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Построение математической модели процессов технической эксплуатации авиационной техники как замкнутой системы массового обслуживания.

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2015
ɇȺɍɑɇɕɃ ȼȿɋɌɇɂɄ ɆȽɌɍ ȽȺ
ʋ 219
ɍȾɄ 629.735.017.85
ɉɈɋɌɊɈȿɇɂȿ ɆȺɌȿɆȺɌɂɑȿɋɄɈɃ ɆɈȾȿɅɂ ɉɊɈɐȿɋɋɈȼ
ɌȿɏɇɂɑȿɋɄɈɃ ɗɄɋɉɅɍȺɌȺɐɂɂ ȺȼɂȺɐɂɈɇɇɈɃ ɌȿɏɇɂɄɂ
ɄȺɄ ɁȺɆɄɇɍɌɈɃ ɋɂɋɌȿɆɕ ɆȺɋɋɈȼɈȽɈ ɈȻɋɅɍɀɂȼȺɇɂə
Ⱥ.Ɋ. ȺɅȿɄɋȺɇəɇ, Ⱥ.Ⱥ. ɂɐɄɈȼɂɑ, ɂ.Ⱥ. ɎȺɃɇȻɍɊȽ
ɉɨɫɬɪɨɟɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɨɜ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ (ɉɌɗ) ɚɜɢɚɰɢɨɧɧɨɣ ɬɟɯɧɢɤɢ (ȺɌ)
ɤɚɤ ɡɚɦɤɧɭɬɨɣ ɫɢɫɬɟɦɵ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ (ɋɆɈ), ɨɬɪɚɠɚɸɳɚɹ ɢɯ ɜɟɪɨɹɬɧɨɫɬɧɨ-ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɩɪɨɰɟɫɫɵ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɨɜ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɫɢɫɬɟɦɚ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ.
ȼ ɪɚɦɤɚɯ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɩɨɥɧɨɝɨ ɢ ɫɜɨɟɜɪɟɦɟɧɧɨɝɨ ɭɞɨɜɥɟɬɜɨɪɟɧɢɹ ɩɨɬɪɟɛɧɨɫɬɟɣ ɚɜɢɚɰɢɨɧɧɨ-ɬɪɚɧɫɩɨɪɬɧɨɣ ɫɢɫɬɟɦɵ ɜ ɢɫɩɪɚɜɧɵɯ ɜɨɡɞɭɲɧɵɯ ɫɭɞɚɯ (ȼɋ), ɨɛɟɫɩɟɱɟɧɢɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɢ
ɪɟɝɭɥɹɪɧɨɫɬɢ ɩɨɥɟɬɨɜ, ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨ ɧɚɡɧɚɱɟɧɢɸ ɩɪɢ ɦɢɧɢɦɚɥɶɧɵɯ ɡɚɬɪɚɬɚɯ ɜɪɟɦɟɧɢ, ɬɪɭɞɚ ɢ ɫɪɟɞɫɬɜ ɧɚ ɬɟɯɧɢɱɟɫɤɨɟ ɨɛɫɥɭɠɢɜɚɧɢɟ ɢ ɪɟɦɨɧɬ (ɌɈɢɊ) ȺɌ ɜɵɩɨɥɧɟɧɨ
ɮɭɧɤɰɢɨɧɚɥɶɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ Integration Definition For Function Modeling (IDFE0) ɫɢɫɬɟɦ ɢ
ɩɪɨɰɟɫɫɨɜ ɷɤɫɩɥɭɚɬɚɰɢɢ (ɋɢɉɗ) ȺɌ, ɨɬɪɚɠɚɸɳɢɯ ɢɯ ɨɪɝɚɧɢɡɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɭɸ ɫɬɪɭɤɬɭɪɭ ɢ
ɤɚɱɟɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. ɗɬɨ ɨɛɟɫɩɟɱɢɥɨ ɫɬɪɭɤɬɭɪɢɡɚɰɢɸ ɉɌɗ ȺɌ ɫ ɭɱɺɬɨɦ ɢɯ ɢɟɪɚɪɯɢɱɟɫɤɨɣ ɫɬɪɭɤɬɭɪɵ [1]. ɇɚ ɨɫɧɨɜɟ ɪɟɡɭɥɶɬɚɬɨɜ ɷɬɨɣ ɪɚɛɨɬɵ ɢ ɨɛɨɛɳɟɧɢɹ ɨɩɵɬɚ ɷɤɫɩɥɭɚɬɚɰɢɢ ȼɋ
ɛɵɥɢ ɪɚɡɪɚɛɨɬɚɧɵ ɭɫɥɨɜɧɵɟ ɚɥɝɨɪɢɬɦɵ ɮɨɪɦɢɪɨɜɚɧɢɹ ɉɌɗ ȺɌ [2]. ȼ ɪɚɡɜɢɬɢɟ ɷɬɢɯ ɪɚɛɨɬ ɪɟɲɟɧɵ ɡɚɞɚɱɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɉɌɗ ȺɌ ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ [3].
ȼ ɧɚɫɬɨɹɳɟɣ ɫɬɚɬɶɟ ɩɨɫɬɪɨɟɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɉɌɗ ɤɚɤ ɋɆɈ, ɨɬɧɨɫɹɳɚɹɫɹ ɤ ɢɦɢɬɚɰɢɨɧɧɨɦɭ ɦɨɞɟɥɢɪɨɜɚɧɢɸ.
ɉɪɨɰɟɫɫɵ ɷɤɫɩɥɭɚɬɚɰɢɢ ɜɤɥɸɱɚɸɬ: ɩɪɨɰɟɫɫɵ ɥɟɬɧɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɩɪɨɰɟɫɫɵ ɤɨɦɦɟɪɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɉɌɗ ȺɌ, ɩɪɨɰɟɫɫɵ ɚɷɪɨɞɪɨɦɧɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɢ ɩɪɨɰɟɫɫɵ ɭɩɪɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɵɦ ɞɜɢɠɟɧɢɟɦ. ɉɌɗ ȺɌ ɩɨɞɪɚɡɞɟɥɹɸɬɫɹ ɧɚ ɩɪɨɰɟɫɫɵ ɌɈɢɊ, ɩɪɨɰɟɫɫɵ ɢɧɠɟɧɟɪɧɨɚɜɢɚɰɢɨɧɧɨɝɨ ɨɛɟɫɩɟɱɟɧɢɹ.
