At this point, alert and/or informed readers may rightly question if we are
simply reinventing the wheel given that concepts of accelerated aging are old
engineering practice and the ranking and selection statistics have a
huge literature (see reference list again). Our first answer is that we are
quantifying and unifying various engineering heuristics under one umbrella.
While there are connections between what we do and that of ranking and
selection statistics, considerable difference in emphasis remains. The
principal difference has to do with the size of population we work with. In
ranking and selection statistics, we are mostly concerned with ranking among
five or ten alternatives as in drug efficacy testing; while in engineering
applications, the number of alternative is in billions. Also in OO we
studiously avoid cardinal notions while the R&S literature is still
concerned with things such as the distance between the best and the rest, a
cardinal notion. Finally, questions such as "Is the observed order a
maximum likelihood estimate of the actual order?" are most intriguing and
elegant in R&S, they are of little concern in OO since the probability of
coincidence of the observed and actual order is so minuscule to be totally
uninteresting.
On the other hand, R&S and the Order Statistics literature are clearly
related to our interest in OO. For example, the additive noise model described
earlier in Eq.(*) is known as the Thurstone-Mosteller-Daniel model in
R&S.