5.8 A canister-type vacuum cleaner consists of the following components. Vacuum cleaner Hose attachment Floor unit Canister Housing Hood assembly Cord and plug Base assembly Motor Filters and gaskets Brush assembly Motor assembly Switch and cord assembly The following components are repairable on failure: brush assembly ( A()=0.01 ), motor assembly (A(1) =0.0078 ), and switch and cord (A(f) = 0.0017 ). All other components are discarded and replaced on failure ( A(1) =0.05 ). All times are in operating hours. (a) If the length of time required to repair the brush assembly is lognormal distributed with s = 0.70 and MTTR = 1.5 hr, how long will it take to do the repair with 90% confidence? (b) What is the system mean repair time if the motor assembly repair time is normal with a mean of 3 hr and a standard deviation of 0.5 hr, the MTTR for the switch and cord is 2 hr, and discard-and-replace repair time has a lognormal distribution with s = I and med = 0.5 hr? (c) The motor assembly is considered to be either discarded or repaired. It has a unit cost of $43, and the cost of repair is $35 x MTTR, while the cost to replace it is $35 x mean replacement time. The fixed costs are assumed to be negligible. Ten percent of all motor assemblies must be condemned. Should the motor be discarded or repaired? (d) If the brush assembly deteriorates according to the intensity p() =0.00001(2.5)/", has a unit cost of $72, and has a failure (repair) cost of $52.50($35 x 1.5 hr), when shall it be replaced