ɉɌɗ ȺɌ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɚɹ ɜɨ ɜɪɟɦɟɧɢ ɫɦɟɧɚ ɫɨɫɬɨɹɧɢɣ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ
ɫ ɩɪɢɧɹɬɨɣ ɫɬɪɚɬɟɝɢɟɣ. Ʉ ɫɨɫɬɨɹɧɢɹɦ ɷɤɫɩɥɭɚɬɚɰɢɢ ɨɬɧɨɫɹɬɫɹ: ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɩɨ ɧɚɡɧɚɱɟɧɢɸ,
ɪɚɡɥɢɱɧɵɟ ɜɢɞɵ ɌɈɢɊ, ɞɢɚɝɧɨɫɬɢɪɨɜɚɧɢɟ, ɬɪɚɧɫɩɨɪɬɢɪɨɜɚɧɢɟ, ɯɪɚɧɟɧɢɟ, ɨɠɢɞɚɧɢɟ ɩɟɪɟɯɨɞɚ ɜ
ɤɚɠɞɨɟ ɢɡ ɷɬɢɯ ɫɨɫɬɨɹɧɢɣ ɢ ɞɪ.
ɂɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɋɢɉɗ ȺɌ – ɦɟɬɨɞ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɩɪɢ ɤɨɬɨɪɨɦ ɢɡɭɱɚɟɦɵɟ
ɋɢɉɗ ȺɌ ɡɚɦɟɧɹɸɬɫɹ ɦɨɞɟɥɶɸ, ɫ ɞɨɫɬɚɬɨɱɧɨɣ ɬɨɱɧɨɫɬɶɸ ɨɩɢɫɵɜɚɸɳɟɣ ɪɟɚɥɶɧɵɣ ɩɪɨɰɟɫɫ, ɫ
ɤɨɬɨɪɨɣ ɩɪɨɜɨɞɹɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɵ ɫ ɰɟɥɶɸ ɩɨɥɭɱɟɧɢɹ ɤɨɥɢɱɟɫɬɜɟɧɧɨɣ ɨɰɟɧɤɢ ɜɟɪɨɹɬɧɨɫɬɧɨ –
ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɮɭɧɤɰɢɨɧɚɥɶɧɵɯ ɦɨɞɟɥɟɣ. ɗɤɫɩɟɪɢɦɟɧɬɢɪɨɜɚɧɢɟ ɫ ɦɨɞɟɥɶɸ
ɧɚɡɵɜɚɸɬ ɢɦɢɬɚɰɢɟɣ (ɢɦɢɬɚɰɢɹ – ɷɬɨ ɩɨɫɬɢɠɟɧɢɟ ɫɭɬɢ ɹɜɥɟɧɢɹ, ɧɟ ɩɪɢɛɟɝɚɹ ɤ ɷɤɫɩɟɪɢɦɟɧɬɚɦ
ɧɚ ɪɟɚɥɶɧɨɦ ɨɛɴɟɤɬɟ).
Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɉɌɗ ɢɫɩɨɥɶɡɭɟɬɫɹ ɦɚɬɟɦɚɬɢɱɟɫɤɢɣ ɚɩɩɚɪɚɬ ɋɆɈ
[4; 5].
ȼ ɤɚɱɟɫɬɜɟ ɩɨɤɚɡɚɬɟɥɟɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɋɆɈ ɢɫɩɨɥɶɡɭɸɬɫɹ: ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɡɚɹɜɨɤ, ɨɛɫɥɭɠɢɜɚɟɦɵɯ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ; ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɡɚɹɜɨɤ ɜ ɨɱɟɪɟɞɢ; ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ; ɜɟɪɨɹɬɧɨɫɬɶ ɨɬɤɚɡɚ ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ ɛɟɡ ɨɠɢɞɚɧɢɹ; ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɱɢɫɥɨ ɡɚɹɜɨɤ
ɜ ɨɱɟɪɟɞɢ ɩɪɟɜɵɫɢɬ ɨɩɪɟɞɟɥɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɢ ɬ.ɩ.
ɋɆɈ, ɜ ɤɨɬɨɪɵɯ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɩɨɬɨɤɚ ɡɚɹɜɨɤ ɡɚɜɢɫɢɬ ɨɬ ɫɨɫɬɨɹɧɢɹ ɋɆɈ, ɚ ɫɚɦɢ ɢɫɬɨɱɧɢɤɢ ɡɚɹɜɨɤ ɹɜɥɹɸɬɫɹ ɜɧɭɬɪɟɧɧɢɦɢ ɷɥɟɦɟɧɬɚɦɢ ɋɆɈ, ɧɚɡɵɜɚɸɬɫɹ ɡɚɦɤɧɭɬɵɦɢ.
47
ɉɨɫɬɪɨɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɩɪɨɰɟɫɫɨɜ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ…
ȼ ɪɟɡɭɥɶɬɚɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɨɩɪɟɞɟɥɹɸɬ ɬɚɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɋɆɈ, ɤɚɤ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɡɚɹɜɨɤ ɜ ɫɢɫɬɟɦɟ, ɫɪɟɞɧɹɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɩɪɟɛɵɜɚɧɢɹ ɡɚɹɜɨɤ ɜ ɫɢɫɬɟɦɟ, ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɡɚɹɜɨɤ
ɜ ɨɱɟɪɟɞɢ, ɫɪɟɞɧɹɹ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɩɪɟɛɵɜɚɧɢɹ ɡɚɹɜɨɤ ɜ ɨɱɟɪɟɞɢ, ɫɪɟɞɧɹɹ ɞɥɢɧɚ ɨɱɟɪɟɞɢ ɢ
ɬ.ɞ. Ɍɚɤɢɟ ɦɨɞɟɥɢ ɢɫɫɥɟɞɭɸɬ ɞɜɭɦɹ ɦɟɬɨɞɚɦɢ, ɞɚɸɳɢɦɢ ɛɥɢɡɤɢɟ ɪɟɡɭɥɶɬɚɬɵ.
