1.A power supply consists of three rectifires in series. Each rectifier has a Weibull failure didtribution with b eqaul to 2.1. However they have different characteristics lifetimes given by 12,000 hr, 18,500 hr and 21,500 hr. Find the MTTF and the design life of the power supply corresponding to a reliability of 0.90.

2. A system has two failure modes. One failure mode due to external conditions, has a constant failure rate of 0.07 failure per year. The second attributed to wearout, has a Weibull distribution with a characteristics life of 10 year and a shape parameter of 1.8. Determine the system reliability for a design life of 1 year. Find by trial and error the median time of failure.

3.A complex machine has a high number of failures. The time to failure was found to be lognormal with s = 1.25. Specifications call for a reliability of 0.95 at 1000 cycles.
a) Determine the median time to failure that must be achieved by engineering
Modifications to meet the specifications. Assume the design changes do not affect the shape parameter s.
b) What is the corresponding MTTF and standard deviation?
c) If the desired median time of the failure is obtained, what is the reliability during the next 1000 cycles given it has operated for 1000 cycles?

4.A rotor used in an AC motor manufactured by the Toole N. Di Company has a time to failure that is lognormal with an MTTF found to be 3600 operating hours and a shape parameter s equal to 2.
a) Current preventive maintenance practices require the rotor to be replaced every 100 operating hours. Determine the probability that a rotor will survive the 100 hr.
b) If at the end of the 100 operating hours the maintenance departments neglects to replace the rotor, what is the probability that it will survive until the next scheduled replacement (assume that it has not failed at 100 hr)?
c) If the rotor is still operating after 200 hr, should it be replaced?
d) From the above analysis, what can you say about the hazard rate and the preventive maintenance policy?