10.2.2 The Air Force (WSEIAC)
Concept (Ref.
[2])
A later definition of system effectiveness resulted from the
work of the Weapon System Effectiveness Industry Advisory Committee (WSEIAC)
established in late 1963 by the Air Force System Command. The WSEIAC
definition of system effectiveness is: “System effectiveness is a measure of
the extent to which a system may be expected to achieve a set of specific
mission requirements and is a function of availability, dependability, and
capability.” The definition may be expressed as:
where:
A = availability
D = dependability
C =
capability
See definitions in Section 10.1.
These are usually expressed as probabilities as follows:
(1) 

“A” is the vector array of various state probabilities
of the system at the beginning of the mission.

(2) 

“D” is a matrix of conditional probabilities over a time
interval, conditional on the effective state of the mission during the
previous time interval.

(3) 

“C” is also a delineal
probability matrix representing the performance spectrum of the
system, given the mission and system conditions, that is, the expected
figures of merit for the
system. 
Basically, the model is a
product of three matrices:
In the most general case, assume that a system can be in
different states and at any given point in time is in either one or the other
of the states. The availability row
vector is then

A = (a_{1} , a_{2} , a_{3}
, . . ., a_{i} , . . . a_{n} ) 
(10.3) 
where a_{i} is the
probability that the system is in State i at a random mission beginning time.
Since the system can be in only one of the n states and n is the number of all
possible states it can be in (including the down states in which the system
cannot start a mission), the sum of all the probabilities a_{i} in the
row vector must be unity, i.e.,
The dependability matrix
D is defined as a square n • n
matrix
where the meaning of the
element d_{ij} is defined as the expected fraction of mission time
during which the system will be in State j if it were in State i at the
beginning of the mission. If system output is not continuous during the
mission but is required only at a specific point in the mission (such as over
the target area), d_{ij} is defined as the probability that the system
will be in State j at the time when output is required if it were in State i
at mission start.
When no repairs are possible or
permissible during a mission, the system upon failure or partial failure
cannot be restored to its original state during the mission and can at best
remain in the State i in which it started the mission or will degrade into
lower states or fail completely. In the case of no repairs during the mission,
some of the matrix elements become zero. If we define State 1 as the highest
state (i.e., everything works perfectly) and n the lowest state (i.e.,
complete failure), the dependability matrix becomes triangular with all
entries below the diagonal being zeros.
If the matrix is properly formulated the sum of the entries in
each row must equal unity. For example, for the first row we must have

d_{11} + d_{12} + . . .
+ d_{1n} = 1 
(10.7) 
and the same must apply to each subsequent row. This provides a
good check when formulating a dependability matrix.
The capability
matrix, C, describes system
performance or capability to perform while in any of the n possible system states. If only a single measure
of system effectiveness is of importance or of interest, C will be a one
column matrix with n elements, such as
where c_{j} represents
system performance when the system is in State j.
System effectiveness,
SE, in the WSEIAC model is then
defined as
Reference [2]
contains several numerical examples of how to perform system effectiveness
calculations using the WSEIAC model. Also, Ref. [3], Chapter
VII, discusses the model at length and provides numerical
examples.