10.2.1 The ARINC Concept of
System Effectiveness (Ref.
[1])
One of the early attempts to develop concepts of system
effectiveness was delineated by ARINC (Aeronautical Radio Inc.) in its book “Reliability
Engineering.” It contains some of the earliest published concepts of systems
effectiveness and represents one of the clearest presentations of these
concepts from which many of the subsequent descriptions have been derived. The
definition of systems effectiveness applied in this early work is: “Systems
effectiveness is the probability that the system can successfully meet an
operational demand within a given time when operated under specified
conditions.” This definition includes the concepts that system
effectiveness
(1) Can be measured as a
probability
(2) Is related to operation
performance
(3) Is a function of
time
(4) Is a function of the
environment or conditions under which it is used
(5) May vary with the
mission to be performed
Although it is not essential to describe system effectiveness in
terms of probability as opposed to other quantitative measures, it has often
been found convenient to do so. The ARINC model may be expressed such that
system effectiveness probability, PSE, is the product of three
probabilities as follows:

P_{SE} = P_{OR} • P_{MR} • P_{DA} 
(10.1) 
where:
P_{OR} = operational
readiness probability
P_{MR} = mission reliability
probability
P_{DA} = design adequacy probability
This equation states that the effectiveness of the system is the
product of three probabilities: (1) the probability that the system is
operating satisfactorily or is ready to be placed in operation when needed;
(2) the probability that the system will continue to operate satisfactorily
for the period of time required for the mission; and (3) the probability that
the system will successfully accomplish its mission, given that it is
operating within design limits.