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Licensed Unlicensed Requires Authentication Published by De Gruyter December 1, 2010

Median Inactivity Time Function and its Reliability Properties

Abd El-Fattah Mohamed Kandil, Mohamed Kayid and Mervat Mahdy Ramadan Mahdy
From the journal


Let the non-negative random variable X denote the life time of a unit, then the random variable X(t) = tX for Xt for a fixed t ∈ {x : FX (x) > 0}, is known as inactivity time or reversed residual life time. In this paper, we define a new non-parametric class of life distributions based on the median of the random variable X(t) and study its reliability properties. Some new results concerning the proposed class are given including some closure properties and characterizations. We also introduce and study a new stochastic ordering based on the median of X(t) and find its relationship with other well-known order relations. Finally, we provide the median inactivity time function of some well-known life time distributions.

Received: 2008-04-03
Published Online: 2010-12-01
Published in Print: 2010-December

© de Gruyter 2010