1.The Breakit Company manufactures anti-clock disk brakes (ABS) for use in automobiles. Anessentialpartofthemanufacturingprocessisthefactoryassembleandintegrationlinking (FAIL)system.Unfortunately,thissystemhasexperiencednumerousfailuresovertheyears under a minimal repair concept that is a non-homogeneous Poisson process having an intensityfunction(t)=1.1510-7t1.3withtmeasuredinoperatinghours.Thesystemaverages 2000 operating hours a year, and it currently 5 years old. When the system fails, the repairtime is lognormal withtmed = 6.2 hours and s =1.2.

a.When the system was new, its manufacturer offered a 500-operating-hr warranty. What is the system reliability during the warrantyperiod?

b.When the system fails, it takes a crew of two to repair it. If the labor rate is $50 per hour and based upon the MTTR, what is the maintenance cost of the FAIL system during its 6th year ofoperation?

c.If the cost of the system is $30,000, what is its optimal (minimum cost) replacement time?