Ⱦɥɹ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɩɭɚɫɫɨɧɨɜɫɤɨɝɨ ɩɨɬɨɤɚ ɦɨɝɭɬ ɩɪɢɦɟɧɹɬɶɫɹ ɚɧɚɥɢɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɬɟɨɪɢɢ ɋɆɈ, ɩɨɡɜɨɥɹɸɳɢɟ ɜɵɩɨɥɧɹɬɶ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɪɚɫɱɺɬɵ ɢ ɜɵɱɢɫɥɹɬɶ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɋɆɈ.
Ɋɚɫɫɦɨɬɪɢɦ ɩɨɫɬɪɨɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɞɥɹ ɉɌɗ ȼɋ «ȼɵɩɨɥɧɟɧɢɟ ɪɟɝɥɚɦɟɧɬɧɵɯ
ɪɚɛɨɬ ɜ ɚɜɢɚɤɨɦɩɚɧɢɢ» ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɡɚɦɤɧɭɬɨɣ ɋɆɈ ɧɚ ɩɪɢɦɟɪɟ ɷɤɫɩɥɭɚɬɚɰɢɢ ɩɚɪɤɚ ɫɚɦɨɥɺɬɨɜ ɬɢɩɚ Ⱥ-320 ɚɜɢɚɤɨɦɩɚɧɢɢ ɈȺɈ «Ʉɨɝɚɥɵɦɚɜɢɚ».
ɉɪɟɞɫɬɚɜɢɦ, ɱɬɨ ɜ ɚɜɢɚɤɨɦɩɚɧɢɢ ɢɦɟɸɬɫɹ: m ȼɋ ɢ n ɦɟɫɬ ɜ ɚɧɝɚɪɟ ɞɥɹ ɬɟɯɧɢɱɟɫɤɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ (ɌɈ) (ɱɢɫɥɨ ɤɚɧɚɥɨɜ ɞɥɹ ɨɛɫɥɭɠɢɜɚɧɢɹ). Ɉɛɨɪɭɞɨɜɚɧɢɟ ɚɧɝɚɪɧɵɯ ɦɟɫɬ ɞɨɩɭɫɤɚɟɬ
«ɜɡɚɢɦɨɩɨɦɨɳɶ» ɬɨɥɶɤɨ ɦɟɠɞɭ l ɝɪɭɩɩɚɦɢ ɨɛɫɥɭɠɢɜɚɧɢɹ. ɇɚ ɤɚɠɞɨɦ ȼɋ ɩɨɫɥɟ ɭɫɬɚɧɨɜɥɟɧɧɨɝɨ
ɧɚɥɺɬɚ (ɥɺɬɧɵɟ ɱɚɫɵ) ɜɵɩɨɥɧɹɟɬɫɹ ɮɨɪɦɚ ɌɈ, ɧɚɩɪɢɦɟɪ A-check. ȼɋ ɩɪɢɛɵɜɚɸɬ ɞɥɹ ɩɪɨɯɨɠɞɟɧɢɹ ɨɱɟɪɟɞɧɨɣ ɮɨɪɦɵ ɌɈ ɜ ɫɪɟɞɧɟɦ ɱɟɪɟɡ ɤɚɠɞɵɟ t ɫɭɬɤɢ. ɉɨɬɨɤ ɩɪɟɛɵɜɚɧɢɹ ɧɚ ɌɈ ɤɚɠɞɨɝɨ
ȼɋ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɩɭɚɫɫɨɧɨɜɫɤɢɦ ɫ ɩɥɨɬɧɨɫɬɶɸ Ȝ. ɉɥɨɬɧɨɫɬɶ ɩɭɚɫɫɨɧɨɜɫɤɨɝɨ ɩɨɬɨɤɚ ɨɛɫɥɭɠɢɜɚɧɢɹ ɤɚɠɞɨɝɨ ɤɚɧɚɥɚ ȝ. ɉɪɢ ɷɬɨɦ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɨɛɫɥɭɠɢɜɚɧɢɹ ɤɚɠɞɨɝɨ ȼɋ ɪɚɜɧɚ lȝ. ȼɟɥɢɱɢɧɚ l ɪɚɜɧɚ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɱɢɫɥɭ ɤɚɧɚɥɨɜ, ɤɨɬɨɪɨɟ ɦɨɠɟɬ ɨɛɫɥɭɠɢɜɚɬɶ ɨɞɧɨ ȼɋ.
Ɋɟɝɥɚɦɟɧɬɧɵɟ ɪɚɛɨɬɵ ɜɵɩɨɥɧɹɸɬɫɹ ɜ ɫɪɟɞɧɟɦ ɜ ɬɟɱɟɧɢɟ T ɫɭɬɨɤ. Ɉɩɪɟɞɟɥɢɦ ɩɚɪɚɦɟɬɪɵ
࢔
૚ ૚
ɉɌɗ ɜ ɚɜɢɚɤɨɦɩɚɧɢɢ ɤɚɤ ɡɚɦɤɧɭɬɨɣ ɋɆɈ ɫ ɩɚɪɚɦɟɬɪɚɦɢ: n; m; l; ࢎ ൌ ቂ ቃ; ࣅ ൌ
;
ࣆൌ
૚
૚
; ࣑ൌ
࣎ ɫɭɬɤɢ
࢔ࣆ
ࣅ
ࢻ࢒
ࣅ
࢒ࣆ
૚ାࢻ࢒
; ࢻ࢒ ൌ ; ࢖ሺ࢒ሻ ൌ
࢒
࢚ ɫɭɬɤɢ
; ࢗሺ࢒ሻ ൌ ૚ െ ࢖ሺ࢒ሻ .
