ǍǏǟǛǙǍǟǕǔǍǣǕǬ ǛǑǚǛǞǟǠǜǒǚǤǍǟǛǐǛ ǗǛǚǟǝǛǘǬ ǗǍǤǒǞǟǏǍ Ǐ ǞǝǒǑǒ MATLAB

ǚǭDZDzdzǺǻǾǿȉ ǵ ǷǭȄDzǾǿǯǻ ǾǸǻdzǺȈȂ ǾǵǾǿDzǹ. Ȳ 2 (10), 2015
ǠǑǗ 681.321
ǍǏǟǛǙǍǟǕǔǍǣǕǬ ǛǑǚǛǞǟǠǜǒǚǤǍǟǛǐǛ ǗǛǚǟǝǛǘǬ
ǗǍǤǒǞǟǏǍ Ǐ ǞǝǒǑǒ MATLAB
Ǐ. Ǐ. ǙǭǽǷDzǸǻǯ, Ǎ. Ǖ. ǏǸǭǾǻǯ, Ǒ. ǒ. ǔǻǿȉDzǯǭ
ȼɜɟɞɟɧɢɟ
Ʉɨɧɬɪɨɥɶ ɤɚɱɟɫɬɜɚ ɢɡɞɟɥɢɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɯɧɢɤɢ ɹɜɥɹɟɬɫɹ ɧɟɨɬɴɟɦɥɟɦɨɣ ɩɪɨɰɟɞɭɪɨɣ ɠɢɡɧɟɧɧɨɝɨ ɰɢɤɥɚ [1]. ȼ ɪɚɛɨɬɟ [2] ɛɵɥɢ ɪɚɫɫɦɨɬɪɟɧɵ ɨɫɨɛɟɧɧɨɫɬɢ ɩɪɢɦɟɧɟɧɢɹ ɩɚɤɟɬɚ MATLAB ɞɥɹ
ɚɧɚɥɢɡɚ ɤɚɱɟɫɬɜɚ ɢɡɞɟɥɢɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɯɧɢɤɢ, ɞɚɧɵ ɪɟɤɨɦɟɧɞɚɰɢɢ ɩɨ ɮɨɪɦɢɪɨɜɚɧɢɸ ɢɫɯɨɞɧɵɯ
ɞɚɧɧɵɯ ɚɧɚɥɢɡɚ ɢ ɢɯ ɨɛɪɚɛɨɬɤɟ.
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɪɚɡɥɢɱɚɸɬ ɫɥɟɞɭɸɳɢɟ ɜɢɞɵ ɫɬɚɬɢɫɬɢɱɟɫɤɨɝɨ ɤɨɧɬɪɨɥɹ ɩɚɪɬɢɢ ɩɪɨɞɭɤɰɢɢ
ɩɨ ɚɥɶɬɟɪɧɚɬɢɜɧɨɦɭ ɩɪɢɡɧɚɤɭ [3–6]:
– ɨɞɧɨɫɬɭɩɟɧɱɚɬɵɣ ɤɨɧɬɪɨɥɶ – ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɤɨɧɬɪɨɥɶ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣɫɹ ɬɟɦ, ɱɬɨ ɪɟɲɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɢɟɦɤɢ ɩɚɪɬɢɢ ɩɪɨɞɭɤɰɢɢ ɩɪɢɧɢɦɚɸɬ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɤɨɧɬɪɨɥɹ ɬɨɥɶɤɨ ɨɞɧɨɣ ɜɵɛɨɪɤɢ;
– ɞɜɭɯɫɬɭɩɟɧɱɚɬɵɣ ɤɨɧɬɪɨɥɶ – ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɤɨɧɬɪɨɥɶ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣɫɹ ɬɟɦ, ɱɬɨ ɪɟɲɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɢɟɦɤɢ ɩɚɪɬɢɢ ɩɪɨɞɭɤɰɢɢ ɩɪɢɧɢɦɚɸɬ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɤɨɧɬɪɨɥɹ ɧɟ ɛɨɥɟɟ
ɞɜɭɯ ɜɵɛɨɪɨɤ, ɩɪɢɱɟɦ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɨɬɛɨɪɚ ɜɬɨɪɨɣ ɜɵɛɨɪɤɢ ɡɚɜɢɫɢɬ ɨɬ ɪɟɡɭɥɶɬɚɬɨɜ ɤɨɧɬɪɨɥɹ
ɩɟɪɜɨɣ ɜɵɛɨɪɤɢ;
– ɦɧɨɝɨɫɬɭɩɟɧɱɚɬɵɣ ɤɨɧɬɪɨɥɶ – ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɤɨɧɬɪɨɥɶ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣɫɹ ɬɟɦ, ɱɬɨ ɪɟɲɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɢɟɦɤɢ ɩɚɪɬɢɢ ɩɪɨɞɭɤɰɢɢ ɩɪɢɧɢɦɚɸɬ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɤɨɧɬɪɨɥɹ ɧɟɫɤɨɥɶɤɢɯ
ɜɵɛɨɪɨɤ, ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɢɫɥɨ ɤɨɬɨɪɵɯ ɭɫɬɚɧɨɜɥɟɧɨ ɡɚɪɚɧɟɟ, ɩɪɢɱɟɦ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɨɬɛɨɪɚ ɩɨɫɥɟɞɭɸɳɟɣ ɜɵɛɨɪɤɢ ɡɚɜɢɫɢɬ ɨɬ ɪɟɡɭɥɶɬɚɬɨɜ ɤɨɧɬɪɨɥɹ ɩɪɟɞɵɞɭɳɢɯ ɜɵɛɨɪɨɤ;
– ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɣ ɤɨɧɬɪɨɥɶ – ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɤɨɧɬɪɨɥɶ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣɫɹ ɬɟɦ, ɱɬɨ ɪɟɲɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɢɟɦɤɢ ɩɚɪɬɢɢ ɩɪɨɞɭɤɰɢɢ ɩɪɢɧɢɦɚɸɬ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɤɨɧɬɪɨɥɹ ɧɟɫɤɨɥɶɤɢɯ
ɜɵɛɨɪɨɤ, ɦɚɤɫɢɦɚɥɶɧɨɟ ɱɢɫɥɨ ɤɨɬɨɪɵɯ ɧɟ ɭɫɬɚɧɨɜɥɟɧɨ ɡɚɪɚɧɟɟ, ɩɪɢɱɟɦ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɜɵɛɨɪɤɢ
ɡɚɜɢɫɢɬ ɨɬ ɪɟɡɭɥɶɬɚɬɨɜ ɤɨɧɬɪɨɥɹ ɩɪɟɞɵɞɭɳɢɯ ɜɵɛɨɪɨɤ.
ȼɨɩɪɨɫɵ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɚɧɚɥɢɡɚ ɜ ɫɪɟɞɟ MATLAB ɦɟɬɨɞɨɜ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɤɨɧɬɪɨɥɹ
ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɞɚɧɧɨɣ ɫɬɚɬɶɟ.
1. Ɇɟɬɨɞɢɤɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɤɨɧɬɪɨɥɹ ɜ ɫɪɟɞɟ MATLAB
ȼ ɪɚɛɨɬɟ [2] ɛɵɥ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɧ IP ɛɥɨɤ ɤɨɞɚ ɞɥɹ ɩɚɤɟɬɚ MatLab, ɤɨɬɨɪɵɣ ɨɛɟɫɩɟɱɢɜɚɟɬ
ɚɧɚɥɢɡ ɩɥɚɧɚ ɤɨɧɬɪɨɥɹ ɩɨ ɨɩɟɪɚɬɢɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ. ɉɪɢ ɨɪɝɚɧɢɡɚɰɢɢ ɤɨɧɬɪɨɥɹ ɜɚɠɧɨ ɭɦɟɬɶ
ɤɨɥɢɱɟɫɬɜɟɧɧɨ ɨɰɟɧɢɬɶ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ ɩɥɚɧɚ [7–10]. Ɉɫɧɨɜɧɨɣ ɜɟɪɨɹɬɧɨɫɬɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɩɥɚɧɚ ɜɵɛɨɪɨɱɧɨɝɨ ɤɨɧɬɪɨɥɹ ɹɜɥɹɟɬɫɹ ɨɩɟɪɚɬɢɜɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ Ɋ(q) [2],
ɬ.ɟ. ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɢɧɹɬɶ ɩɚɪɬɢɸ ɩɪɨɞɭɤɰɢɢ ɫ ɞɨɥɟɣ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɪɚɜɧɨɣ q. ɉɪɨɚɧɚɥɢɡɢɪɭɟɦ ɨɩɟɪɚɬɢɜɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɩɥɚɧɚ ɤɨɧɬɪɨɥɹ. ɉɭɫɬɶ ɧɚ ɤɨɧɬɪɨɥɶ ɩɨɫɬɭɩɚɟɬ ɩɚɪɬɢɹ ɩɪɨɞɭɤɰɢɢ
ɨɛɴɟɦɨɦ N ɢɡɞɟɥɢɣ, ɜ ɤɨɬɨɪɨɣ D ɢɡɞɟɥɢɣ ɢɦɟɸɬ ɞɟɮɟɤɬ. ɉɪɢ ɷɬɨɦ ɱɢɫɥɨ D ɧɟɢɡɜɟɫɬɧɨ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɞɨɥɹ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ q = D/N [2].
