, . .
, . , ( ) 100 % , . .
: 0,9 , 65 75 , 0,99 50 80 .
, , .
N k . n1,n2,nk, 1,2,, .
1,2, .
.
n *=∑ (ti/n) i=1 | (3.20) |
n S* =√∑(ti-Tcp)/n-1 i=1 | (3.21) |
S* -
n
σ = √ ∑(ti-Tcp)2 / n
i=1
:
σ* () = σ/√n | (3.22) |
n -
3.22 . σ.
n 20-30 = *, σ = S*
, , . , , .
, , f(t) (-∞; - ε ][ ε;+∞) .
ε, ( ε ≤≤ +ε) =1-α
( ε ≤≤ +ε) =1-α | (3.23) |
, ( )
γ=1- α = [ε/σ()] = [(ε √n)/σ *] = [(ε √n)/S*] =(Z)=2(Z) | (3.24) |
γ , ε.
= (Z*S*)/√n | (3,25) |
Z = (E√n)/s*
|
|
ti 16 .
n
* = ∑ti/n, T*cp = 2000
i=1
:
S* = [√∑(ti T*cp)2/(n-1)] = 340
γ = 0,9 .
- 2(z) =0,9 z=1.64
z .
ε = 1,64*340/√16 = 140
1860<Tcp<2140 0,9
.
50 ε = 50
Z = (E√n)/s*=(50√16)/340
(0,59) = 0,22
:
γ = 2(0,59)= 0,446
, .
, ≠, σ≠S*
, , :
t = (Tcp*-Tcp)/ S* | (3.26) |
n σ*(Tcp) = σ*/√n = S* =√(∑(ti Tcp)2/n(n-1)) | (3.27) |
i=1
t . , σ, , n
tα . - -tα tα ([-tα; tα]). :
tα tα γ = P{- tα ≤ t ≤ tα} = ∫ Sn(t)dt= 2 ∫ Sn(t)dt -tα 0 | (3.28) |
tα
γ = P{-tαS*≤Tcp*-T≤ tαS*} = 2 ∫ Sn(t)td
tα = ε / S* = Tcp* -Tcp / S*
tα, n γ γ
ε = tαS* | (3.29) |
.
n
S* =√[∑(ti Tcp)2/n(n-1)]; S* = 85
i=1
γ = 0,9. n = 16 tα = 1,75
3.29 ε= 1,75 * 85 = 149.
.
[N,,r] . , .
U = 2S(r) λ = 2S(r) / Tcp
S(r) .
, U 2r .
χ2
n S (r) = ∑ti +(N-r)tr i=1 |
U χ21 χ22 f2r(U) χ21, χ22
:
χ22 ∞ ∞
|
|
γ = P{ χ21 ≤ U ≤ χ22 } = ∫ f2r (U) dU = ∫ f2r(U) dU-∫f2r(U)dU (3.30)
χ21 χ21 χ22
∞
∫f2r(U)dU
χ22
λ,λ, χ21 χ22 .
γ λ,λ
f2r(U) [ 0, χ21],[ χ22;∞)
χ21, χ22
0,5(1+γ); 0,5 (1-γ)
: γ, 0.5(1+γ); 0.5 (1-γ) 2r χ2 χ21 χ22. λ,λ .
χ21 (2r) ≤ 2S(r)λ ≤ χ22 (2r) | (3.31) |
≤ =
λn = χ21 (2r) / 2S(r) | (3.32) |
λ = χ22 (2r) / 2S(r) | (3.33) |
= 1/λn; = 1/ λ