(
)
()
1
1
1
1
,,
1
,
,
1
,
0,
t
u
Г
o
F
t
u
e
du
Г
u
v
du
dv
u
v
t
−−
−
−
−
=
=
==
=
=
=
(
)
(
)
1
0
1
0
1
1
,
t
v
t
v
v
e
dv
Г
v
e
dv
Г
−
−
−−
=
=
=
We have:
()
(
)
1
0
1
,,
t
v
v
e
dv
t
Г
−−
=
(4)
Where
(
)
,
t
is the incomplete gamma-function (it depends from two
parameters
,
t
). Therefore,
(
)
(
)
(
)
,,
,
.
Г
PX
t
F
t
t
=
=
(5)
Let us review the task, when consumption of raw materials in the main production
(manufacturing leather products) is a random value with the intensity of 20
conventional units of value per hour. We know that to cover the consumption there are
systematic weekly (30 hours) supplies of raw materials equaling to the volume of 640
conventional units of value.
We designate Xt
= as a time interval (optimal value for guaranteeing the
absence of scarcity of raw materials), when the general consumption of raw materials
equals to their supply (
). We assume that value Xt
= has gamma-distribution with
parameters
(volume of supply of raw material in conventional units of value) and
(the intensity of consumption of raw materials per hour in conventional units of
value). Then the scarcity of raw material occurs if random value
Xt
=
has lower level
compared with a specified interval between supplies of raw materials, namely
30
Xt
=
Therefore, we need to compute the integral gamma-distribution function for three
parameters
20,
30,
640
t
=
=
=
, or the incomplete gamma-function for two
parameters.
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