ɉɭɚɫɫɨɧɨɜɫɤɢɣ ɩɨɬɨɤ ɫɨɛɵɬɢɣ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɚɦɢ ɫɬɚɰɢɨɧɚɪɧɨɫɬɢ, ɨɪɞɢɧɚɪɧɨɫɬɢ ɢ ɨɬɫɭɬɫɬɜɢɹ ɩɨɫɥɟɞɟɣɫɬɜɢɹ.
ɉɨɬɨɤ ɫɨɛɵɬɢɣ ɹɜɥɹɟɬɫɹ ɫɬɚɰɢɨɧɚɪɧɵɦ, ɟɫɥɢ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɩɚɞɚɧɢɹ ɫɨɛɵɬɢɹ ɧɚ ɢɧɬɟɪɜɚɥ
ɜɪɟɦɟɧɢ ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɜɟɥɢɱɢɧɵ ɢɧɬɟɪɜɚɥɚ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɪɚɫɩɨɥɨɠɟɧɢɹ ɷɬɨɝɨ ɢɧɬɟɪɜɚɥɚ
ɧɚ ɨɫɢ ɜɪɟɦɟɧɢ [4; 5; 6].
ɉɨɬɨɤ ɫɨɛɵɬɢɣ ɹɜɥɹɟɬɫɹ ɨɪɞɢɧɚɪɧɵɦ, ɟɫɥɢ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɧɚ ɦɚɥɵɣ ɭɱɚɫɬɨɤ ǻt,
ɩɪɢɦɵɤɚɸɳɢɣ ɤ ɦɨɦɟɧɬɭ ɜɪɟɦɟɧɢ t, ɩɨɩɚɞɚɟɬ ɛɨɥɶɲɟ ɨɞɧɨɝɨ ɫɨɛɵɬɢɹ, ɩɪɟɧɟɛɪɟɠɢɦɨ ɦɚɥɚ ɩɨ
ɫɪɚɜɧɟɧɢɸ ɫ ɜɟɪɨɹɬɧɨɫɬɶɸ ɬɨɝɨ, ɱɬɨ ɧɚ ɷɬɨɬ ɠɟ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ ɩɨɩɚɞɚɟɬ ɪɨɜɧɨ ɨɞɧɨ ɫɨɛɵɬɢɟ
(ɩɨɬɨɤ ɫɚɦɨɥɺɬɨɜ, ɩɨɫɬɭɩɚɸɳɢɯ ɧɚ ɪɟɝɥɚɦɟɧɬɧɵɟ ɪɚɛɨɬɵ).
ǻt
0
t
t
ɉɨɬɨɤ ɫɱɢɬɚɟɬɫɹ ɩɨɬɨɤɨɦ ɛɟɡ ɩɨɫɥɟɞɟɣɫɬɜɢɹ, ɟɫɥɢ ɞɥɹ ɥɸɛɵɯ ɞɜɭɯ ɧɟɩɟɪɟɤɪɵɜɚɸɳɢɯɫɹ
ɭɱɚɫɬɤɨɜ ࣎૚ ɢ࣎૛ ɱɢɫɥɨ ɫɨɛɵɬɢɣ, ɩɨɩɚɞɚɸɳɢɯ ɧɚ ɨɞɢɧ ɢɡ ɧɢɯ, ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɫɤɨɥɶɤɨ ɫɨɛɵɬɢɣ ɩɨɩɚɥɨ ɧɚ ɞɪɭɝɨɣ.
0
t
ȿɫɥɢ ɱɢɫɥɨ ȼɋ, ɞɨɫɬɢɝɲɢɯ ɨɩɪɟɞɟɥɺɧɧɨɝɨ ɧɚɥɺɬɚ ɢ ɩɪɢɛɵɜɲɢɯ ɞɥɹ ɩɪɨɯɨɠɞɟɧɢɹ ɌɈ, ɥɟɠɢɬ ɜ ɩɪɟɞɟɥɚɯ h < j < n, ɬɨ ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ ɭɱɚɫɬɜɭɸɬ ɜɫɟ n ɤɚɧɚɥɨɜ, ɪɚɫɩɪɟɞɟɥɹɹɫɶ ɛɨɥɟɟ ɢɥɢ
ɦɟɧɟɟ ɪɚɜɧɨɦɟɪɧɨ ɦɟɠɞɭ ɜɫɟɦɢ j ɩɪɢɛɵɜɲɢɦɢ ɞɥɹ ɩɪɨɯɨɠɞɟɧɢɹ ɌɈ ȼɋ, ɩɪɢ ɷɬɨɦ ɤɚɠɞɨɟ ȼɋ
ɨɛɫɥɭɠɢɜɚɟɬɫɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɧɟ ɛɨɥɟɟ ɱɟɦ l ɤɚɧɚɥɚɦɢ. ȿɫɥɢ ɱɢɫɥɨ ȼɋ, ɞɨɫɬɢɝɲɢɯ ɨɩɪɟɞɟɥɺɧɧɨɝɨ ɧɚɥɺɬɚ ɢ ɩɪɢɛɵɜɲɢɯ ɞɥɹ ɩɪɨɯɨɠɞɟɧɢɹ ɌɈ k ɥɟɠɢɬ ɜ ɩɪɟɞɟɥɚɯ ݊ ൑ ݇ ൑ ݉, ɬɨ ɪɨɜɧɨ n ȼɋ
ɨɛɫɥɭɠɢɜɚɟɬɫɹ (ɤɚɠɞɨɟ ȼɋ ɨɛɫɥɭɠɢɜɚɟɬɫɹ ɨɞɧɢɦ ɤɚɧɚɥɨɦ) ɢ (k – n) ɨɠɢɞɚɟɬ ɨɱɟɪɟɞɢ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɟ.
