cpe317-lec2 - CpE 317 CpE Fault-Tolerant Digital...

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Unformatted text preview: CpE 317 CpE Fault-Tolerant Digital Fault-Tolerant Systems Systems Dr. Minsu Choi Fundamentals of Reliability Part 2 Mean-Time-Between-Failure (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 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 Program ...
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