Presentation given in 2007 Applied Reliability Conference on problems using MTBF

1. ARS, North America 2007
San Diego, California USA
Track 2, Session 9
Trapped by MTBF
Fred Schenkelberg
Ops A La Carte, LLC

2. Introduction
 How does your organization talk about
Reliability?
 How do your customers talk about
Reliability?
Applied Reliability Symposium, North America 2007
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 2

3. Outline
 MTBF – calculation
 MTBF – a very poor four letter acronym
 History of Use
 It’s Misleading
 A Better Metric
Applied Reliability Symposium, North America 2007
 Actually, we’ve been talking about MTTF
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 3

4. MTBF Calculation
# hours
MTBF =
# failures
Applied Reliability Symposium, North America 2007
MTBF = 1
λ
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 4

5. Mean (M)
 The mean in MTBF
 What does it mean to you?
(no pun intended!)
Applied Reliability Symposium, North America 2007
 Average?
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 5

6. Start 1000 units, MTBF = 100 hrs
1200
1000
368 still alive at 101 hours
800
Applied Reliability Symposium, North America 2007
600
400
200
0
1 8 15 22 29 36 43 50 57 64 71 78 85 92 99
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 6

7. Note the exponential decay
1200
1000
800
Applied Reliability Symposium, North America 2007
600
400
200
0
1 21 41 61 81 101 121 141 161 181 201 221 241 261 281
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 7

8. Other Issues
 Time – just because it is hours…
 Between – note the duration of the failure-
free period!
Applied Reliability Symposium, North America 2007
 Failure – use the customer definition
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 8

9. History of Use
 Remember Slide Rule and Mechanical
Adding Machines
 Victor Adding Machine
Applied Reliability Symposium, North America 2007
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 9

10. History of Use
 Early Parts Count based on adding failure
rates of components (60’s and early 70’s)
− λ1t − λ 2t − λ nt
Applied Reliability Symposium, North America 2007
R(t ) = e •e • • e
− ( λ1 + λ 2 + + λ n ) t
R(t ) = e
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 10

11. 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
Applied Reliability Symposium, North America 2007
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
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 11

12. 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
Applied Reliability Symposium, North America 2007
.001
Fraction Failing
.0003
.0001
.00003
.00001
.000003
.000001
.0000003
.0000001
.00000003
.00000001
1 10 100 1000 10000 100000
Depth In
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 12

13. 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 by t hours
Applied Reliability Symposium, North America 2007
Applied Reliability, 2nd Ed., pg 29
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 13

14. The four (five) elements
 Function
 Duration
 Probability
 Environment
Applied Reliability Symposium, North America 2007
 They all change over time
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 14

15. Use better models/distributions
 Weibull −( t )β
η
 Type I Gumbel RWeibull (t ) = e
 Exponential − ( et )
 Lognormal
RGumbel (t ) = e
RExponential ( t ) = e − λt
 Etc.
Applied Reliability Symposium, North America 2007
 t 
ln
 T 
 50 
Rlognormal (t ) = 1 − Φ  
 σ 

 

Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 15

16. Other metric
 What is the cost of a field failure?
 Warranty $ per unit shipped
 Returns/field failure $ per unit shipped
Applied Reliability Symposium, North America 2007
 What else could you use?
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 16

17. Actually…
 MTBF is or should be used for repairable
systems
 MTTF is what I’ve been talking about
 MTTF is calculated the same way as MTBF
when we assume
Applied Reliability Symposium, North America 2007
 Negligible repair time
 Interarrival times as from an independent sample of
non-repairable parts
 Exponential distribution for lifetime of parts
 See Chap 10, Applied Reliability for more info
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 17

18. Summary
MTBF
Applied Reliability Symposium, North America 2007
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 18

19. 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,
Applied Reliability Symposium, North America 2007
2000, Vol 1, Issue 1.
 Ops A La Carte, LLC provides a full range of
reliability engineering services including
assessments, FMEA facilitation, HALT and ALT
testing, data analysis and customized training.
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 19

20. Presenter’s Biographical Sketch
 Fred Schenkelberg, Consultant
 Independent Reliability Engineering and
Management Consultant for past 3 years.
Previously at HP Corporate Reliability
Engineering Program for 5 years.
 MS Statistics Stanford, BS Physics USMA
Applied Reliability Symposium, North America 2007
 fms@opsalacarte.com
 (408) 710-8248
 www.opsalacarte.com
Fred Schenkelberg, Ops A La Carte, LLC Track 2 Session 9 Slide Number: 20