48
Ⱥ.Ɋ. Ⱥɥɟɤɫɚɧɹɧ, Ⱥ.Ⱥ. ɂɰɤɨɜɢɱ, ɂ.Ⱥ. Ɏɚɣɧɛɭɪɝ
ɋɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ ࣑࢑ , ݇ ൌ Ͳǡ ݅ǡ ݆ǡ ݊ ൅ ‫ ݎ‬ɛɭɞɟɦ ɫɜɹɡɵɜɚɬɶ ɫ ɱɢɫɥɨɦ i ȼɋ, ɞɨɫɬɢɝɲɢɯ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɱɢɫɥɚ ɧɚɥɺɬɚ ɢ ɩɪɢɛɵɜɲɢɯ ɞɥɹ ɩɪɨɯɨɠɞɟɧɢɹ ɌɈ [6]:
࣑࢏ – ɞɨɫɬɢɝɥɨ ɨɩɪɟɞɟɥɺɧɧɨɝɨ ɧɚɥɺɬɚ ɢ ɩɪɢɛɵɥɨ ɧɚ ɌɈ ɪɨɜɧɨ ȼɋ ሺ݅ ൌ Ͳǡͳǡ ǥ ǡ ݄ሻ ɢ ɜɫɟ ɨɧɢ
ɧɚɯɨɞɹɬɫɹ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɢ; ɤɚɠɞɨɟ ȼɋ ɨɛɫɥɭɠɢɜɚɟɬɫɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ࢒ ɤɚɧɚɥɚɦɢ;
࣑࢐ – ɞɨɫɬɢɝɥɨ ɨɩɪɟɞɟɥɺɧɧɨɝɨ ɧɚɥɺɬɚ ɢ ɩɪɢɛɵɥɨ ɧɚ ɌɈ ɪɨɜɧɨ ࢐ ȼɋ ሺ݆ ൌ ݄ ൅ ͳǡ ǥ ǡ ݊ െ ͳሻ ɢ ɜɫɟ
ɨɧɢ ɧɚɯɨɞɹɬɫɹ ɧɚ ɨɛɫɥɭɠɢɜɚɧɢɢ; ɜ ɨɛɫɥɭɠɢɜɚɧɢɢ ɭɱɚɫɬɜɭɸɬ ɨɞɧɨɜɪɟɦɟɧɧɨ ɜɫɟ n ɤɚɧɚɥɨɜ, ɪɚɫɩɪɟɞɟɥɹɹɫɶ ɩɪɨɢɡɜɨɥɶɧɨ ɦɟɠɞɭ ɩɪɢɛɵɜɲɢɦɢ ɞɥɹ ɩɪɨɯɨɠɞɟɧɢɹ ɌɈ ȼɋ, ɧɨ ɬɚɤ, ɱɬɨ ɜɫɟ ࢔ ɤɚɧɚɥɨɜ ɡɚɧɹɬɵ ɨɛɫɥɭɠɢɜɚɧɢɟɦ;
࣑࢔ା࢘ – ɞɨɫɬɢɝɥɨ ɨɩɪɟɞɟɥɺɧɧɨɝɨ ɧɚɥɺɬɚ ɢ ɩɪɢɛɵɥɨ ɧɚ ɌɈ ɪɨɜɧɨ ݊ ൅ ‫ ݎ‬ȼɋ ሺ‫ ݎ‬ൌ ͲǡͳǤ Ǥ ǡ ݉ െ ݊ሻ;
ɢɡ ɧɢɯ ࢔ ɨɛɫɥɭɠɢɜɚɸɬɫɹ (ɤɚɠɞɨɟ ȼɋ ɨɞɧɢɦ ɤɚɧɚɥɨɦ) ɢ ࢘ ɨɠɢɞɚɸɬ ɜ ɨɱɟɪɟɞɢ ɧɚ ɌɈ.
Ƚɪɚɮ ɫɨɫɬɨɹɧɢɣ ɫɢɫɬɟɦɵ ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ. 1.
Ɋɢɫ. 1. Ƚɪɚɮ ɫɨɫɬɨɹɧɢɣ ɢ ɩɟɪɟɯɨɞɨɜ ɫɢɫɬɟɦɵ
ɇɚɣɞɺɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɜɫɟ ȼɋ ɧɚɯɨɞɹɬɫɹ ɜ ɷɤɫɩɥɭɚɬɚɰɢɢ (ɫɨɫɬɨɹɧɢɟ ࣑૙ )
‫݌‬଴ ൌ ೃሺ೘ǡ೓ǡ೛೗ሻ
೜೘
ሺ೗ሻ
ଵ
ುሺ೓ǡ೓ሻೃሺ೘ష೓షభǡഖሻ
ା
ುሺ೚ǡ೓ሻುሺ೘ǡഖሻ
.
(1)
ɇɚɣɞɺɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ȼɋ ɞɨɫɬɢɝɥɨ ɭɫɬɚɧɨɜɥɟɧɧɨɝɨ ɧɚɥɺɬɚ ɱɚɫɨɜ ɢ ɩɪɢɛɵɥɨ ɧɚ ɌɈ
ɪɨɜɧɨ ࢏ ȼɋ (ɫɨɫɬɨɹɧɢɟ ࣑࢏ )
ܲ௜ ൌ
஻ሺ௠ǡ௜ǡ௣೗ ሻ
೘
௤ሺ೗ሻ
‫݌‬଴ .
(2)
ɇɚɣɞɺɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ȼɋ ɞɨɫɬɢɝɥɨ ɭɫɬɚɧɨɜɥɟɧɧɨɝɨ ɧɚɥɺɬɚ ɱɚɫɨɜ ɢ ɩɪɢɛɵɥɨ ɧɚ ɌɈ
ɪɨɜɧɨ ࢐ ȼɋ (ɫɨɫɬɨɹɧɢɟ ࣑࢐ )
ܲ௝ ൌ
௉ሺ௛ǡ௛ሻ௉ሺ௠ି௝ǡఞሻ
௉ሺ଴ǡ௛ሻ௉ሺ௠ǡఞሻ
‫݌‬଴ .
