Weibull Analysis Of Failures - Barringer and Associates, Inc.

Weibull AnalysisIt’s Not About Complicated Statistics.Weibull Analysis Tells The “Medicine”You Need For Solving Your Problems.Paul Barringer, P.E.Barringer & Associates, Inc.P.O. Box 3985Humble, TX 77347 Phone: 1-281-852-6810Email: hpaul@barringer1.com http://www.barringer1.comFor More Reliability Tools: See http://www.barringer1.com/nov07prb.htmApril 9, 2009© Barringer & Associates, Inc. 2009 1

Wallodi WeibullEnglish Pronunciation: Wah-Low-D Y-Bull• Wallodi Weibull (1887-1979) invented thelife data analysis technique. He livedmost of his life in Sweden working onproblems with materials, fatigue, strength,rupture, and bearing fatigue life.• His statistics are based on a concept offailure of the weakest link in a chain.• His most famous Weibull engineeringpaper was published by ASME in 1951.© Barringer & Associates, Inc. 2009 2

Weibull Plots For Components• Collect age-to-failure data for eachcomponent. This is tombstone data: timeat death less time at birth = age-to-failure.• Each age-to-failure data for components isplotted in rank order as the X-value.• The Y-value is determined by Benard’smedian rank calculation to reduce bias inthe plot.© Barringer & Associates, Inc. 2009 3

What Does The Data Say?• We have 3 similar units operating for less than ayear. We’ve had 5 failures. The ages-to-failure(hours of operating time) are: 1200, 2200, 3000,4500, 5100 as shown in rank order. (X-axis data)• The Y-axis plot position in Benard’s rank order is:12.96%, 31.48%, 50%, 68.52%, 87.04%.• What’s the failure mode? What’s thecharacteristic life (typical life) of thecomponent?© Barringer & Associates, Inc. 2009 4

The Bathtub Curve TellsAbout Human Failure RatesAverage Age At Death: 20 th Century 77 yrs, 17 th Century 32 yrs--Why?Late 20 th CenturyHuman Mortality RatesInfantChanceOld AgeBathtubCombinedRatesYou see bathtubcurves for humans.Why don’t you seebathtub curvesfor equipment?Beyond the age of 10 years,infant mortality is not abig problem ------------------>0 20 40 60 80 100Age

Failure StatisticsWeibull DistributionsProbability distribution function, f(t)PDFCurvef infant ( t )f chance ( t )f wearout ( t )f( t ) . t ( ) . 1 et0.0020.001Infant = 0.5Wearout = 5Chance = 100 1000 2000tInstantaneous failure rate, h(t)Hazard 0.002Curveh( t ) .h infant ( t )h chance ( t )h wearout( t )t 10.0010Wearout, > 10 1000 2000tChance, =1Infant < 1 = 1000

What Does The Plot Tell Us?63.2%This is a double logarithmic scaleX(hours)Y%1200 12.962200 31.483000 50.004500 68.525100 87.04pve% is a goodness ofcurve fit criteria and needsto be 10% or greater• For components: < 1 = infant mortality ≈ 1 = chance failures > 1 = wear out failures• For components = characteristic life asthis distribution has along tail to the rightUnreliability = 1.789= line slope = 3724n = number ofdatapointss = number ofsuspended data = 3724Long tail to the rightThis is a logarithmic scaleThe red trendline tells what percent of the population will die by a give time. Relative Frequency Of Occurrence© Barringer & Associates, Inc. 2009 Linear Age Scale 7

Why Weibull’s• They tell HOW things die—i.e. you get technicalsupport for failure modes• They give objective evidence for FMEA’s toguide RCM decisions with facts—not opinions• They use data from your CMMS (or fromstores, or from purchasing, or frommaintenance work orders, etc.)• They make sense from the apparent nonsenseof failure details to answer businessquestions for maintenance and engineering© Barringer & Associates, Inc. 2009 8

Conditional Reliability• Suppose I have a similar component 81.6%that is still alive at 4,000 hours.67.9%From the graph the probability offailure is 67.9% or reliability is 32.1%.• What probability do I have for thecomponent surviving for a life of5,000 hours? From the graph theprobability of failure is 81.6% orreliability is 18.38%.• Condition reliability for living another 1000 hrs =R(5000hrs)/R(4000 hrs) = 18.38%/32.1% = 57.25%• Probability of survival = 57.25%Probability of failure = 42.75%,Unreliability© Barringer & Associates, Inc. 2009 95%10%20%30%40%50%60%70%80%90% Your odds for living another1000 hours are better than youhad for getting from 0 hoursto 4000 hours.Reliability

Use Weibulls To DoUse previousWeibull dataTimed Replacements?• Cost for a plannedreplacement = $5,000• Cost of an unplannedreplacement = $20,000• Run to failure? Do atimed replacement?—If so, when?• Weibull’s and $’s savearguments and time!!• When in doubt—useyour brains + technologyHigh Cost OfPMs Too EarlyCost $/hr= 1.789, = 3724 hrs,C p = $5,000, C up = $20,000Optimum replacement@ 2,400 hrs where cost is$5.13/hr. Run to failurecost is $5.45/hr.OptimumReplacement =5.13/hrEquipment Age (hours)High Cost OfPMs Too LateRunTowardFailure =$5.45/hr= $0.32/hrWorthOptimumReplacement?© Barringer & Associates, Inc. 2009 10

Use Weibulls To PredictHow Many Replacements?Use previousWeibull data• We have the followingparts in service: 1@30005@2000, 6 @1500,10@1000hrs. When theyfail we’ll replace with = 10,000 hrs upgrades.• How many parts will weneed in the next 5 years?71 replacementsrequired in next5 years. Newparts have = 1.789and = 10,000 hoursOld parts with 3724 hour lifehave been used up. New andmore durable replacements© Barringer & Associates, Inc. 2009 are being installed and usedwith 10,000 hour life.11

Weibull Analysis Of Failures• Weibull analysis of failure data tellshow the component died (infant, chanceor wear-out). The failure mode suggestsspecific corrective action.• One set of math handles tailed data.• Use age-to-failure data (and useproduction data for process Weibulls).• About 85-95% of all life data makes astraight line on a Weibull plot. When indoubt, use the Weibull plots for life data.WhatWhyWhenWhere© Barringer & Associates, Inc. 2009 12

Sharpen Your TechnicalSkills With Weibull Analysis• Use your CMMS failure data to be fact driven withfailure modes determined by technical Weibull analysis• Use Weibull analysis to forecast future failures• Use Weibull analysis for timed replacement decisionsbased on financial decisions• Use Weibull analysis to support your RCM technicaldecisions by providing persuasive arguments and crispdecisions for money saving actions• Which are you using? Weibull technical facts aboutfailure modes? Or seat of pants opinion for engineeringand maintenance conclusions.© Barringer & Associates, Inc. 2009 13

Reading Resources• Weibull’s Biography:http://www.barringer1.com/weibull_bio.htm• Weibull’s Collection Of Technical Papershttp://www.barringer1.com/wa.htm• The New Weibull Handbook, 5 th edition US$98http://www.barringer1.com/tnwhb.htm• International Weibull Standard IEC-61649-2008http://www.iec.ch• Worked Out Weibull Exampleshttp://www.barringer1.com/problem.htmFreeDownloadFreeDownload~US$250FreeDownload© Barringer & Associates, Inc. 2009 14