Ⱦɥɹ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɩɥɚɧɚ ɨɩɟɪɚɬɢɜɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
P( q)
Pn ( m d c )
¦ Pn (m),
c
ɩɪɨɝɪɚɦɦɧɚɹ ɪɟɚɥɢɡɚɰɢɹ ɤɨɬɨɪɨɣ ɜ ɫɪɟɞɟ MatLab ɩɪɟɞɫɬɚɜɥɟɧɚ
m 0
ɧɚ ɪɢɫ. 1.
34
ǟDzȂǺǻǸǻǰǵȄDzǾǷǵDz ǻǾǺǻǯȈ ǼǻǯȈȅDzǺǵȌ ǺǭDZDzdzǺǻǾǿǵ ǵ ǷǭȄDzǾǿǯǭ ǵǴDZDzǸǵǶ
Ɋɢɫ. 1. Ʌɢɫɬɢɧɝ ɩɪɨɝɪɚɦɦɵ MATLAB ɞɥɹ ɨɰɟɧɤɢ ɨɩɟɪɚɬɢɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɩɥɚɧɚ
(m – ɱɢɫɥɨ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɜɵɛɨɪɤɟ ɨɛɴɟɦɨɦ n (ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ);
Ɋn(m) – ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɹɜɥɟɧɢɹ m ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɜɵɛɨɪɤɟ ɨɛɴɟɦɨɦ n)
ɇɚ ɪɢɫ. 2 ɩɪɢɜɟɞɟɧɚ ɫɯɟɦɚ ɩɪɨɜɟɞɟɧɢɹ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɤɨɧɬɪɨɥɹ.
Ɋɢɫ. 2. ɋɯɟɦɚ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɤɨɧɬɪɨɥɹ (m – ɱɢɫɥɨ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɜɵɛɨɪɤɟ ɨɛɴɟɦɨɦ
n, c – ɩɪɢɟɦɨɱɧɨɟ ɱɢɫɥɨ, d – ɛɪɚɤɨɜɨɱɧɨɟ ɱɢɫɥɨ)
ɉɪɢ ɫɬɚɬɢɫɬɢɱɟɫɤɨɦ ɤɨɧɬɪɨɥɟ ɤɚɱɟɫɬɜɚ ɩɪɨɞɭɤɰɢɢ ɢɫɩɨɥɶɡɭɸɬ ɫɥɭɱɚɣɧɭɸ ɛɟɫɩɨɜɬɨɪɧɭɸ
ɜɵɛɨɪɤɭ ɢ ɩɪɢ ɪɚɫɱɟɬɟ ɨɩɟɪɚɬɢɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ɋ(q) ɢɫɯɨɞɹɬ ɢɡ ɝɢɩɟɪɝɟɨɦɟɬɪɢɱɟɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ, ɡɚɞɚɜɚɟɦɨɝɨ ɮɨɪɦɭɥɨɣ
Pn ( m)
CDmC Nn mD
,
C Nn
ɝɞɟ C Nn – ɱɢɫɥɨ ɫɨɱɟɬɚɧɢɣ ɢɡ N ɷɥɟɦɟɧɬɨɜ ɩɨ n.
Ʉɨɞ ɮɭɧɤɰɢɢ MatLab ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɮɚɤɬɨɪɢɚɥɚ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 3.
Ɋɢɫ. 3. Ʌɢɫɬɢɧɝ ɩɪɨɝɪɚɦɦɵ MATLAB ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɮɚɤɬɨɪɢɚɥɚ
35
ǚǭDZDzdzǺǻǾǿȉ ǵ ǷǭȄDzǾǿǯǻ ǾǸǻdzǺȈȂ ǾǵǾǿDzǹ. Ȳ 2 (10), 2015
Ɉɞɧɚɤɨ, ɭɱɢɬɵɜɚɹ ɨɬɫɭɬɫɬɜɢɟ ɧɟɨɛɯɨɞɢɦɵɯ ɪɚɫɱɟɬɧɵɯ ɬɚɛɥɢɰ ɩɪɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɹɯ N ɢ n,
ɦɨɠɧɨ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɬɶ ɬɪɟɛɭɟɦɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɛɢɧɨɦɢɚɥɶɧɵɦ ɡɚɤɨɧɨɦ ɢɥɢ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ
ɉɭɚɫɫɨɧɚ. ȿɫɥɢ ɨɛɴɟɦ ɜɵɛɨɪɤɢ n ɧɟ ɩɪɟɜɵɲɚɟɬ 10 % ɨɛɴɟɦɚ ɩɚɪɬɢɢ ( n d 0,1N ), ɬɨ ɦɨɠɧɨ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɬɶ ɝɢɩɟɪɝɟɨɦɟɬɪɢɱɟɫɤɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɛɢɧɨɦɢɚɥɶɧɵɦ, ɡɚɞɚɜɚɟɦɵɦ ɮɨɪɦɭɥɨɣ:
Pn ( m) Cnm q m p n m ,
ɝɞɟ ɪ = 1 – q – ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɹɜɥɟɧɢɹ ɝɨɞɧɨɝɨ ɢɡɞɟɥɢɹ.
ȿɫɥɢ n d 0,1N ɢ q d 0,1 , ɬɨ ɪɚɫɱɟɬɵ ɦɨɠɧɨ ɟɳɟ ɛɨɥɶɲɟ ɭɩɪɨɫɬɢɬɶ, ɢɫɩɨɥɶɡɭɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɉɭɚɫɫɨɧɚ. Ɍɨɝɞɚ
Pn ( m )
O m e O
,
m!
ɝɞɟ Ȝ = n p – ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɱɢɫɥɚ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɜɵɛɨɪɤɟ ɨɛɴɟɦɨɦ n.
Ɋɢɫ. 4. Ʌɢɫɬɢɧɝ ɩɪɨɝɪɚɦɦɵ MATLAB ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ Ɋn(m)
ɋ ɜɨɡɪɚɫɬɚɧɢɟɦ ɩɪɢɟɦɨɱɧɨɝɨ ɱɢɫɥɚ c ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ n ɛɭɞɟɬ ɪɚɫɬɢ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɢɧɹɬɢɹ
ɩɚɪɬɢɢ ɫ ɡɚɞɚɧɧɵɦ ɭɪɨɜɧɟɦ ɤɚɱɟɫɬɜɟ q, ɚ ɫ ɜɨɡɪɚɫɬɚɧɢɟɦ ɨɛɴɟɦɚ ɜɵɛɨɪɤɢ n ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ c ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɢɟɦɤɢ ɩɚɪɬɢɢ Ɋ(q) ɫ ɡɚɞɚɧɧɵɦ ɭɪɨɜɧɟɦ ɤɚɱɟɫɬɜɚ q ɛɭɞɟɬ ɭɦɟɧɶɲɚɬɶɫɹ. ɗɬɢ ɫɜɨɣɫɬɜɚ
ɢɥɥɸɫɬɪɢɪɭɸɬɫɹ ɧɚ ɪɢɫ. 5.
Ɋɢɫ. 5. ɋɟɦɟɣɫɬɜɨ ɨɩɟɪɚɬɢɜɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɥɚɧɨɜ ɤɨɧɬɪɨɥɹ [2]
ɋ ɜɨɡɪɚɫɬɚɧɢɟɦ ɫ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ n, q0, qm ɪɢɫɤ ɩɨɫɬɚɜɳɢɤɚ Į ɭɦɟɧɶɲɚɟɬɫɹ, ɚ ɪɢɫɤ ɩɨɬɪɟɛɢɬɟɥɹ ȕ ɜɨɡɪɚɫɬɚɟɬ. ɗɬɨ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɩɪɨɬɢɜɨɪɟɱɢɜɨɫɬɢ ɬɪɟɛɨɜɚɧɢɣ ɩɨɫɬɚɜɳɢɤɚ ɢ ɩɨɬɪɟɛɢɬɟɥɹ ɤ ɩɥɚɧɭ ɤɨɧɬɪɨɥɹ.
