TABLE OF CONTENTS Most units would be operating for a finite interval. Practically, the working time of units is finite in actual fields. Very few papers treated with replacements for a finite time span. The optimum sequential policy [1] and the asymptotic costs [105], [106] of age replacement for a finite interval were obtained.
This section summarizes inspection policies for an operating unit for a finite interval (0, S] (0 < S< ?) in which its failure is detected only by inspection. Generally, it would be more difficult to compute optimum inspection policies in a finite case than those in an infinite one. We consider three inspection models of periodic and sequential inspections in Section 8.1, and asymptotic inspection in Section 8.2.
In periodic inspection, an interval Sis divided equally into Nparts and a unit is checked at periodic times ? T( ? = 1, 2, , N) where NT= S. When the failure time is exponential, we first compute a checking time in an infinite case, and using the partition method, we derive an optimum policy that shows how to compute an optimum number N* of checks in a finite case.
In sequential inspection, we show how to compute optimum checking times. Such computations might be troublesome, because we have to solve some simultaneous equations, however, they would be easier than those of Algorithm 1 in Section 8.1 as recent personal...
