Abstract
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 ≥ t 1) the sys-tem 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.
Acknowledgments
The research was supported by the Science and Technology Program of Gansu Province, China (Project No. 1010RJZA076).