The mean residual of record values at the level of previous records

Abstract

In the study of reliability of the technical systems, records model plays an important role. Suppose that a technical system is subject to shocks, e. g. peaks of voltages or stresses. The successive large shocks may be viewed as realizations of records from a sequence of identically independent voltages. Assume that the lower limit value of the mth record voltage (stress) is v > 0. Under these conditions, we propose a mean residual of records (MRR's) for the future records. We study several properties of MRR. We show that the proposed MRR uniquely characterizes the distribution function that generated the sequence of records. It is proved that when the model under study has an increasing hazard rate the corresponding MRR is decreasing. We also compare between two record systems based on their MRR's when these systems are ordered in terms of their hazard rates. © 2009 Springer-Verlag.