(3)
ɇɚɣɞɺɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ȼɋ ɞɨɫɬɢɝɥɨ ɭɫɬɚɧɨɜɥɟɧɧɨɝɨ ɧɚɥɺɬɚ ɱɚɫɨɜ ɢ ɩɪɢɛɵɥɨ ɧɚ ɌɈ
ɪɨɜɧɨ ࢔ ൅ ࢘ ȼɋ (ɫɨɫɬɨɹɧɢɟ ࣑࢔ା࢘ )
ܲ௡ା௥ ൌ
௉ሺ௛ǡ௛ሻ௉ሺ௠ିሺ௡ା௥ሻǡఞሻ
௉ሺ଴ǡ௛ሻ௉ሺ௠ǡఞሻ
ɇɚɣɞɺɦ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɨɛɫɥɭɠɢɜɚɟɦɵɯ ȼɋ
‫݌‬଴ .
(4)
49
ɉɨɫɬɪɨɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɩɪɨɰɟɫɫɨɜ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ…
‫ݏ‬ҧ ൌ
௣బ
௤೘
σ௛௜ୀ଴ ݅‫ܤ‬൫݉ǡ ݅ǡ ‫݌‬ሺ௟ሻ ൯ ൅
௣బ ௉ሺ௛ǡ௛ሻ
௉ሺ଴ǡ௛ሻ௉ሺ௠ǡఞሻ
ሼ݉ሾܴ ሺ݉ െ ݄ െ ͳǡ ߯ሻ െ
െܴሺ݉ െ ݊ െ ͳǡ ߯ሻሿ െ ߯ሾܴ ሺ݉ െ ݄ െ ʹǡ ߯ሻ െ ܴሺ݉ െ ݊ െ ʹǡ ߯ሻሿሽ ൅
݊‫݌‬଴ ܲሺ݄ǡ ݄ሻ
൅
ܴ ሺ݉ െ ሺ݊ ൅ ͳሻǡ ߯ሻǡ
ܲሺͲǡ ݄ሻܲሺ݉ǡ ߯ሻ
(5)
௠ି௜
௜ ௜
ɝɞɟ ‫ܤ‬൫݉ǡ ݅ǡ ‫݌‬ሺ௟ሻ ൯ ൌ ‫ܥ‬௠
‫݌‬ሺ௟ሻ ‫ݍ‬ሺ௟ሻ
;
௞ ௠ି௞
௛
௞
ܴ൫݉ǡ ݄ǡ ‫݌‬ሺ௟ሻ ൯ ൌ σ௞ୀ଴ ‫ܥ‬௠ ‫݌‬ሺ௟ሻ ‫ݍ‬ሺ௟ሻ .
ɋɪɟɞɧɟɟ ɱɢɫɥɨ ȼɋ, ɨɠɢɞɚɸɳɢɯ ɩɪɨɯɨɠɞɟɧɢɹ ɪɟɝɥɚɦɟɧɬɧɵɯ ɪɚɛɨɬ, ɧɚɯɨɞɢɦ ɢɡ ɜɵɪɚɠɟɧɢɹ
௣బ ௉ሺ௛ǡ௛ሻ
ൈ ሾሺ݉ െ ݊ሻܴሺ݉ െ ݊ െ ͳǡ ߯ሻ െ ܴ߯ ሺ݉ െ ݊ െ ʹǡ ߯ሻሿ.
(6)
ɋɪɟɞɧɟɟ ɱɢɫɥɨ ȼɋ, ɨɠɢɞɚɸɳɢɯ ɢ ɩɪɨɯɨɞɹɳɢɯ ɪɟɝɥɚɦɟɧɬɧɵɟ ɪɚɛɨɬɵ, ɛɭɞɟɬ
݈ ҧ ൌ ‫ݏ‬ҧ ൅ ‫ݎ‬ҧ .
ȼɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɨɬɞɟɥɶɧɨ ɜɡɹɬɵɣ ɫɚɦɨɥɺɬ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɷɤɫɩɥɭɚɬɚɰɢɢ
(7)
‫ݎ‬ҧ ൌ
௉ሺ଴ǡ௛ሻ௉ሺ௠ǡఞሻ
௟ҧ
ߦ ൌͳെ .
(8)
ଵିక
‫ݐ‬ഥɩ ൌ ‫ݐ‬ഥɪ
.
(9)
௠
ɋɪɟɞɧɟɟ ɜɪɟɦɹ ɩɪɨɫɬɨɹ ȼɋ ɛɭɞɟɬ
క
ɋɪɟɞɧɟɟ ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ
തത ൌ
‫ݐ‬തതɨɱ
௉ሺ௛ǡ௛ሻ௣బ
௉ሺ଴ǡ௛ሻ௉ሺ௠ǡఞሻ
σ௠ି௡ିଵ
ܲሺ݉ െ ሺ݊ ൅ ‫ݎ‬ሻǡ ߯ሻ߮ሺ݊ߤǡ ‫ݎ‬ሻ,
௥ୀ଴
ɝɞɟ
σ௠ି௡ିଵ
ܲሺ݉ െ ሺ݊ ൅ ‫ݎ‬ሻǡ ߯ሻ߮ሺ݊ߤǡ ‫ݎ‬ሻ ൌ
௥ୀ଴
௉ሺ଴ǡ௡ሻ௉ሺ௠ǡఞሻ ଵ ଵିక ‫כ‬
௉ሺ௡ǡ௡ሻ௣బ
‫כ‬
ቂ
ఒ
క‫כ‬
(10)
ଵ
െ ቃ.
(11)
ఓ
Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɫɪɟɞɧɟɝɨ ɜɪɟɦɟɧɢ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɝɨ ȼɋ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɪɚɜɟɧɫɬɜɨɦ
തതɨɱ
തത.
