Unformatted text preview: CpE 317
Dr. Minsu Choi
Fundamentals of Reliability
Part 2 Mean-Time-Between-Failure
(MTBF) MTBF is the average time a system will
run between failures – commonly used in
The MTBF of a system is usually
expressed in hours and is given by
expressed It is the area underneath the reliability
curve R(t) plotted versus t.
curve Reliability Curve and MTBF
Reliability MTBF and Exponential Failure
Law So, the MTBF of a system is the reciprocal
of the failure rate.
Example Assume an IC on average fails every 10
yrs; λIC = 1 failure/ 10 yrs =
MTBFIC = 1/ λIC =
What if a system contains 1000 ICs? When t = MTBF
When R(t) = e –λt =
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,
Maintainability When a system fails,
normally carried out.
The probability that a failed system will be
restored to working order within a
specified time .
In other words, it is the probability of
isolating and repairing a “fault” in a system
within a given time.
within Repair Rate and MTTR
Repair Repair rate
MTTR and μ are related to maintainability
as follows: Example
Example Relation between MTBF and
Availability The probability that the system will be
functioning according to its specification at
the instant t during its scheduled working
Reliability assumes correct operation
during the time interval
, availability requires correct operation
only for the instant t.
Continued, Availability = System up-time/(System uptime + System down-time) 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
- Reliability theory, Failure rate, MTBF