TABLE OF CONTENTS In this section, we consider an inspection policy for a single standby electric generator. We check a standby generator frequently to guarantee the upper bound of the probability that it has failed at the time of the electric power supply stoppage, but to reduce unnecessary costs do not check it too frequently.
The details of the model are described as follows.
The failure time of a standby generator has a general distribution F(t)and its failure is detected only at the next checking time.
A failed standby generator, which was detected at some check, undergoes repair immediately and its repair time has a general distribution G( t).
The time required for the check is negligible and a standby generator becomes as good as new upon inspection or repair.
The next checking time is scheduled at constant time T(0 < T ? ?) after either the prior check or the repair completion.
Costs c 0 and c 1 are incurred for each repair and check, respectively, and cost C 2 is incurred for the failure of a generator when the electric power supply stops, where c 2 > c 0 ? c 1.
The policy terminates with the time of electric power supply stoppage, which occurs according to an exponential distribution (1 ? e ? ? t).
Under the assumptions above, we consider two optimization problems: (a) an optimum checking time T* that...