ɂɡ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɫɜɨɣɫɬɜ ɨɩɟɪɚɬɢɜɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɥɟɞɭɟɬ, ɱɬɨ ɜɫɟɝɞɚ ɦɨɠɧɨ ɜɵɛɪɚɬɶ
ɬɚɤɨɣ ɩɥɚɧ ɤɨɧɬɪɨɥɹ, ɤɨɬɨɪɵɣ ɝɚɪɚɧɬɢɪɨɜɚɥ ɛɵ ɡɧɚɱɟɧɢɹ ɪɢɫɤɨɜ Į ɢ ȕ ɩɪɢ ɡɚɞɚɧɧɵɯ ɩɪɢɟɦɥɟɦɨɦ
q0 ɢ ɛɪɚɤɨɜɨɱɧɨɦ qm ɭɪɨɜɧɹɯ ɤɚɱɟɫɬɜɚ.
Ⱦɥɹ ɩɪɨɢɡɜɨɞɫɬɜɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɧɟ ɬɨɥɶɤɨ ɪɟɡɭɥɶɬɚɬ ɩɪɢɟɦɨɱɧɨɝɨ ɤɨɧɬɪɨɥɹ ɨɞɧɨɣ
ɩɚɪɬɢɢ ɢɡɞɟɥɢɣ, ɧɨ ɢ ɨɰɟɧɤɢ, ɩɨɥɭɱɟɧɧɵɟ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɤɨɧɬɪɨɥɹ ɫɨɜɨɤɭɩɧɨɫɬɢ ɩɚɪɬɢɢ [3].
36
ǟDzȂǺǻǸǻǰǵȄDzǾǷǵDz ǻǾǺǻǯȈ ǼǻǯȈȅDzǺǵȌ ǺǭDZDzdzǺǻǾǿǵ ǵ ǷǭȄDzǾǿǯǭ ǵǴDZDzǸǵǶ
Ɋɚɫɫɦɨɬɪɢɦ ɩɥɚɧ ɤɨɧɬɪɨɥɹ, ɤɨɝɞɚ ɨɬɤɥɨɧɟɧɧɵɟ ɩɚɪɬɢɢ ɢɡɞɟɥɢɣ ɩɨɞɜɟɪɝɚɸɬɫɹ ɫɩɥɨɲɧɨɦɭ
ɤɨɧɬɪɨɥɸ, ɬ.ɟ. ɤɨɧɬɪɨɥɢɪɭɸɬɫɹ ɜɫɟ ɨɫɬɚɜɲɢɟɫɹ (N – n) ɢɡɞɟɥɢɣ ɩɚɪɬɢɢ, ɚ ɜɵɹɜɥɟɧɧɵɟ ɞɟɮɟɤɬɧɵɟ
ɢɡɞɟɥɢɹ ɡɚɦɟɧɹɸɬɫɹ ɝɨɞɧɵɦɢ. ɉɪɢɦɟɧɟɧɢɟ ɬɚɤɨɝɨ ɩɥɚɧɚ, ɨɱɟɜɢɞɧɨ, ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɩɪɢ ɧɟɪɚɡɪɭɲɚɸɳɟɦ ɤɨɧɬɪɨɥɟ. ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɞɟɮɟɤɬ ɜɨ ɜɪɟɦɹ ɤɨɧɬɪɨɥɹ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɩɭɳɟɧ, ɢ
ɩɨɷɬɨɦɭ ɨɬɤɥɨɧɟɧɧɵɟ ɩɚɪɬɢɢ ɩɨɫɥɟ ɩɪɨɜɟɞɟɧɢɹ ɫɩɥɨɲɧɨɝɨ ɤɨɧɬɪɨɥɹ ɫɨɫɬɨɹɬ ɬɨɥɶɤɨ ɢɡ ɝɨɞɧɵɯ
ɢɡɞɟɥɢɣ.
ɉɭɫɬɶ ɧɚ ɤɨɧɬɪɨɥɶ ɩɨɫɬɭɩɚɸɬ ɩɚɪɬɢɢ ɢɡɞɟɥɢɣ ɫ ɩɨɫɬɨɹɧɧɨɣ ɞɨɥɟɣ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ q.
Ɍɨɝɞɚ ɜ ɫɥɭɱɚɟ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɤɨɧɬɪɨɥɹ ɫ ɜɟɪɨɹɬɧɨɫɬɶɸ Ɋ(q) ɩɚɪɬɢɢ ɢɡɞɟɥɢɣ ɩɪɢɧɢɦɚɸɬɫɹ, ɢ
N n
ɞɨɥɹ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɩɪɢɧɹɬɵɯ ɩɚɪɬɢɹɯ ɪɚɜɧɚ q
, a ɫ ɜɟɪɨɹɬɧɨɫɬɶɸ [1 – Ɋ(q)] ɩɚɪɬɢɢ
N
ɨɬɤɥɨɧɹɸɬɫɹ ɢ ɩɨɞɜɟɪɝɚɸɬɫɹ ɫɩɥɨɲɧɨɦɭ ɤɨɧɬɪɨɥɸ. ɉɨɫɥɟ ɷɬɨɝɨ ɞɨɥɹ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɨɬɤɥɨɧɟɧɧɵɯ ɩɚɪɬɢɹɯ ɪɚɜɧɚ 0.
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɫɪɟɞɧɹɹ ɞɨɥɹ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɩɪɢɧɹɬɵɯ ɩɚɪɬɢɹɯ
qɫɪ
q
N n
N n
P ( q ) 0[1 P ( q)] q
P( q) .
N
N
ȼɟɥɢɱɢɧɭ qɫɪ ɧɚɡɵɜɚɸɬ ɫɪɟɞɧɢɦ ɜɵɯɨɞɧɵɦ ɭɪɨɜɧɟɦ ɞɟɮɟɤɬɧɨɫɬɢ.
ȿɫɥɢ ɨɛɴɟɦ ɜɵɛɨɪɤɢ n ɦɚɥ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɨɛɴɟɦɨɦ ɩɚɪɬɢɢ N, ɬɨ ɦɨɠɧɨ ɩɪɢɧɹɬɶ, ɱɬɨ
qɫɪ | q ˜ P( q) .
ɋɪɟɞɧɢɣ ɜɵɯɨɞɧɨɣ ɭɪɨɜɟɧɶ ɞɟɮɟɤɬɧɨɫɬɢ qɫɪ = 0 ɩɪɢ q = 0 ɢ q = 1, ɬɚɤ ɤɚɤ ɩɪɢ q = 1 ɜɟɪɨɹɬɧɨɫɬɶ Ɋ(q) = 0 ɢ ɜɫɟ ɩɚɪɬɢɢ ɛɭɞɭɬ ɩɨɞɜɟɪɝɚɬɶɫɹ ɫɩɥɨɲɧɨɦɭ ɤɨɧɬɪɨɥɸ ɫ ɡɚɦɟɧɨɣ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɧɚ ɝɨɞɧɵɟ.
Ɍɚɤ ɤɚɤ qɫɪ – ɧɟɨɬɪɢɰɚɬɟɥɶɧɚɹ ɮɭɧɤɰɢɹ ɨɬ q, ɪɚɜɧɚɹ ɧɭɥɸ ɩɪɢ q = 0 ɢ q = 1, ɬɨ ɜɧɭɬɪɢ ɢɧɬɟɪɜɚɥɚ 0 < q < 1 ɫɪɟɞɧɢɣ ɜɵɯɨɞɧɨɣ ɭɪɨɜɟɧɶ ɞɟɮɟɤɬɧɨɫɬɢ ɢɦɟɟɬ ɦɚɤɫɢɦɭɦ qL .
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɞɥɹ ɡɚɞɚɧɧɨɝɨ ɩɥɚɧɚ ɤɨɧɬɪɨɥɹ ɫɪɟɞɧɢɣ ɜɵɯɨɞɧɨɣ ɭɪɨɜɟɧɶ ɞɟɮɟɤɬɧɨɫɬɢ qL
ɧɚɡɵɜɚɸɬ ɩɪɟɞɟɥɨɦ ɫɪɟɞɧɟɝɨ ɜɵɯɨɞɧɨɝɨ ɭɪɨɜɧɹ ɞɟɮɟɤɬɧɨɫɬɢ.
