Lord Rayleigh (1880) introduced the Rayleigh distribution in connection
with a problem in the field of acoustics. Since then, extensive
work has taken place related to this distribution in different
areas of science and technology. It has some nice relations with
some of the well-known distributions such as Weibull, chi-square,
or extreme value distributions. An important characteristic of the
Rayleigh distribution is that its hazard function is an increasing
function of time. It means that when the failure times are distributed
according to the Rayleigh law, an intense aging of the
equipment/item takes place. Estimations, predictions, and inferential
issues for one-parameter Rayleigh distribution have been
extensively studied by several authors. Interested readers could
have a look at the book by Johnson, Kotz, and Balakrishnan
(1994) for an excellent exposure to the Rayleigh distribution, and
see also Abd-Elfattah, Hassan, and Ziedean (2006), Dey and Das
(2007), and Dey (2009) for some recent references.