Choice of the best time scale for preventive maintenance in heterogeneous environments

A principal feature of the model considered in this paper is the presence of several time scales for lifetime measurements when similar objects operate in heterogeneous conditions. A typical example is lifetimes of an aircraft module which can be measured in the total time in air and in the number of flights. A family of lifetimes can be generated by considering a linear combination of the above two principal time scales. We consider a problem of finding an optimal maintenance period for an equipment operating during a single maintenance/replacement cycle, in heterogeneous environmental conditions. Our main concern is finding the time scale which provides the maximal value of the return (cost) functional. We consider two ‘principal’ time scales (the operation time and the total number of shocks) and show numerically that the optimal linear combination of these two scales has also the minimal coefficient of variation (c.v.) of system lifetime. We develop some general theory to connect the optimality in terms of the return functional with the optimality in terms of c.v.