Математическое моделирование при планировании экспериментов на трех, четырех, пяти уровнях фактора и при неодинаковом количестве уровней первого и второго фактора. Черный А.А. - 17 стр.

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17
)xxx(Pxxxt
rn
m
r
m
n
mm
sr
m
s
m
r
mm
++
−⋅+−⋅=
1
;
]x)x[(Pa)xxx(at
n
m
n
mmm
sn
m
s
m
n
mmm
22
2
−+−⋅=
+
;
)xxx(a)x(xt
r
m
n
m
rn
mm
r
m
r
mm
−−+−=
+
2
22
3
;
])x(x[at
tt
d
n
m
n
mmm
mm
m
222
3
21
−⋅+
+
=
; (26)
mmmm
Pade
+
⋅
=
; (27)
(
)
n
mm
r
mm
s
mm
xexdxf ⋅+⋅+−=
; (28)
n
mm
r
mm
xaxt ⋅+=
4
;
n
mm
rn
m
n
mmm
xaxxtt
2
45
⋅−−⋅=
+
;
mm
r
mm
rn
mm
r
mm
atxtxaxt ⋅−⋅−⋅+=
+
54
2
6
;
sn
mm
sr
mmm
s
mmm
xaxPtxtt
++
⋅−−⋅+⋅=
547
;
(
)
2
2
n
m
n
m
wn
m
w
m
n
m
m
xx
xxx
z
−
−⋅
=
+
;
wn
mm
wr
m
w
mmmmm
xaxxtztt
++
⋅−−⋅+⋅=
458
;
sn
mm
sr
mm
s
mm
xexdxt
++
⋅+⋅+=
2
9
;
rn
mm
r
mm
sr
mm
xexdxt
++
⋅+⋅+=
2
10
;
n
mm
rn
mm
sn
mm
xexdxt
2
11
⋅+⋅+=
++
;
n
mm
r
mm
s
mm
xexdxt ⋅+⋅+=
12
;
wn
mm
wr
mm
ws
mm
xexdxt
+++
⋅+⋅+=
13
;
111214 m
n
mmm
txtt −⋅= ;
mm
s
mmm
Ptxttt ⋅−⋅−=
1412915
; 
             t m1 = x mr ⋅ x ms − x rm+ s + Pm ( x mn ⋅ x mr − x mn + r )
                                                                                           ;

      t m 2 = a m ( x mn ⋅ x ms − x nm+ s ) + a m Pm [( x mn )2 − x m2 n ]
                                                                                           ;

                     t m3 = x m2 r − ( x mr )2 + 2a m ( xmn + r − xmn − xmr )
                                                                                               ;

                                                            t m1 + t m 2
                                dm =                                                   ;           (26)
                                            t m3 +   a m2   ⋅ [ x m2 n − ( x mn )2 ]

                                            em = d m ⋅ a m + Pm ;                                  (27)

                                        (
                           f m = − x ms + d m ⋅ x mr + em ⋅ x mn ;           )                     (28)

                                    t m 4 = x mr + a m ⋅ x mn ;

t m5 = t m 4 ⋅ xmn − xmn + r − a m ⋅ xm2 n ;

t m 6 = x m2 r +a m ⋅ x mn + r − t m 4 ⋅ x mr − t m 5 ⋅ a m ;

t m 7 = t m 4 ⋅ x ms +t m 5 ⋅ Pm − x mr + s − a m ⋅ x mn + s ;

         x mn ⋅ x mw − x mn + w
zm =                                ;
            x m2 n   −   ( )
                         x mn
                                2



t m8 = t m5 ⋅ z m + t m 4 ⋅ xmw − xmr + w −a m ⋅ xmn + w ;

t m9 = x m2 s + d m ⋅ x mr + s + em ⋅ x mn + s ;

t m10 = x mr + s + d m ⋅ x m2 r + em ⋅ x mn + r ;

t m11 = x mn + s + d m ⋅ x mn + r + em ⋅ x m2 n ;
t m12 = x ms + d m ⋅ x mr + em ⋅ x mn ;
t m13 = x ms + w + d m ⋅ x mr + w + em ⋅ x mn + w ;
t m14 = t m12 ⋅ x mn − t m11 ;
t m15 = t m9 − t12 ⋅ x ms − t m14 ⋅ Pm ;




                                                     17

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