User Manual

Reliability Demonstration Report
MaxBotix
®
Inc.
Document Release: 05/12/2010, pg. 9 of 10
10
0
MaxBotix, MaxSonar, XL & WR are trademarks of MaxBotix Inc.
v1.1b • 07/2009 • Copyright 2005-2010
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4.5 High Temperature Operational Life (MTBF)
Because we observed no failures during our test we computed MTBF using a Chi-
squared distribution. For the purposes of this test a level of confidence of 90% was
considered acceptable. The MTBF formula using a Chi-squared distribution is:
( ) [ ]
)1(2,
)(2
2
+
⋅⋅⋅
=
nX
ATN
MTBF
f
α
where:
MTBF = Mean time between failures
2 is the
N is the Number of elements = 50 sensors
T = Total test time = 1340.5 hours
A
f
= Acceleration factor from Arrenhius equation = 8.00 (reference Appendix 4.6)
α = 0.1 (Confidence level of 90%)
n = number of failures (used to calculate degrees of freedom) Our test did not have any
failures so, n = 0
X
2
[α,(2(n+1))] = Chi-squared distribution function = 4.605
Using this equation and substituting the above values yields a MTBF of 232,896 hours at
a confidence level of 90%. This is to say that the “mean life” for our product is more
than 90% likely to meet or exceed 232,896 hours based upon the data we collected with
no failures.