ɇɚ ɩɪɚɤɬɢɤɟ ɱɚɫɬɨ ɞɨɥɹ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɩɚɪɬɢɹɯ ɩɪɨɞɭɤɰɢɢ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ
q1 ( q q1 ) . ȼ ɷɬɢɯ ɫɥɭɱɚɹɯ ɤɚɱɟɫɬɜɨ ɩɪɨɞɭɤɰɢɢ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɨɰɟɧɢɜɚɬɶ ɩɨ ɜɟɥɢɱɢɧɟ qcp,
ɧɚɣɞɟɧɧɨɣ ɞɥɹ ɡɧɚɱɟɧɢɹ ɫɪɟɞɧɟɝɨ ɜɯɨɞɧɨɝɨ ɭɪɨɜɧɹ ɞɟɮɟɤɬɧɨɫɬɢ q [3–5].
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɥɚɧɚ, ɤɨɝɞɚ ɨɬɤɥɨɧɟɧɧɵɟ ɩɚɪɬɢɢ ɢɡɞɟɥɢɣ ɩɨɞɜɟɪɝɚɸɬɫɹ ɫɩɥɨɲɧɨɦɭ
ɤɨɧɬɪɨɥɸ, ɱɢɫɥɨ ɩɪɨɤɨɧɬɪɨɥɢɪɨɜɚɧɧɵɯ ɜ ɩɚɪɬɢɢ ɢɡɞɟɥɢɣ ɟɫɬɶ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ, ɩɪɢɧɢɦɚɸɳɚɹ ɡɧɚɱɟɧɢɟ n ɫ ɜɟɪɨɹɬɧɨɫɬɶɸ Ɋ(q) ɢ ɡɧɚɱɟɧɢɟ N ɫ ɜɟɪɨɹɬɧɨɫɬɶɸ [1 – Ɋ(q)]. ɉɨɷɬɨɦɭ ɫɪɟɞɧɟɟ
ɱɢɫɥɨ ɩɪɨɤɨɧɬɪɨɥɢɪɨɜɚɧɧɵɯ ɢɡɞɟɥɢɣ ɜ ɩɚɪɬɢɢ: nɫɪ n ˜ P( q) N [1 P( q)] (ɪɢɫ. 6).
Ɋɢɫ. 6. Ʌɢɫɬɢɧɝ ɩɪɨɝɪɚɦɦɵ MATLAB ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɫɪɟɞɧɢɯ ɡɧɚɱɟɧɢɣ
ɗɬɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɡɜɨɥɹɸɬ ɨɰɟɧɢɬɶ ɫɪɟɞɧɸɸ ɞɨɥɸ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɩɪɨɞɭɤɰɢɢ
ɩɨɫɥɟ ɤɨɧɬɪɨɥɹ, ɤɚɤɨɜɨ ɛɵ ɧɢ ɛɵɥɨ ɤɚɱɟɫɬɜɨ ɩɨɫɬɭɩɚɸɳɟɣ ɧɚ ɤɨɧɬɪɨɥɶ ɩɪɨɞɭɤɰɢɢ.
2. ɉɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ ɮɭɧɤɰɢɢ ɫɪɟɞɧɟɝɨ ɜɵɯɨɞɧɨɝɨ ɭɪɨɜɧɹ ɞɟɮɟɤɬɧɨɫɬɢ
Ɋɚɫɫɦɨɬɪɢɦ ɩɥɚɧ ɤɨɧɬɪɨɥɹ ɫ ɩɚɪɚɦɟɬɪɚɦɢ N = 200, n = 10 ɢ c = 2, ɤɨɝɞɚ ɨɬɤɥɨɧɟɧɧɵɟ ɩɚɪɬɢɢ
ɩɨɞɜɟɪɝɚɸɬɫɹ ɫɩɥɨɲɧɨɦɭ ɤɨɧɬɪɨɥɸ [11, 12].
Ɍɚɤ ɤɚɤ n < 0,lN, ɬɨ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ qɫɪ(q) ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɛɢɧɨɦɢɚɥɶɧɵɦ ɡɚɤɨɧɨɦ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ. Ɍɨɝɞɚ
qɫɪ
0,95 ˜ P ( q)
0,95q ¦ P10 ( m )
2
m 0
37
0,95q ¦
2
m 0
10 m
m
m
C10 ˜ q (1 q)
.
ǚǭDZDzdzǺǻǾǿȉ ǵ ǷǭȄDzǾǿǯǻ ǾǸǻdzǺȈȂ ǾǵǾǿDzǹ. Ȳ 2 (10), 2015
ɉɨɫɥɟ ɧɟɫɥɨɠɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɢɦ:
qɫɪ
0,95q ˜ (1 q)8 ˜ [(1 q)2 10q(1 q) 45q 2 ] .
Ɋɢɫ. 7. ɋɪɟɞɧɢɣ ɜɵɯɨɞɧɨɝɨ ɭɪɨɜɟɧɶ ɞɟɮɟɤɬɧɨɫɬɢ ɩɥɚɧɚ n = 10 ɢ ɫ = 2
ɉɨɞɫɬɚɜɥɹɹ ɪɚɡɥɢɱɧɵɟ ɡɧɚɱɟɧɢɹ ɫɪɟɞɧɟɝɨ ɜɯɨɞɧɨɝɨ ɭɪɨɜɧɹ ɞɟɮɟɤɬɧɨɫɬɢ q (0 < q < 1), ɩɨɥɭɱɢɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɡɧɚɱɟɧɢɹ qɫɪ. ɇɚ ɪɢɫ. 7 ɩɪɟɞɫɬɚɜɥɟɧ ɝɪɚɮɢɤ ɮɭɧɤɰɢɢ ɫɪɟɞɧɟɝɨ ɜɵɯɨɞɧɨɝɨ
ɭɪɨɜɧɹ ɞɟɮɟɤɬɧɨɫɬɢ qɫɪ. ɂɡ ɪɢɫɭɧɤɚ ɜɢɞɧɨ, ɱɬɨ ɩɪɢ q = q1 = 0,29 ɮɭɧɤɰɢɹ qcp ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɭɦɚ
qL = 0,19. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɩɥɚɧɚ ɤɨɧɬɪɨɥɹ ɫ ɪɚɡɛɪɚɤɨɜɤɨɣ ɩɪɢ n = 10 ɢ ɫ = 2 ɫɪɟɞɧɹɹ ɞɨɥɹ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɜ ɩɪɨɞɭɤɰɢɢ ɩɨɫɥɟ ɤɨɧɬɪɨɥɹ ɧɟ ɩɪɟɜɵɫɢɬ qL = 0,19, ɤɚɤɨɜɨ ɛɵ ɧɢ ɛɵɥɨ ɤɚɱɟɫɬɜɨ
(q) ɩɨɫɬɭɩɚɸɳɟɣ ɧɚ ɤɨɧɬɪɨɥɶ ɩɪɨɞɭɤɰɢɢ.
3. ɉɨɫɬɪɨɟɧɢɟ ɩɥɚɧɚ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɤɨɧɬɪɨɥɹ
ɉɪɢ ɪɚɡɪɚɛɨɬɤɟ ɩɥɚɧɚ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɜɵɛɨɪɨɱɧɨɝɨ ɤɨɧɬɪɨɥɹ ɩɪɢ ɩɪɢɟɦɤɟ ɜɨɫɩɨɥɶɡɭɟɦɫɹ
ɡɚɤɨɧɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɉɭɚɫɫɨɧɚ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɉɭɚɫɫɨɧɚ ɩɪɢɛɥɢɠɚɟɬɫɹ ɤ ɛɢɧɨɦɢɚɥɶɧɨɦɭ ɩɪɢ ɪ' < 0,10 ɢ ɩɪ' < 5. ɗɬɨ ɩɪɢɛɥɢɠɟɧɢɟ ɥɨɝɢɱɟɫɤɢ ɜɩɨɥɧɟ ɨɩɪɚɜɞɚɧɨ, ɬɚɤ ɤɚɤ ɩɪɢ ɜɵɛɨɪɨɱɧɨɦ ɢɡɭɱɟɧɢɢ ɤɚɱɟɫɬɜɟɧɧɵɯ ɩɪɢɡɧɚɤɨɜ, ɩɪɢ ɤɨɬɨɪɨɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɨɰɟɧɬ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ, ɤɚɤ ɩɪɚɜɢɥɨ, ɦɵ ɢɦɟɟɦ ɞɟɥɨ ɢɦɟɧɧɨ ɫ ɛɢɧɨɦɢɚɥɶɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ [2].
