1. An electronic component in a video recorder has an exponential time-to-failure distribution. What is the minimum mean time to failure of the component if it is to have a probability of 0.92 of successful operation after 6000 hours of operation?
2. An optical sensor has a Weibull time-to-failure distribution with a scale parameter of 300 hours and a shape parameter of 0.5. What is the reliability of the sensor after 500 hours of operation? Find the mean time to failure.
3. A remote control unit has 40 components in series. The reliability of each component is 0.9994. What is the reliability of the remote control unit? If a redesign has 25 components in series, what is the reliability of the unit?