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The following table shows the time between failures for a software system.

Error Number 1 2 3 4 5
Time since last failure(hours) 6 4 8 5 6

The reliability of the system for one hour of operation assuming an exponential model is :

  1. 0.45
  2. 0.63
  3. 0.84
  4. 0.95
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MTBF is the mean (average) of a distribution of product life time or life between successive failures.

{\displaystyle {\text{MTBF}}={\frac {\sum {({\text{start of downtime}}-{\text{start of uptime}})}}{\text{number of failures}}}.}

MTBF=(6+4+8+5+6)/5=29/5

the probability or reliability that the product will work for a defined period of time without failure is given by the following equation: R(T)=exp(-T/MTBF)

here T= 1hour

R(1)=e^(-5/29)=e^(-0.1724)=0.84

Reference:

http://www.profaceamerica.com/sites/default/files/cms/cms/resource_library/files/6fef09c498f66461/mtbf_communique.pdf

https://en.wikipedia.org/wiki/Mean_time_between_failures

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if T is 1 then calculation should be  e^(-1/29)
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