Ɉɞɢɧ ɢɡ ɩɥɚɧɨɜ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɜɵɛɨɪɨɱɧɨɝɨ ɤɨɧɬɪɨɥɹ ɩɨ ɚɥɶɬɟɪɧɚɬɢɜɧɨɦɭ ɩɪɢɡɧɚɤɭ ɩɨ
ɩɪɨɰɟɧɬɭ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ, ɩɪɢɜɟɞɟɧɧɵɣ ɜ ɚɦɟɪɢɤɚɧɫɤɨɦ ɜɨɟɧɧɨɦ ɫɬɚɧɞɚɪɬɟ 105, ɞɚɟɬ ɩ = 300
ɢ ɫ = 5, ɝɞɟ ɩ – ɨɛɴɟɦ ɜɵɛɨɪɤɢ, ɚ ɫ – ɩɪɢɟɦɨɱɧɨɟ ɱɢɫɥɨ. ɗɬɨɬ ɩɥɚɧ ɜ ɨɫɧɨɜɧɨɦ ɫɜɨɞɢɬɫɹ ɤ ɫɥɟɞɭɸɳɟɦɭ: ɢɡɜɥɟɱɶ ɞɥɹ ɩɪɨɜɟɪɤɢ ɩɪɟɞɫɬɚɜɢɬɟɥɶɧɭɸ ɜɵɛɨɪɤɭ ɨɛɴɟɦɨɦ 300 ɢɡɞɟɥɢɣ, ɩɪɢɧɹɬɶ ɩɚɪɬɢɸ,
ɟɫɥɢ ɜ ɜɵɛɨɪɤɟ ɨɤɚɠɟɬɫɹ ɩɹɬɶ ɢɥɢ ɦɟɧɟɟ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ, ɢ ɨɬɤɥɨɧɢɬɶ ɟɟ, ɟɫɥɢ ɢɯ ɛɭɞɟɬ ɛɨɥɶɲɟ ɩɹɬɢ. Ɋɟɲɟɧɢɟ ɩɪɢɧɹɬɶ ɢɥɢ ɨɬɤɥɨɧɢɬɶ ɩɚɪɬɢɸ ɨɫɧɨɜɵɜɚɟɬɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɧɚ ɪɟɡɭɥɶɬɚɬɚɯ
ɬɚɤɨɣ ɨɞɧɨɤɪɚɬɧɨɣ ɜɵɛɨɪɤɢ.
ɑɟɦɭ ɪɚɜɧɚ ɜɟɥɢɱɢɧɚ ɪɢɫɤɚ, ɫ ɤɨɬɨɪɵɦ ɫɜɹɡɚɧɨ ɩɪɢɦɟɧɟɧɢɟ ɷɬɨɝɨ ɩɥɚɧɚ ɞɥɹ ɩɨɫɬɚɜɳɢɤɚ ɢ
ɞɥɹ ɩɨɬɪɟɛɢɬɟɥɹ?
ȼɟɥɢɱɢɧɭ ɪɢɫɤɚ ɱɚɳɟ ɜɫɟɝɨ ɝɪɚɮɢɱɟɫɤɢ ɢɡɨɛɪɚɠɚɸɬ ɤɪɢɜɨɣ, ɤɨɬɨɪɭɸ ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ
ɤɪɢɜɨɣ ɨɩɟɪɚɬɢɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɥɚɧɚ ɜɵɛɨɪɨɱɧɨɝɨ ɤɨɧɬɪɨɥɹ (ɫɨɤɪɚɳɟɧɧɨ ɤɪɢɜɚɹ Ɉɋ).
38
ǟDzȂǺǻǸǻǰǵȄDzǾǷǵDz ǻǾǺǻǯȈ ǼǻǯȈȅDzǺǵȌ ǺǭDZDzdzǺǻǾǿǵ ǵ ǷǭȄDzǾǿǯǭ ǵǴDZDzǸǵǶ
Ʉɪɢɜɚɹ ɨɩɟɪɚɬɢɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɜɵɛɨɪɨɱɧɨɝɨ ɤɨɧɬɪɨɥɹ ɫɬɪɨɢɬɫɹ
ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
1. ɉɪɨɫɬɚɜɢɬɶ ɧɚɡɜɚɧɢɹ ɫɬɨɥɛɰɨɜ ɬɚɛɥɢɰɵ ɢ ɡɧɚɱɟɧɢɹ ɫɬɨɥɛɰɚ Ɋɚ.
Ɍɚɛɥɢɰɚ 1
Ⱦɚɧɧɵɟ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɨɩɟɪɚɬɢɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ.
n
nɪ'
ɪ'
Ɋɚ
Ɋɚɪ'
ȼ ɬɚɛɥ. 1: n – ɨɛɴɟɦ ɜɵɛɨɪɤɢ; ɩɪ' – ɱɢɫɥɨ, ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ; ɪ'– ɞɨɥɹ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ;
Ɋɚ – ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɢɧɹɬɢɹ ɩɚɪɬɢɢ; Ɋɚ ɪ' – ɫɪɟɞɧɟɟ ɜɵɯɨɞɧɨɟ ɤɚɱɟɫɬɜɨ (AOQ).
ɉɪɢɧɹɬɵɟ ɡɧɚɱɟɧɢɹ Ɋɚ ɞɚɞɭɬ ɡɧɚɱɟɧɢɹ ɞɥɹ ɨɫɢ ɨɪɞɢɧɚɬ; ɢɦ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɧɚ ɨɫɢ ɚɛɫɰɢɫɫ
ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɡɧɚɱɟɧɢɹ ɪ', ɩɨɫɥɟ ɬɨɝɨ ɤɚɤ ɨɧɢ ɛɭɞɭɬ ɩɨɥɭɱɟɧɵ, ɚ ɡɚɬɟɦ ɫɬɪɨɢɬɫɹ ɤɪɢɜɚɹ ɨɩɟɪɚɬɢɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (Ɉɋ).
2. ɇɚɣɬɢ ɡɚɞɚɧɧɨɟ ɡɧɚɱɟɧɢɟ Ɋɚ ɞɥɹ ɞɚɧɧɨɝɨ ɩɪɢɟɦɨɱɧɨɝɨ ɱɢɫɥɚ ɫ (ɢɥɢ ɛɥɢɠɚɣɲɟɟ ɤ ɧɟɦɭ).
(ȼ ɩɨɫɥɟɞɧɟɦ ɫɥɭɱɚɟ ɫɥɟɞɭɟɬ ɡɚɦɟɧɢɬɶ ɨɬɫɭɬɫɬɜɭɸɳɟɟ ɡɧɚɱɟɧɢɟ Ɋɚ ɛɥɢɠɚɣɲɢɦ ɤ ɧɟɦɭ ɡɧɚɱɟɧɢɟɦ,
ɜɧɟɫɹ ɢɫɩɪɚɜɥɟɧɢɟ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɫɬɨɥɛɟɰ ɫɨɫɬɚɜɥɹɟɦɨɣ ɬɚɛɥɢɰɵ).
3. ɉɪɨɫɬɚɜɢɬɶ ɡɧɚɱɟɧɢɟ ɩɪ', ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɞɚɧɧɨɦɭ ɡɧɚɱɟɧɢɸ Ɋɚ, ɜ ɫɬɨɥɛɰɟ ɩɪ'.
4. Ɋɚɡɞɟɥɢɬɶ ɷɬɨ ɡɧɚɱɟɧɢɟ ɩɪ’ ɧɚ ɩ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɚɟɦ ɡɧɚɱɟɧɢɟ ɪ', ɤɨɬɨɪɨɟ ɛɭɞɟɬ ɩɨɫɬɚɜɥɟɧɨ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɞɚɧɧɨɦɭ Ɋɚ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɤɪɢɜɨɣ ɨɩɟɪɚɬɢɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (Ɉɋ).
