Unformatted text preview: CpE 317
CpE
FaultTolerant Digital
FaultTolerant
Systems
Systems
Dr. Minsu Choi
Fundamentals of Reliability
Part 2 MeanTimeBetweenFailure
(MTBF)
(MTBF) MTBF is the average time a system will
MTBF
run between failures – commonly used in
practice.
practice.
The MTBF of a system is usually
The
expressed in hours and is given by
expressed It is the area underneath the reliability
It
curve R(t) plotted versus t.
curve Reliability Curve and MTBF
Reliability MTBF and Exponential Failure
Law
Law So, the MTBF of a system is the reciprocal
So,
of the failure rate.
of Example
Example Assume an IC on average fails every 10
Assume
yrs; λIC = 1 failure/ 10 yrs =
failures/hr.
failures/hr.
MTBFIC = 1/ λIC =
hrs/failure.
What if a system contains 1000 ICs? When t = MTBF
When R(t) = e –λt =
R(t)
Let t=MTBF, then… Example above: when MTBF = 1/λ. Plot R(t) without λ Example
Example For previous example, find t (
when R(t) = 99.9%.
when ) Continued,
Continued, Continued,
Continued, Maintainability
Maintainability When a system fails,
is
When
normally carried out.
normally
The probability that a failed system will be
The
restored to working order within a
specified time .
In other words, it is the probability of
In
isolating and repairing a “fault” in a system
within a given time.
within Repair Rate and MTTR
Repair Repair rate
(repair/hr).
Repair
MTTR (
)=
(hrs/repair).
MTTR and μ are related to maintainability
MTTR
as follows: Example
Example Relation between MTBF and
MTTR
MTTR Availability
Availability The probability that the system will be
The
functioning according to its specification at
the instant t during its scheduled working
period.
period.
Reliability assumes correct operation
Reliability
during the time interval
, availability requires correct operation
only for the instant t.
only Continued,
Continued, Availability = System uptime/(System uptime + System downtime) Example
Example Previous example: where MTBFSYS = 87.6
hrs/failure and use MTTRSYS = 1 hr/repair.
hrs/failure Program Completed
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 Fall '09
 KOSBAR
 Reliability theory, Failure rate, MTBF

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