Further results on geometric and harmonic mean failure rates, the associated aging intensity orders and classes of lifetime distribution

Abstract In this paper, we study conditions under which geometric and harmonic mean failure rate, their aging intensity orders and related aging classes of lifetime distributions are preserved under the structure of the dynamic proportional hazard rate model proposed by Nanda and Das (J. Stat. Plan. Inference 141(6):2108–2119, 2011). Preservation of the considered stochastic orders and also of the associated aging classes under the structure of an $(n-k+1)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mi>k</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:math> -out-of- n system with independent and identically distributed component lifetimes and also their conservation under maximum order statistics, which arises from dependent and identically distributed random variables with an Archimedean copula, are facilitated.