Mean Time Failure and other Formulas

Important formula for Mean Time Failures

MTTF - Mean Time To Failure

 MTTF = 1 / failure rate = Total #hours of operation / Total #units

 MTTF is an averaged value. In reality failure rate changes over time

because it may depend on age of component.

 Failure rate = 1 / MTTF (assuming average value over time)

 MTTR - Mean Time to Recovery / Repair

 MTTR = Total #hours for maintenance / Total #repairs

 MTTD - Mean Time to Diagnose

 MTBF - Mean Time Between Failures

 MTBF = MTTD + MTTR + MTTF

MTTF - Serial assembly 

 MTTF of system = 1 / SUM (1/MTTFi) for all components i

 Failure rate of system = SUM(1/MTTFi) for all components i

MTTF - Parallel assembly 

MTTF of system = SUM(MTTFi) for all components i

 Availability = Time system is UP and accessible / Total time observed

 Availability = MTTF / (MTTD* + MTTR + MTTF)

or

 Availability = MTTF / MTBF

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Cache performance and Access time of memories

• Cache hit

✓ When CPU refers to memory and find the data or instruction within the Cache Memory

• Cache miss

✓ If the desired data or instruction is not found in the cache memory and CPU refers to the

main memory to find that data or instruction

Hit + Miss = Total CPU Reference

Hit Ratio h = Hit / ( Hit + Miss )

Average access time of any memory system consists of two levels:

✓ Cache Memory

✓ Main Memory

• If Tc is time to access cache memory and Tm is the time to access main

memory and h is the cache hit ration, then

Tavg = Average time to access memory

Tavg = h * Tc + ( 1-h ) * ( Tm + Tc )

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Host/author is not responsible for these posts.