Q1) A software system is designed so that after every hour of normal operation, it stops and relaunches from its initial state. This process is known software rejuvenation. Suppose that mean time to failure for software is measured to be 10 hours and mean time to repair is 5 minutes. Repair means restoring software to the operating condition by relaunching it from its initial state.

a) Determine the reliability of system after 4 successful hours of execution and four successful rejuvenations?

b)** **Find the probability of failure of system for any 4 hours of operation?

c) What is the availability of system where R(t) = e ^{-λt} , where R is reliability, c is reciprocal of mean time to failure, and t is execution time. Note that e^{x} is approximately (1 + x) for small x. Using R(t) = e ^{-λt}

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