4. Ⱥɧɚɥɢɡ ɤɪɢɜɨɣ ɫɪɟɞɧɟɝɨ ɜɵɯɨɞɧɨɝɨ ɭɪɨɜɧɹ ɞɟɮɟɤɬɧɨɫɬɢ
ɋɪɟɞɧɢɣ ɜɵɯɨɞɧɨɣ ɭɪɨɜɟɧɶ ɞɟɮɟɤɬɧɨɫɬɢ ɹɜɥɹɟɬɫɹ ɜɚɠɧɵɦ ɩɨɤɚɡɚɬɟɥɟɦ ɞɥɹ ɩɨɬɪɟɛɢɬɟɥɹ,
ɬɚɤ ɤɚɤ ɟɝɨ ɜɟɥɢɱɢɧɚ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɪɟɚɥɶɧɨɟ ɤɚɱɟɫɬɜɨ ɩɪɨɞɭɤɰɢɢ, ɤɨɬɨɪɭɸ ɨɧ ɩɨɥɭɱɢɬ ɩɨɫɥɟ ɩɪɨɜɟɪɤɢ [13–16]. ɉɪɟɞɭɫɦɚɬɪɢɜɚɟɦɵɟ ɩɥɚɧɨɦ ɤɨɧɬɪɨɥɹ ɦɟɪɵ ɩɨ ɡɚɦɟɧɟ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɝɨɞɧɵɦɢ ɧɚɩɪɚɜɥɟɧɵ ɧɚ ɬɨ, ɱɬɨɛɵ ɫɪɟɞɧɢɣ ɜɵɯɨɞɧɨɣ ɭɪɨɜɟɧɶ ɞɟɮɟɤɬɧɨɫɬɢ ɛɵɥ ɥɭɱɲɟ ɢɥɢ, ɩɨ ɤɪɚɣɧɟɣ
ɦɟɪɟ, ɧɟ ɯɭɠɟ ɜɯɨɞɧɨɝɨ ɭɪɨɜɧɹ ɞɟɮɟɤɬɧɨɫɬɢ.
ȼɨ-ɩɟɪɜɵɯ, ɩɪɢ ɜɯɨɞɧɨɦ ɭɪɨɜɧɟ ɞɟɮɟɤɬɧɨɫɬɢ ɫ ɧɭɥɟɜɵɦ ɱɢɫɥɨɦ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ ɫɪɟɞɧɢɣ
ɜɵɯɨɞɧɨɣ ɭɪɨɜɟɧɶ ɞɟɮɟɤɬɧɨɫɬɢ ɛɭɞɟɬ ɬɚɤɠɟ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶɫɹ ɧɭɥɟɜɵɦ ɩɪɨɰɟɧɬɨɦ ɛɪɚɤɚ [2–6].
ȼɨ-ɜɬɨɪɵɯ, ɟɫɥɢ ɜɡɹɬɶ ɞɪɭɝɭɸ ɤɪɚɣɧɨɫɬɶ, ɧɚɩɪɢɦɟɪ, ɢɫɯɨɞɢɬɶ ɢɡ ɜɯɨɞɧɨɝɨ ɤɚɱɟɫɬɜɚ ɫ 10 %
ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ, ɬɨ ɫɪɟɞɧɢɣ ɜɵɯɨɞɧɨɣ ɭɪɨɜɟɧɶ ɞɟɮɟɤɬɧɨɫɬɢ ɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɛɭɞɟɬ ɩɪɚɤɬɢɱɟɫɤɢ ɫɬɨɩɪɨɰɟɧɬɧɵɦ, ɬɚɤ ɤɚɤ ɩɚɪɬɢɢ, ɤɚɱɟɫɬɜɨ ɤɨɬɨɪɵɯ ɨɤɚɠɟɬɫɹ ɧɢɠɟ ɩɪɢɟɦɥɟɦɨɝɨ, ɞɨɥɠɧɵ ɛɵɬɶ
ɢɫɩɪɚɜɥɟɧɵ. ȼɫɟ ɩɚɪɬɢɢ, ɫɨɞɟɪɠɚɳɢɟ 10 % ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ, ɛɭɞɭɬ ɨɬɤɥɨɧɟɧɵ ɢ ɩɨɞɜɟɪɝɧɭɬɵ
ɫɩɥɨɲɧɨɣ ɩɪɨɜɟɪɤɟ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɬɨɪɨɣ ɩɪɨɰɟɧɬ ɞɟɮɟɤɬɧɵɯ ɢɡɞɟɥɢɣ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣ ɫɪɟɞɧɟɟ
ɜɵɯɨɞɧɨɟ ɤɚɱɟɫɬɜɨ, ɛɭɞɟɬ ɪɚɜɟɧ ɧɭɥɸ. Ɇɟɠɞɭ ɷɬɢɦɢ ɞɜɭɦɹ ɤɪɚɣɧɢɦɢ ɬɨɱɤɚɦɢ ɪɚɫɩɨɥɨɠɟɧɵ ɪɚɡɥɢɱɧɵɟ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɡɧɚɱɟɧɢɹ ɜɵɯɨɞɧɨɝɨ ɭɪɨɜɧɹ ɞɟɮɟɤɬɧɨɫɬɢ.
Ɂɚɤɥɸɱɟɧɢɟ
ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɩɪɢɜɟɞɟɧɵ ɪɟɤɨɦɟɧɞɚɰɢɢ ɩɨ ɨɰɟɧɤɟ ɩɚɪɚɦɟɬɪɨɜ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɤɨɧɬɪɨɥɹ ɤɚɱɟɫɬɜɚ ɜ ɫɪɟɞɟ MatLab. ɉɪɚɤɬɢɱɟɫɤɚɹ ɰɟɧɧɨɫɬɶ ɪɚɛɨɬɵ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɩɪɨɜɟɞɟɧɧɵɣ
ɚɧɚɥɢɡ ɫɢɫɬɟɦ ɫɬɚɬɢɫɬɢɱɟɫɤɨɝɨ ɤɨɧɬɪɨɥɹ ɢ ɩɪɟɞɥɨɠɟɧɧɵɣ ɢɧɫɬɪɭɦɟɧɬɚɪɢɣ ɜ ɫɪɟɞɟ MATLAB ɩɨɡɜɨɥɹɟɬ ɫɞɟɥɚɬɶ ɚɪɝɭɦɟɧɬɢɪɨɜɚɧɧɵɣ ɜɵɛɨɪ ɧɟɨɛɯɨɞɢɦɵɯ ɦɟɬɨɞɢɤ ɨɰɟɧɤɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɟɲɚɟɦɵɯ ɡɚɞɚɱ ɧɚ ɩɪɟɞɩɪɢɹɬɢɢ ɢ ɧɟɨɛɯɨɞɢɦɨɝɨ ɧɚɛɨɪɚ ɮɭɧɤɰɢɣ ɬɪɟɛɭɟɦɨɣ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɤɚɱɟɫɬɜɚ.
ȼɨɩɪɨɫɵ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɚɧɚɥɢɡɚ ɜ ɫɪɟɞɟ MATLAB ɩɨ ɨɫɬɚɥɶɧɵɦ ɜɢɞɚɦ ɫɬɚɬɢɫɬɢɱɟɫɤɨɝɨ
ɤɨɧɬɪɨɥɹ ɜ ɫɪɟɞɟ MatLab ɛɭɞɭɬ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɫɥɟɞɭɸɳɢɯ ɫɬɚɬɶɹɯ ɰɢɤɥɚ.
ɋɩɢɫɨɤ ɥɢɬɟɪɚɬɭɪɵ
1.
Ʉɨɧɫɬɪɭɤɬɨɪɫɤɨ-ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɟ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɷɥɟɤɬɪɨɧɧɵɯ ɫɪɟɞɫɬɜ / Ʉ. ɂ. Ȼɢɥɢɛɢɧ, Ⱥ. ɂ. ȼɥɚɫɨɜ,
Ʌ. ȼ. ɀɭɪɚɜɥɟɜɚ ɢ ɞɪ. ; ɩɨɞ ɨɛɳ. ɪɟɞ. ȼ. Ⱥ. ɒɚɯɧɨɜɚ. – Ɇ. : ɂɡɞ-ɜɨ ɆȽɌɍ ɢɦ. ɇ. ɗ. Ȼɚɭɦɚɧɚ, 2005. –
568 ɫ.
39
ǚǭDZDzdzǺǻǾǿȉ ǵ ǷǭȄDzǾǿǯǻ ǾǸǻdzǺȈȂ ǾǵǾǿDzǹ. Ȳ 2 (10), 2015
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Ɇɚɪɤɟɥɨɜ, ȼ. ȼ. Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɦɟɬɨɞɨɜ ɜɯɨɞɧɨɝɨ ɫɬɚɬɢɫɬɢɱɟɫɤɨɝɨ ɤɨɧɬɪɨɥɹ ɩɪɢ ɭɩɪɚɜɥɟɧɢɢ ɤɚɱɟɫɬɜɨɦ ɢɡɞɟɥɢɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɯɧɢɤɢ ɜ ɫɪɟɞɟ MATLAB / ȼ. ȼ. Ɇɚɪɤɟɥɨɜ, Ⱥ. ɂ. ȼɥɚɫɨɜ, Ⱦ. ȿ. Ɂɨɬɶɟɜɚ //
ɇɚɞɟɠɧɨɫɬɶ ɢ ɤɚɱɟɫɬɜɨ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ. – 2014. – ʋ 3. – ɋ. 38–44.
