TABLE OF CONTENTS The conditional reliability function may be used in the case of replacing those units that fail by a prescribed operating time [1, Vol. 2, pp. 351-362]. Identical units operate a prescribed period of time, T 1, from age zero; those that are found to have failed after T 1 hours of operation are replaced by fresh ones, and the replaced and nonreplaced units operate an additional T hours. The reliability of N 0 such units for the first T 1 hours of operation is R( T 1), and from Eq. (14.7) the number that will fail by T 1 hours of operation is
These are replaced by fresh ones and they operate T hours thereafter. The number of these replaced units that will fail after T additional hours of operation, using Eq. (14.13), would be
The number of those that do not fail by T 1 is
The number of these units that will fail while operating T additional hours, using Eq. (14.15), would be
or
Consequently, the total number of such units that will fail by ( T 1 ? T) hours of operation, under the condition that those that fail by T 1 hours are replaced, is given by the sum of Eqs. (14.13), (14.14) and (14.16), or
Simplification of Eq. (14.17) yields
Eqeuation (14.18) gives the average number of spares...
