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A system has a history of malfunctioning at an average rate of once in every 400...

  1. A system has a history of malfunctioning at an average rate of once in every 400 days.

            The malfunctions are known to be random and independent and may be described by an

            exponential distribution.

            Determine,                                                                                                                             

      a.   What percentage of components will fail in 200 days?  

  1. If the manufacture wants to replace only 5% of the components, for how long should the manufacturer stated warranty on the component be?  
  2. By redesigning the component, the manufacturer could increase the life. What does the mean time-to-failure have to be so that the manufacturer can offer 100 days of warranty, yet still replace at most 5% of the components?  

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