Median Inactivity Time Function and its Reliability Properties

Kandil Abd El-Fattah Mohamed (), Kayid Mohamed () and Mahdy Mervat Mahdy Ramadan ()
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Kandil Abd El-Fattah Mohamed: Dept. of Mathematics, Insurance and Statistics, Benha University, College of Commerce, Egypt.
Kayid Mohamed: Dept. of Mathematics, Faculty of Science (Suez), Suez Canal University, Egypt.
Mahdy Mervat Mahdy Ramadan: Dept. of Mathematics, Insurance and Statistics, Benha University, College of Commerce, Egypt.

Stochastics and Quality Control, 2010, vol. 25, issue 2, 253-268

Abstract: Let the non-negative random variable X denote the life time of a unit, then the random variable X(t) = t – X for X ≤ t 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.

Keywords: Median inactivity time function; lifetime distributions; convolution; series systems; increasing median inactivity time class; increasing mean inactivity time class (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1515/eqc.2010.018

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