are defined. TS is planned in the time interval 
,
where 
is the techniucal reource
of the aircraft until the end of its technical exploitation(TE)[1]. The first
CWA is done in moment 
, and the
last one in the moment 
. According
to [2] the full average loses(expenses) of time -
are defined at the reviewed STS - 
.
As 
(1)
-mathematical
expectancy of the full average financial and time loses(expences); 
-
average value of the losses with one CWA; 
- losses of finances while determining the AS in a condition of hidden fault;
- conditional possibility for “false
fault” in the interval 
; 
-
conditional possibility for “inability to find a fault” in the interval 
;
- average value of loses at a repeated
CWA(RCWA). Setting - B. One STS - 
,
is called minimaximal if condition [2] is satisfied:
, (2)
-
multitude of composition of moments çà CWA
;
- the worst possible function of
distribution of the times for ÊÐ;
-
multitude of fuctions for distribution.
from the multitude 
.
The expression, which is argument of the integral in equation (1) is marked
with the following function:
(3)
,
-
function, defining the loses caused by faults of AS after the ê-th CWA. After
each distribution function 
from
multitude A, the following inequality are satisfied:
(4)
- mathematical expectancy of the loses of the usage of corresponding STS. Equation
(4) means that for each STS - 
is correct. The equation:
. (5)
of the time until
fault of AS(found in equation (1)), is a function with single fluctuation in a
point 
. For the demonstration of
the optimality of MSTS(minimaximal STS for the Bulgarian Military Airforces) the
demonstration of the following is necessary: Theorem. If 
is a minimaximal STS: a) The amount of CWA in the interval 
is represented as the maximal positive number 
,
for which the inequation is satisfied:
; (6)
. (7)
for AS
with a distribution function 
,
including
CWA, done for a time 
with 
. The union of all multitudes
of STS, containing from 0 to 
CWA
we mark with 
, while 
.
Then lets mark with 
, the multitude
of STS, including the 
CWA, which
moments of execution 
are defined
by the condition:
. (8)
.
For the demonstration of the above theorem the demonstration of the following
is necessary:
exists and 
, therefore at
least one STS ÑÒÎ 
for which 
can be found;
is satisfied;
for the minimaximal STS is equal to 
taken form the multitude of 
.
For 
. (8)
-
interval of examination of STS. From (4) at 
we obtain that 
, ֌ 
.
Therefore:
(9)
, 
.
From (9) we obtain that for the belonging to each STS multitude of 
the following equation is satisfied:
(10)
condition
(8) is satisfied, and from (10) we obtain the equation:
. (11)
which means that with the rendering of (11), we have 
(12)
, we obtain
the following:
. (13)
. (14)
from equation (13) in (14), we obtain a formula for loses of STS 
(15)
,
it is necessary the term of the fraction from (13) must be positive or zero in
order to be satisfied 
:
. (16)
. (17)
which means the following:
. (17)
we do a examination of the relation between 
, as 
, 
and 
CWA. 
. 
we determine the difference 
,
ò.å.:
(19)
.
, where n is a random amount of CWA. Fro this purpose we must prove that STS 
,
for which the condition (8) is satisfied:
(20)
(21)
the following if satisfied:
(22)
(23)
. (24)
:
(25)
(26)
, (27)
(28)
. Therefore:
. (29)
.
Therefore:
(30)
,
leads to less loses than STS with the same amoung of ÊÐ, but not from the multitude 
,
and in the second part is obtained 
,
therefore:
(31)
and STS 
with 
:
,
(32)
; 
; We put in equation (32)
the loses during usage of STS at 
- control of the work ability
in the interval 
. (33)
are not
raising with the increase of 
while the term is negative. Therefore the number of CWA 
,
minimizes the loses 
, (34)
which had to be demonstrated.
with formula (12)
expressed through 
, according
to:
(35)
Therefore a demonstration of the
second part of the current theorem is done. 
; 
; 
;
; 
; 
.
; 
h.