TABLE OF CONTENTS The computing procedure for obtaining the optimum inspection schedule was specified in [1]. Unfortunately, it is difficult to compute Algorithm 1 numerically, because the computations are repeated until the procedures are determined to the required degree by changing the first checking time. To avoid this, a nearly optimum inspection policy that depends on a single parameter pwas suggested in [22]. This policy was used for Weibull and gamma distribution cases [23], [24]. Furthermore, the procedure of introducing a continuous intensity n( t) of checks per unit of time was proposed in [29], [30]. This section summarizes four approximate calculations of optimum checking procedures.
When a unit is checked at periodic times ? T( ? = 1, 2, ), the total expected cost is, from (8.1),
where 
, which is the mean duration of time elapsed between a failure and its detection.
Suppose that F(t)has the piecewise linear approximation:
Then, E{ D} = T/2; i.e., the mean duration of undetected failure is half the time between the checking times. The result is also given when the failure times between successive checking times are independent and distributed uniformly. In this case, the optimum checking time is 
. This time is also derived from (8.5) by putting e ? T ?, 1 + ? T+ ( ? T) 2/2 approximately and ? = 1//
