ABSTRACT
For its high reliability, k-out-of-N systems has been more and more used in the equipments of modern advanced technology, such as the systems of aircraft, warship, or missile. An example is the Active Phased Array Radar (APAR). This radar has a cubical shape. On each of the four sides, it has a so-called face, consisting of thousands of transmit and receive elements. A certain percentage of the total number of elements per face is allowed to fail, without losing the function of the specific radar face. Say that this percentage is 10% and that the total number of elements is 3000, then we have a 2700-out-of-3000 system. And the operational availability of these systems is affected by the number of spare parts, repair teams and so on. By analyzing the operational availability with the different number of spare parts and repair teams under the different maintenance policy, we can give support to the decision of maintenance of these systems. For these systems, Ref.[1] provides a simple policy of condition-based maintenance (we call it m-maintenance policy here), and gives the model of operational availability of a k-out-of-N system under this policy. The m-maintenance policy is the policy that the system asks for the repair of spare parts when there are m failed components in the system (the available ones are reduced to N −m). But actually, Because of the limit of spare parts, system can be restored to the state during which the number of available components
is less than N for the rapid restoration of the repairing equipments. This can be called (m, NG) maintenance policy. And the (m, NG) maintenance policy means that replacement of components is only initiated if the number of available components is less than N − m. And after the repair, the number of available components at least is more than NG(N − m < NG ≤ N ) before the system will be transited back to the user. When NG = N , (m, NG) maintenance policy is just m-maintenance policy.