‫ݐ‬തതതതത
(12)
ɨɛɫ ൌ ‫ݐ‬ഥɩ െ ‫ݐ‬
Ɋɚɫɫɦɨɬɪɢɦ ɜ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɪɚɛɨɬɭ ɚɷɪɨɞɪɨɦɚ, ɤ ɤɨɬɨɪɨɦɭ ɩɪɢɩɢɫɚɧɨ 20 ȼɋ. ɇɚ ɚɷɪɨɞɪɨɦɟ ɢɦɟɸɬɫɹ 4 ɚɧɝɚɪɚ ɞɥɹ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɌɈ ȼɋ. Ɉɛɨɪɭɞɨɜɚɧɢɟ ɚɧɝɚɪɨɜ ɞɨɩɭɫɤɚɟɬ «ɜɡɚɢɦɨɩɨɦɨɳɶ» ɩɪɢ ɌɈ ȼɋ ɬɨɥɶɤɨ ɦɟɠɞɭ ɞɜɭɦɹ ɛɪɢɝɚɞɚɦɢ, ɜɵɩɨɥɧɹɸɳɢɦɢ ɌɈ. Ʉɚɠɞɵɣ ɫɚɦɨɥɺɬ ɜ
ɫɪɟɞɧɟɦ ɱɟɪɟɡ 5 ɫɭɬɨɤ ɞɨɥɠɟɧ ɩɪɨɯɨɞɢɬɶ ɌɈ, ɤɨɬɨɪɨɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɬɟɱɟɧɢɟ ɨɞɧɢɯ ɫɭɬɨɤ.
Ɉɩɪɟɞɟɥɢɦ ɩɚɪɚɦɟɬɪɵ ɪɚɛɨɬɵ ɚɷɪɨɞɪɨɦɚ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɌɈ ȼɋ:
࢔
૚ ૚
ଵ
૚
࢔ࣆ
࢔ ൌ Ͷ; ࢓ ൌ ʹͲ; ࢒ ൌ ʹ; ࢎ ൌ ቂ ቃ ൌ ૛; ࣅ ൌ
ൌ Ͳǡʹ
; ࣆൌ૚
; ࣑ ൌ ൌ ʹͲ;
ࢻ࢒ ൌ
ࣅ
࢒ࣆ
࢒
ൌ Ͳǡͳ; ࢖ሺ࢒ሻ ൌ
ࢻ࢒
૚ାࢻ࢒
ൌ
଴ǡଵ
૞ ɫɭɬɤɢ
ଵା଴ǡଵ
ɫɭɬɤɢ
ɫɭɬɤɢ
ࣅ
ൌ ͲǡͲͻͳ; ࢗሺ࢒ሻ ൌ ૚ െ ࢖ሺ࢒ሻ ൌ ͲǡͻͲͻ.
ɉɨ ɮɨɪɦɭɥɟ (1) ɧɚɣɞɺɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɜɫɟ ȼɋ ɧɚɯɨɞɹɬɫɹ ɜ ɷɤɫɩɥɭɚɬɚɰɢɢ.
ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɨɩɪɟɞɟɥɢɦ ɡɧɚɱɟɧɢɟ ɫɥɟɞɭɸɳɟɣ ɮɭɧɤɰɢɢ
ோ൫௠ǡ௛ǡ௣ሺ೗ሻ ൯
೘
௤ሺ೗ሻ
଴ ଴
ଵ ଵ
ଶ ଶ
௞ ௞
ൌ σ௛௞ୀ଴ ‫ܥ‬௠
ߙሺ௟ሻ ൌ ‫ܥ‬ଶ଴
ߙሺ௟ሻ ൅ ‫ܥ‬ଶ଴
ߙሺ௟ሻ ൅ ‫ܥ‬ଶ଴
ߙሺ௟ሻ .
௞
ɉɨ ɬɚɛɥɢɰɚɦ ɛɢɧɨɦɢɚɥɶɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɧɚɯɨɞɢɦ ɡɧɚɱɟɧɢɟ ‫ܥ‬௠
଴
ଵ
ଶ
‫ܥ‬ଶ଴
ൌ ͳǢ‫ܥ‬ଶ଴
ൌ ʹͲǢ‫ܥ‬ଶ଴
ൌ ͳͻͲ.
Ɍɨɝɞɚ
ோ൫௠ǡ௛ǡ௣ሺ೗ሻ ൯
೘
௤ሺ೗ሻ
ൌ ͳ ൅ ሺʹͲ ൈ Ͳǡͳሻ ൅ ሺͳͻͲ ൈ ͲǡͲͳሻ ൌ ͶǡͻͲ.
Ⱦɚɥɟɟ ɩɨ ɬɚɛɥɢɰɚɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɉɭɚɫɫɨɧɚ [5] ɧɚɯɨɞɢɦ:
ܲሺ݄ǡ ݄ሻ ൌ ܲሺʹǡʹሻ ൌ ܴത ሺͳǡʹሻ െ ܴതሺʹǡʹሻ ൌ ͲǡͷͻͶ െ Ͳǡ͵ʹ͵ ൌ Ͳǡʹ͹ͳ;
ܲሺͲǡ ݄ሻ ൌ ܲሺͲǡʹሻ ൌ ͳ െ ܴതሺͲǡʹሻ ൌ ͳ െ Ͳǡͺ͸ͷ ൌ Ͳǡͳ͵ͷ;
ܲሺ݉ǡ ߯ሻ ൌ ܲሺʹͲǡʹͲሻ ൌ ܴത ሺͳͻǡʹͲሻ െ ܴതሺʹͲǡʹͲሻ ൌ Ͳǡͷʹͻ െ ͲǡͶͶͳ ൌ ͲǡͲͺͺͺ;
ܴሺ݉ െ ݄ െ ͳǡ ߯ሻ ൌ ܴሺʹͲ െ ʹ െ ͳǡʹͲሻ ൌ ͳ െ ܴതሺͳ͹ǡʹͲሻ ൌ ͳ െ Ͳǡ͹Ͳ͵ ൌ Ͳǡʹͻ͹.
50
Ⱥ.Ɋ. Ⱥɥɟɤɫɚɧɹɧ, Ⱥ.Ⱥ. ɂɰɤɨɜɢɱ, ɂ.Ⱥ. Ɏɚɣɧɛɭɪɝ
ɋɥɟɞɨɜɚɬɟɥɶɧɨ
‫݌‬଴ ൌ
ଵ
బǡమళభൈబǡమవళ
ସǡଽ଴ା
బǡభయఱൈబǡబఴఴఴ
ൌ ͲǡͲͺ͸.
