Inspection schedules when the lifetime distribution of a single-unit system is completely unknown

In this paper, we derive four optimum inspection policies using the inspection density n(x) proposed by Keller under the assumption of entirely unknown system lifetime distribution; this is often found to be realistic in practice. The models discussed are: (1) the basic model, (2) the basic model with imperfect inspection, (3) the basic model with inspection time, and (4) the basic model with imperfect inspection and inspection time. For each model, we obtain the minimax inspection schedules minimising the total expected cost by applying the calculus of variations.