Presentation at 2008 ASQ World Quality Congress International

1. Perils of an Old Metric:
MTBF
Fred Schenkelberg, CRE CQE
Reliability Engineering Consultant
Ops A La Carte, LLC

2. Introduction
• How does your organization
talk about Reliability?
• How do your customers
talk about Reliability?

3. Learning Objectives
• Understand MTBF definition
• Understand MTBF misuses
• Understand better measures

4. 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

5. MTBF Calculation
# hours
MTBF =
# failures
MTBF = 1
λ

6. Mean (M)
• The mean in MTBF
• What does it mean to you?
(no pun intended!)
• Average?

7. 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

8. Note the exponential decay
1200
1000
800
600
400
200
0
1 21 41 61 81 101 121 141 161 181 201 221 241 261 281

9. Other Issues
• Time – just because it is hours…
• Between – note the duration of the failure
free period!
• Failure – use the customer definition

10. 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

11. History of Use
• Remember Slide Rule and Mechanical
Adding Machines
• Victor Adding Machine

12. 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
.03
Fraction Failing
.02
.01
.005
.003
.001
.0005
.0003
.0002
.0001
10^-01 10^00 10^01 10^02 10^03 10^04
DEPTH.CUT

13. 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

14. 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

15. The four (five) elements
• Function
• Duration
• Probability
• Environment
• They all change over time

16. 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 

 


17. 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?

18. 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

19. MTBF

20. Learning Objectives
• Understand MTBF definition
• Understand MTBF misuses
• Understand better measures

21. 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.

22. 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