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# Perils of an Old Metric: MTBF

## on Jan 01, 2013

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Presentation at 2008 ASQ World Quality Congress International

Presentation at 2008 ASQ World Quality Congress International

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• 1000 started 1/100 chance of failing each hour Remainng units times same chance of failure for each hour to determine how many are left.

## Perils of an Old Metric: MTBFPresentation Transcript

• Perils of an Old Metric: MTBF Fred Schenkelberg, CRE CQEReliability Engineering Consultant Ops A La Carte, LLC
• Learning Objectives• Understand MTBF definition• Understand MTBF misuses• Understand better measures
• Outline• MTBF – calculation• MTBF – a very poor four letter acronym• History of Use• It’s Misleading• A better measure• Actually, we’ve been talking about MTTF
• MTBF Calculation # hoursMTBF = # failures MTBF = 1 λ
• Mean (M)• The mean in MTBF• What does it mean to you? (no pun intended!)• Average?
• Start 1000 units, MTBF = 100 1200 368 still alive at 101 hours 1000 800 600 400 200 0 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99
• Note the exponential decay12001000800600400200 0 1 21 41 61 81 101 121 141 161 181 201 221 241 261 281
• Other Issues• Time – just because it is hours…• Between – note the duration of the failure free period!• Failure – use the customer definition
• History of Use• Early Parts Count based on adding failure rates of components (60’s and early 70’s) − λ1t − λ 2t − λnt R(t ) = e •e •• e − ( λ1 + λ 2 ++ λ n ) t R(t ) = e
• History of Use• Remember Slide Rule and Mechanical Adding Machines• Victor Adding Machine
• Beta = 0.63 Depth Cut Response data Weibull Probability Plot .5 Weibull Distribution ML Fit Exponential Distribution ML Fit .3 95% Pointwise Confidence Intervals .2 .1 .05 .03Fraction Failing .02 .01 .005 .003 .001 .0005 .0003 .0002 .0001 10^-01 10^00 10^01 10^02 10^03 10^04 DEPTH.CUT
• Beta = 1.97 test7.df data Weibull Probability Plot .7 Weibull Distribution ML Fit .3 Exponential Distribution ML Fit 95% Pointwise Confidence Intervals .1 .03 .01 .003 Fraction Failing .001 .0003 .0001 .00003 .00001 .000003 .000001 .0000003 .0000001.00000003.00000001 1 10 100 1000 10000 100000 Depth In
• Use Reliability• R(t) is the probability that a random unit drawn from the population will still be operating by t hours• R(t) is the fraction of all units in the population that will survive t hours Applied Reliability, 2nd Ed., pg 29
• The four (five) elements• Function• Duration• Probability• Environment• They all change over time
• Use better models/distributions −( t ) β• Weibull RWeibull (t ) = e η• Type I Gumbel − ( et )• Exponential RGumbel (t ) = e• Log Normal − λt Rexp onential (t ) = e• Etc.  t   ln T   50  Rlog normal (t ) = Φ    σ     
• Other Measures• What is the cost of a field failure?• Warranty \$ per unit shipped• Returns/field failure \$ per unit shipped• What else could you use?
• Actually…• MTBF is or should be used for repairable systems• MTTF is what I’ve been talking about• MTTF is calculated the same as MTBF when we assume – negligible repair time – Interarrival times as from an independent sample of nonrepairable parts – Expontential distribution for lifetime of parts• See Chap 10, Applied Reliability for more info
• MTBF
• Learning Objectives• Understand MTBF definition• Understand MTBF misuses• Understand better measures
• Where to Get More Information• Tobias, Paul A. and Trindade, David C., Applied Reliability, 2nd Ed. Chapman & Hall, New York, 1995.• “The Limitations of Using the MTTF as a Reliability Specification” Reliability Edge, Qtr 2, 2000, Vol 1, Issue 1.
• Presenter’s Biographical Sketch• Fred Schenkelberg, Consultant• Independent Reliability Engineering and Management Consultant for past 5 years. Previously at HP Corporate Reliability Engineering Program for 5 years.• MS Statistics Stanford, BS Physics USMA• fms@opsalacarte.com• (408) 710-8248• www.opsalacarte.com