TABLE OF CONTENTS System reliability can be improved by providing some standby units. Especially, even a single standby unit plays an important role in the case where failures of an operating unit are costly and/or dangerous. A typical example is the case of standby electric generators in nuclear power plants, hospitals, and other public facilities. It is, however, extremely serious if a standby generator fails at the very moment of electric power supply stoppage. Hence, frequent inspections are necessary to avoid such unfavorable situations.
Similar examples can be found in army defense systems, in which all weapons are on standby, and hence, must be checked at suitable times. For example, missiles are stored for a great part of their lifetimes after delivery. However, their reliabilities are known to decrease with time because some parts deteriorate with time. Thus, it would be important to test the functions of missiles as to whether they can operate normally. We need to check them periodically to monitor their reliabilities and to repair them if necessary.
Earlier work has been done on the problem of checking a single unit. The optimum schedules of inspections that minimize two expected costs until failure detection and per unit of time were summarized in [1]. The modified models where checking times are nonnegligible, a unit is inoperative during checking times, and checking hastens failures and failure symptoms, were considered in [2], [3], [4], [5]. Furthermore, the availability of a periodic inspection model [6] and the...
