The requirements for a machine call for a reliability of 0.9 at 10,000 operating hours. It is known that the time-to-failure follows a Weibull distribution with β= 2.
a) What should be the median time to failure of the Weibull distribution to meet the reliability requirement?
b) Suppose this reliability cannot be met, and the actual median is 20,000. So the company instead implements a preventive maintenance policy with a maintenance cycle of 4,000 hours. What is the new reliability at 10,000 hours?