearout failure modes, you will observe flatter betas!!—with many mixed failure modes the beta à 1.

So where would you find the correct beta for rubber belts?—see the January 2010 problem of the month based on my experience and words from belt manufacturers—you should not expect them to widely publish this data.  Bottom line, do not accept data with mixed failure modes. Failure modes MUST be physically separated. Mixed failure modes when combined into a single dataset will produce junk information.  Unfortunately knowing about failure modes takes experience which most young engineers who run the tests do not have!  Therefore treat most reported beta’s in the literature with some skepticism! Many people expect manufactures should report their beta/eta values—ask this question, what reward does the manufacture obtain by reporting there data when the competitor can claim his betas/etas are “better” to make a sale?

In general, a literature search will give you beta values of questionable use.  Treat the beta results with a jaundiced eye.  Too many engineers expect the Weibull analysis software to separate failure modes. Don’t rely on the computer to separate failure modes as the computer cannot do this without having enormous dataset sizes.  No one will pay for large datasets.  That’s the reason good engineering involves both art and science AND the use of frugal datasets. 

I find too many doubtful results in the literature. Better information for Weibull betas/etas resides in the databases of manufactures and end users. They decline to disclose their databases because of economic restrictions; however, in technical meetings and discussions they will frequently describe the information verbally but rarely write it down and publish the information into the public domain.  

Remember the correct values for beta are hidden from competitors and inquiring eyes by both manufactures and end users who have the correct values for their specific cases.  They will not widely disclose this valuable information because they use their data for warranty costs, repair costs, and guaranteed maintenance contracts involving substantial sums of money.

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Last revised 2/22/2010

This database may be revised at any time to correct values or to reinterpret operating conditions.