Reliability properties of record values from non-identically distributed random variables

Abstract

In reliability theory, order statistics and record values are used for statistical modelling. The r-th order statistic in a sample of size n represents the life—length of a (n−r+l)-out-of-n system, and record values are used in shock models. In recent years, reliability properties of order statistics and record values have been investigated. The two models are included in Pfeifer's concept of record values from non-identically distributed random variables. Here, some results on the transmission of distributional properties, such as increasing failure rate, are shown for such records, which contain the results for order statistics and ordinary record values as particular cases.

Keywords:

• order statistics
• record values
• non-identical distributions
• reliability theory
• increasing failure rate
• decreasing failure rate