ɏɷɧɫɟɧ, Ȼ. Ʌ. Ʉɨɧɬɪɨɥɶ ɤɚɱɟɫɬɜɚ. Ɍɟɨɪɢɹ ɢ ɩɪɢɦɟɧɟɧɢɟ : ɩɟɪ. ɫ ɚɧɝɥ. / Ȼ. Ʌ. ɏɷɧɫɟɧ. – Ɇ. : ɉɪɨɝɪɟɫɫ,
1968. – 257 ɫ.
ɇɨɭɥɟɪ, Ʌ. ɋɬɚɬɢɫɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɤɨɧɬɪɨɥɹ ɤɚɱɟɫɬɜɚ ɩɪɨɞɭɤɰɢɢ : ɩɟɪ. ɫ ɚɧɝɥ. / Ʌ. ɇɨɭɥɟɪ. – Ɇ. :
ɂɡɞ-ɜɨ ɫɬɚɧɞɚɪɬɨɜ, 1989. – 96 ɫ.
ɍɩɪɚɜɥɟɧɢɟ ɤɚɱɟɫɬɜɨɦ ɷɥɟɤɬɪɨɧɧɵɯ ɫɪɟɞɫɬɜ : ɭɱɟɛ. ɞɥɹ ɜɭɡɨɜ / Ɉ. ɉ. Ƚɥɭɞɤɢɧ ɢ ɞɪ. – Ɇ. : ȼɵɫɲɚɹ ɲɤɨɥɚ, 1999. – 414 ɫ.
Ƚɥɭɞɤɢɧ, Ɉ. ɉ. ȼɫɟɨɛɳɟɟ ɭɩɪɚɜɥɟɧɢɟ ɤɚɱɟɫɬɜɨɦ : ɭɱɟɛ. ɞɥɹ ɜɭɡɨɜ / Ɉ. ɉ. Ƚɥɭɞɤɢɧ. – Ɇ. : Ɋɚɞɢɨ ɢ ɫɜɹɡɶ,
1999. – 179 ɫ.
Ɇɚɪɤɟɥɨɜ, ȼ. ȼ. ɋɢɫɬɟɦɧɵɣ ɚɧɚɥɢɡ ɩɪɨɰɟɫɫɚ ɭɩɪɚɜɥɟɧɢɹ ɤɚɱɟɫɬɜɨɦ ɢɡɞɟɥɢɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɯɧɢɤɢ /
ȼ. ȼ. Ɇɚɪɤɟɥɨɜ, Ⱥ. ɂ. ȼɥɚɫɨɜ, ɗ. ɇ. Ʉɚɦɵɲɧɚɹ // ɇɚɞɟɠɧɨɫɬɶ ɢ ɤɚɱɟɫɬɜɨ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ. – 2014. –
ʋ 1. – ɋ. 35–43.
Ɇɚɪɤɟɥɨɜ, ȼ. ȼ. ɍɩɪɚɜɥɟɧɢɟ ɢ ɤɨɧɬɪɨɥɶ ɤɚɱɟɫɬɜɚ ɢɡɞɟɥɢɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɯɧɢɤɢ. ɋɟɦɶ ɨɫɧɨɜɧɵɯ ɢɧɫɬɪɭɦɟɧɬɨɜ ɫɢɫɬɟɦɧɨɝɨ ɚɧɚɥɢɡɚ ɩɪɢ ɭɩɪɚɜɥɟɧɢɢ ɤɚɱɟɫɬɜɨɦ ɢɡɞɟɥɢɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɯɧɢɤɢ / ȼ. ȼ. Ɇɚɪɤɟɥɨɜ, Ⱥ. ɂ. ȼɥɚɫɨɜ, Ⱦ. ȿ. Ɂɨɬɶɟɜɚ // Ⱦɚɬɱɢɤɢ ɢ ɫɢɫɬɟɦɵ. – 2014. – ʋ 8. – ɋ. 55–67.
ȼɥɚɫɨɜ, Ⱥ. ɂ. ȼɢɡɭɚɥɶɧɵɟ ɦɨɞɟɥɢ ɭɩɪɚɜɥɟɧɢɹ ɤɚɱɟɫɬɜɨɦ ɧɚ ɩɪɟɞɩɪɢɹɬɢɹɯ ɷɥɟɤɬɪɨɧɢɤɢ / Ⱥ. ɂ. ȼɥɚɫɨɜ,
Ⱥ. M. ɂɜɚɧɨɜ // ɇɚɭɤɚ ɢ ɨɛɪɚɡɨɜɚɧɢɟ. – 2011. – ʋ 11. – ɋ. 34–36.
ɋɨɜɪɟɦɟɧɧɵɟ ɦɟɬɨɞɵ ɢ ɫɪɟɞɫɬɜɚ ɨɛɟɫɩɟɱɟɧɢɹ ɤɚɱɟɫɬɜɚ ɜ ɭɫɥɨɜɢɹɯ ɤɨɦɩɥɟɤɫɧɨɣ ɚɜɬɨɦɚɬɢɡɚɰɢɢ /
ȼ. Ƚ. Ⱦɭɞɤɨ, Ʉ. Ⱦ. ȼɟɪɟɣɧɨɜ, Ⱥ. ɂ. ȼɥɚɫɨɜ, Ⱥ. Ƚ. Ɍɢɦɨɲɤɢɧ // ȼɨɩɪɨɫɵ ɪɚɞɢɨɷɥɟɤɬɪɨɧɢɤɢ. ɋɟɪ.
ȺɋɍɉɊ. – 1996. – ʋ 2. – ɋ. 54–72.
ȿɥɚɧɰɟɜ, Ⱥ. ȼ. Ⱥɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɣ ɤɨɧɬɪɨɥɶ ɢ ɢɫɩɵɬɚɧɢɹ ɷɥɟɤɬɪɨɧɧɨɣ ɚɩɩɚɪɚɬɭɪɵ / Ⱥ. ȼ. ȿɥɚɧɰɟɜ,
ȼ. ȼ. Ɇɚɪɤɟɥɨɜ. – Ɇ. : ɂɡɞ-ɜɨ ɆȽɌɍ, 1990. – 51 ɫ.
ȼɥɚɫɨɜ, Ⱥ. ɂ. ɋɢɫɬɟɦɧɵɣ ɚɧɚɥɢɡ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɩɪɨɢɡɜɨɞɫɬɜɚ ɫɥɨɠɧɵɯ ɬɟɯɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɜɢɡɭɚɥɶɧɵɯ ɦɨɞɟɥɟɣ / Ⱥ. ɂ. ȼɥɚɫɨɜ // Ɇɟɠɞɭɧɚɪɨɞɧɵɣ ɧɚɭɱɧɨɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɣ ɠɭɪɧɚɥ. – 2013. – ʋ 10, ɱ. 2. – ɋ. 17–26.
Ⱥɞɚɦɨɜɚ, Ⱥ. Ⱥ. Ɇɟɬɨɞɨɥɨɝɢɱɟɫɤɢɟ ɨɫɧɨɜɵ ɨɛɟɫɩɟɱɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɧɨɫɬɢ ɷɥɟɤɬɪɨɧɧɵɯ ɫɪɟɞɫɬɜ /
Ⱥ. Ⱥ. Ⱥɞɚɦɨɜɚ, Ⱥ. ɉ. Ⱥɞɚɦɨɜ, Ƚ. ɏ. ɂɪɡɚɟɜ. – ɋɉɛ. : ɉɨɥɢɬɟɯɧɢɤɚ, 2008. – 258 ɫ.
Ȼɚɪɚɧɨɜ, ɇ. Ⱥ. ɍɩɪɚɜɥɟɧɢɟ ɫɨɫɬɨɹɧɢɟɦ ɝɨɬɨɜɧɨɫɬɢ ɫɢɫɬɟɦɵ ɛɟɡɨɩɚɫɧɨɫɬɢ ɤ ɨɬɪɚɠɟɧɢɸ ɭɝɪɨɡɵ /
ɇ. Ⱥ. Ȼɚɪɚɧɨɜ, ɇ. Ⱥ. ɋɟɜɟɪɰɟɜ // Ɍɪɭɞɵ ɦɟɠɞɭɧɚɪɨɞɧɨɝɨ ɫɢɦɩɨɡɢɭɦɚ ɇɚɞɟɠɧɨɫɬɶ ɢ ɤɚɱɟɫɬɜɨ. – 2012. –
Ɍ. 1. – ɋ. 8–10.
