Optimal Structures and Maintenance Policies for PABX Power Systems

A power system for a private automatic branch exchange (PABX) consists of n independent and identical rectifiers hooked up in parallel. The lifetime of each component is an exponential random variable with a known mean (MTBF). The system fails when the number of operating rectifiers is less than m(m ≤ n).

Rectifiers are distinguished by two main characteristics: the current they carry and their MTBF. The minimal number of units, m, is determined by technological considerations: for each type of rectifier, m is calculated so that the system can carry a given maximal current. This maximal current is specified for each PABX.

The system is maintained by a technician who may visit the exchange regularly every v units of time or when it fails. Several maintenance policies are considered. For each type of exchange and for each form of maintenance policy, we determine the optimal set of parameters, {m, n, MTBF, and v}, to minimize the operating cost for a required level of reliability. These results are then used as guidelines for standardizing PABX power systems.