In order to eliminate this deficiency, a new definition with
an extension in contents is given for the concept of reliability.
This conceptual extension is done in such a way that
in the case of a system with many levels of activity,
the new comprehensive concept of reliability has an analogous
empirical interpretation to the concept of traditional reliability of
an operable or inoperableš system,
for a two level operable or inoperableš system, the
new concept of reliability coincides with the traditional concept of
reliability, and
the new concept stays within the limits of the general
mathematical definition of reliability.
The quantitative definition of the comprehensive
concept of reliability is specified in the form of the following
quantitative characteristics:
Availability with the level c of activity, A(c,t), is
the probability A(c,t) = Prob(The level of activity of the system at
time t is not less than c).
Availability of the mean proportion of activity, A(t),
is the expected value for the proportion of activity of the
system at time t.
Reliability with the level c of activity, R(c,t), is
the probability R(c,t) = Prob(The level of activity of the system does
not become less than c during the time interval from 0 to t).
Mean time to system failure below the level c of
activity, T(c), is the mean of that time period after which the
level of activity of the system for the first time becomes less than c.
Further, expressions for calculating the new
characteristics of reliability straight on the basis of the state
probabilities of the system are derived in the paper. Also remarks
on empirical interpretation and statistical estimation of these
characteristics are given.
(The Finnish Journal of Business Economics 3-1976, 399-
416.)