User Manual

Reliability Demonstration Report
MaxBotix
®
Inc.
Document Release: 05/12/2010, pg. 10 of 10
10
0
MaxBotix, MaxSonar, XL & WR are trademarks of MaxBotix Inc.
v1.1b • 07/2009 • Copyright 2005-2010
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4.6 Temperature Cycling (MTBF)
The equation below is used to model the relation between increased temperature and the
acceleration of the aging of a product as compared to its normal operational temperature.














−×
















∆
∆
=
MaxTMaxSt
s
s
t
f
TTk
Ea
e
H
H
T
T
A
11
333.09.1
A
f
= acceleration factor
Ea = activation energy in electon-volts (eV) = 0.53 eV
k = Boltzmann’s constant = 8.617 x 10
-5
eV/T
k
∆T
s
= Difference in Temperature during normal operation* = 20°C
∆T
t
= Difference in Temperature during test operation = (+65°C – (-40°C )) = 105°C
H
s
= Cycle frequency in the field (Cycles/24hours) = 1
H
t
= Cycle frequency in the lab = 13.4
e = 2.71828 (mathematical constant)
T
MaxS
= Temperature during normal operation* in Kelvin= 304°K (21°C+273°K)
T
MaxT
= Maximum Temperature during test operation in Kelvin= 338°K (65°C+273°K)
*Temperature of normal operation assumed to be 21°C +/- 10°C for these calculations.
This equation yeilds an acceleration factor of 47.405. With 20 units tested for 317 hours
with no failures being observed this calculatea an MTBF value of 229,139 hours.