Preservation of some reliability properties by certain record statistics

Abstract

Record values are closely connected with the occurrence times of a corresponding non-homogeneous Poisson process and in reliability theory, they are used in shock models. In this paper, first, some distribution properties of current records are presented. It is then shown that the hazard (reversed hazard) function of the upper (lower) current records can be expressed in terms of the hazard (reversed hazard) function of the parent distribution. Some reliability relationships between the original variable X and the corresponding current records and with record ranges are established. Also, preservation of some uncertainty measure based on current records is discussed.

Keywords:

• Record values
• Reversed hazard function
• Minimal repair
• IFR(DFR)
• IFRA(DFRA)
• NBU(NWU)
• NBUE(NWUE)
• IMRL(DMRL)
• IURL(DULR)

Acknowledgements

The authors are thankful to an anonymous referee for valuable comments about this work which led to a considerable improvement in the presentation of this paper.