MRL and MPL Functions of Parallel Systems with INID Components under Double Monitoring

摘要

This article investigates parallel systems with n independent but not identically distributed (INID) components. Under the condition that, at time t_1, (t_1 > 0) the total number of failures of the components is r (r < n), and at time t_2 (t_2 - h) the sys~ tern is still working or it has failed, the mean residual life (MRL) function of the parallel system and the mean past lifetime (MPL) function of the components are conducted. Some representations and corresponding properties of the MRL function and the MPL function under several specific conditions are obtained.