Ⱦɟɞɤɨɜ, ȼ. Ʉ. Ʉɨɦɩɶɸɬɟɪɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɧɚɞɟɠɧɨɫɬɢ ɧɟɫɬɚɪɟɸɳɢɯ ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɦɵɯ ɨɛɴɟɤɬɨɜ / ȼ. Ʉ. Ⱦɟɞɤɨɜ, ɇ. Ⱥ. ɋɟɜɟɪɰɟɜ // Ɍɪɭɞɵ ɦɟɠɞɭɧɚɪɨɞɧɨɝɨ ɫɢɦɩɨɡɢɭɦɚ ɇɚɞɟɠɧɨɫɬɶ ɢ ɤɚɱɟɫɬɜɨ. – 2010. – Ɍ. 1. – ɋ. 368–370.
ɘɪɤɨɜ, ɇ. Ʉ. Ɍɟɯɧɨɥɨɝɢɹ ɩɪɨɢɡɜɨɞɫɬɜɨ ɷɥɟɤɬɪɨɧɧɵɯ ɫɪɟɞɫɬɜ : ɭɱɟɛ. / ɇ. Ʉ. ɘɪɤɨɜ. – Ɇ. : Ʌɚɧɶ, 2014. –
480 ɫ.
Ɇɚɪɤɟɥɨɜ ȼɢɤɬɨɪ ȼɚɫɢɥɶɟɜɢɱ
ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɞɨɰɟɧɬ,
ɤɚɮɟɞɪɚ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢ ɬɟɯɧɨɥɨɝɢɢ ɩɪɨɢɡɜɨɞɫɬɜɚ
ɪɚɞɢɨɷɥɟɤɬɪɨɧɧɨɣ ɚɩɩɚɪɚɬɭɪɵ,
Ɇɨɫɤɨɜɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ
ɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ ɢɦ. ɇ. ɗ. Ȼɚɭɦɚɧɚ
(105005, Ɋɨɫɫɢɹ, Ɇɨɫɤɜɚ, 2-ɹ Ȼɚɭɦɚɧɫɤɚɹ ɭɥ., 5, ɫɬɪ. 1)
8-(499)-263-62-26
E-mail: info@iu4.bmstu.ru
Markelov Viktor Vasil'evich
candidate of technical sciences, associate professor,
sub-department of engineering and manufacturing
technology of radio-electronic equipment,
Moscow State Technical University
named after N. A. Bauman
(105005, page 1, 5, 2-ya Baumanskaya street,
Moscow, Russia)
ȼɥɚɫɨɜ Ⱥɧɞɪɟɣ ɂɝɨɪɟɜɢɱ
ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɞɨɰɟɧɬ,
ɤɚɮɟɞɪɚ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢ ɬɟɯɧɨɥɨɝɢɢ ɩɪɨɢɡɜɨɞɫɬɜɚ
ɪɚɞɢɨɷɥɟɤɬɪɨɧɧɨɣ ɚɩɩɚɪɚɬɭɪɵ,
Ɇɨɫɤɨɜɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ
ɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ ɢɦ. ɇ. ɗ. Ȼɚɭɦɚɧɚ
(105005, Ɋɨɫɫɢɹ, Ɇɨɫɤɜɚ, 2-ɹ Ȼɚɭɦɚɧɫɤɚɹ ɭɥ., 5, ɫɬɪ. 1)
8-(499)-263-62-26
E-mail: vlasov@iu4.ru
Vlasov Andrey Igorevich
candidate of technical sciences, associate professor,
sub-department of engineering and manufacturing
technology of radio-electronic equipment,
Moscow State Technical University
named after N. A. Bauman
(105005, page 1, 5, 2-ya Baumanskaya street,
Moscow, Russia)
40
ǟDzȂǺǻǸǻǰǵȄDzǾǷǵDz ǻǾǺǻǯȈ ǼǻǯȈȅDzǺǵȌ ǺǭDZDzdzǺǻǾǿǵ ǵ ǷǭȄDzǾǿǯǭ ǵǴDZDzǸǵǶ
Ɂɨɬɶɟɜɚ Ⱦɚɪɶɹ ȿɜɝɟɧɶɟɜɧɚ
ɫɬɭɞɟɧɬɤɚ,
ɤɚɮɟɞɪɚ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɢ ɬɟɯɧɨɥɨɝɢɢ ɩɪɨɢɡɜɨɞɫɬɜɚ
ɪɚɞɢɨɷɥɟɤɬɪɨɧɧɨɣ ɚɩɩɚɪɚɬɭɪɵ,
Ɇɨɫɤɨɜɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ
ɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ ɢɦ. ɇ. ɗ. Ȼɚɭɦɚɧɚ,
(105005, Ɋɨɫɫɢɹ, Ɇɨɫɤɜɚ, 2-ɹ Ȼɚɭɦɚɧɫɤɚɹ ɭɥ., 5, ɫɬɪ. 1)
8-(499)-263-65-53
E-mail: maxaonk@ya.ru
Zot'eva Dar'ya Evgen'evna
student,
sub-department of engineering and manufacturing
technology of radio-electronic equipment,
Moscow State Technical University
named after N. A. Bauman,
(105005, page 1, 5, 2-ya Baumanskaya street,
Moscow, Russia)
Ⱥɧɧɨɬɚɰɢɹ. ɉɪɨɚɧɚɥɢɡɢɪɨɜɚɧɵ ɜɨɡɦɨɠɧɨɫɬɢ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɦɟɬɨɞɨɜ ɜɯɨɞɧɨɝɨ ɫɬɚɬɢɫɬɢɱɟɫɤɨɝɨ ɤɨɧɬɪɨɥɹ ɩɪɢ ɭɩɪɚɜɥɟɧɢɢ ɤɚɱɟɫɬɜɨɦ ɢɡɞɟɥɢɣ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɯɧɢɤɢ ɜ ɫɪɟɞɟ MATLAB. Ⱦɚɧɧɚɹ ɪɚɛɨɬɚ ɩɨɫɜɹɳɟɧɚ ɢɫɫɥɟɞɨɜɚɧɢɸ ɦɟɬɨɞɨɜ ɫɬɚɬɢɫɬɢɱɟɫɤɨɝɨ
ɤɨɧɬɪɨɥɹ ɩɨ ɚɥɶɬɟɪɧɚɬɢɜɧɨɦɭ ɩɪɢɡɧɚɤɭ. ɂɫɫɥɟɞɨɜɚɧɵ ɨɞɧɨɫɬɭɩɟɧɱɚɬɵɣ, ɞɜɭɯɫɬɭɩɟɧɱɚɬɵɣ, ɦɧɨɝɨɫɬɭɩɟɧɱɚɬɵɣ ɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ ɤɨɧɬɪɨɥɢ. Ɉɫɧɨɜɧɨɟ
ɜɧɢɦɚɧɢɟ ɭɞɟɥɟɧɨ ɦɟɬɨɞɢɤɚɦ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɤɨɧɬɪɨɥɹ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɢɧɫɬɪɭɦɟɧɬɵ ɜ ɫɪɟɞɟ MATLAB
ɞɥɹ ɨɛɪɚɛɨɬɤɢ ɪɟɡɭɥɶɬɚɬɨɜ ɫɬɚɬɢɫɬɢɱɟɫɤɨɝɨ ɤɨɧɬɪɨɥɹ.
Abstract. The paper presents a single-stage control automation techniques in the management of quality electronic products in the environment MATLAB. This
work is devoted to a single-stage statistical control by
attributes. Tools presented in MATLAB environment
for obtaining and processing the results of a singlestage control. Considered a single-stage plan for the
control and the curve average output level of defects.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɨɞɧɨɫɬɭɩɟɧɱɚɬɵɣ ɤɨɧɬɪɨɥɶ, ɭɩɪɚɜɥɟɧɢɟ ɤɚɱɟɫɬɜɨɦ, ɷɥɟɤɬɪɨɧɧɚɹ ɚɩɩɚɪɚɬɭɪɚ, MATLAB.
Key words: input control, quality management, electronic equipment, MATLAB.
ɍȾɄ 681.321
Ɇɚɪɤɟɥɨɜ, ȼ. ȼ.
Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɝɨ ɤɨɧɬɪɨɥɹ ɤɚɱɟɫɬɜɚ ɜ ɫɪɟɞɟ MATLAB / ȼ. ȼ. Ɇɚɪɤɟɥɨɜ,
Ⱥ. ɂ. ȼɥɚɫɨɜ, Ⱦ. ȿ. Ɂɨɬɶɟɜɚ // ɇɚɞɟɠɧɨɫɬɶ ɢ ɤɚɱɟɫɬɜɨ ɫɥɨɠɧɵɯ ɫɢɫɬɟɦ. – 2015. – ʋ 2 (10). – ɋ. 34–41.
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