ɋɪɟɞɧɟɟ ɱɢɫɥɨ ȼɋ, ɩɪɨɯɨɞɹɳɢɯ ɌɈ, ɧɚɣɞɺɦ ɩɨ ɮɨɪɦɭɥɟ (5), ɩɪɢ ɷɬɨɦ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ
ɨɩɪɟɞɟɥɢɦ ɡɧɚɱɟɧɢɟ ɫɥɟɞɭɸɳɢɯ ɮɭɧɤɰɢɣ:
σ௛௜ୀ଴ ݅‫ܤ‬൫݉ǡ ݅ǡ ‫݌‬ሺ௟ሻ ൯ ൌ σଶ௜ୀ଴ ݅‫ܤ‬ሺʹͲǡ ݅ǡ ͲǡͲͻͳሻ ൌ ‫ܤ‬ሺʹͲǢ ͳǢ ͲǡͲͻͳሻ ൅ ʹ‫ܤ‬ሺʹͲǢ ʹǢ ͲǡͲͻͳሻ;
௠ି௜
௜ ௜
‫ܤ‬൫݉ǡ ݅ǡ ‫݌‬ሺ௟ሻ ൯ ൌ ‫ܥ‬௠
‫݌‬ሺ௟ሻ ‫ݍ‬ሺ௟ሻ
;
ଵ
ଵ
ଵଽ
‫ܤ‬ሺʹͲǢ ͳǢ ͲǡͲͻͳሻ ൌ ‫ܥ‬ଶ଴ ͲǡͲͻͳ ͲǡͻͲͻ ൌ ʹͲ ൈ ͲǡͲͻͳ ൈ Ͳǡͳ͸͵ ൌ Ͳǡʹͻ͹;
ଶ
‫ܤ‬ሺʹͲǢ ʹǢ ͲǡͲͻͳሻ ൌ ‫ܥ‬ଶ଴
ͲǡͲͻͳଶ ͲǡͻͲͻଵ଼ ൌ ͳͻͲ ൈ ͲǡͲͲͺ͵ ൈ Ͳǡͳ͹ͻ ൌ Ͳǡʹͺʹ;
σ௛௜ୀ଴ ݅‫ܤ‬൫݉ǡ ݅ǡ ‫݌‬ሺ௟ሻ ൯ ൌ Ͳǡʹͻ͹ ൅ ʹ ൈ Ͳǡʹͺʹ ൌ Ͳǡͺ͸ͳ;
ܴሺ݉ െ ݊ െ ͳǡ ߯ሻ ൌ ܴሺʹͲ െ Ͷ െ ͳǡʹͲሻ ൌ ͳ െ ܴതሺͳͷǡʹͲሻ ൌ ͳ െ ͲǡͺͶ͵ ൌ Ͳǡͳͷ͹;
ܴሺ݉ െ ݊ െ ʹǡ ߯ሻ ൌ ܴሺʹͲ െ Ͷ െ ʹǡʹͲሻ ൌ ͳ െ ܴതሺͳͶǡʹͲሻ ൌ ͳ െ Ͳǡͺͻͷ ൌ ͲǡͳͲͷ;
ܴሺ݉ െ ሺ݊ ൅ ͳሻǡ ߯ሻ ൌ ܴሺʹͲ െ Ͷ െ ͳǡʹͲሻ ൌ ͳ െ ܴതሺͳͷǡʹͲሻ ൌ Ͳǡͳͷ͹;
ܴሺ݉ െ ݄ െ ʹǡ ߯ሻ ൌ ܴሺʹͲ െ ʹ െ ʹǡʹͲሻ ൌ ͳ െ ܴതሺͳ͸ǡʹͲሻ ൌ ͳ െ Ͳǡ͹͹ͻ ൌ Ͳǡʹʹͳ.
Ɍɨɝɞɚ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ȼɋ, ɩɪɨɯɨɞɹɳɢɯ ɌɈ, ɨɩɪɟɞɟɥɹɟɦ ɩɨ ɮɨɪɦɭɥɟ (5)
ͲǡͲͺ͸
ͲǡͲͺ͸ ൈ Ͳǡʹ͹ͳ
‫ݏ‬ҧ ൌ
ൈ Ͳǡͺ͸ͳ ൅
ሼʹͲሾͲǡʹͻ͹ െ Ͳǡͳͷ͹ሿ െ
ͲǡͳͶͺ
Ͳǡͳ͵ͷ ൈ ͲǡͲͺͺͺ
ସൈ଴ǡ଴଼଺ൈ଴ǡଶ଻ଵ
ൈ Ͳǡͳͷ͹ ൌ ʹǡ͸͹.
െʹͲሾͲǡʹʹͳ െ ͲǡͳͲͷሿሽ ൅
଴ǡଵଷହൈ଴ǡ଴଼଼଼
ɋɪɟɞɧɟɟ ɱɢɫɥɨ ȼɋ, ɨɠɢɞɚɸɳɢɯ ɩɪɨɯɨɠɞɟɧɢɹ ɌɈ, ɧɚɣɞɺɦ ɩɨ ɮɨɪɦɭɥɟ (6)
଴ǡ଴଼଺ൈ଴ǡଶ଻ଵ
‫ݎ‬ҧ ൌ
ൈ ሾሺʹͲ െ Ͷሻ ൈ Ͳǡͳͷ͹ െ ʹͲ ൈ ͲǡͳͲͷሿ ൌ ͲǡͺͲ.
଴ǡଵଷହൈ଴ǡ଴଼଼଼
ɋɪɟɞɧɟɟ ɱɢɫɥɨ ȼɋ, ɩɪɨɯɨɞɹɳɢɯ ɢ ɨɠɢɞɚɸɳɢɯ ɩɪɨɯɨɠɞɟɧɢɟ ɌɈ (ɬ.ɟ. ȼɋ, ɤɨɬɨɪɵɟ ɧɟ ɧɚɯɨɞɹɬɫɹ ɜ ɷɤɫɩɥɭɚɬɚɰɢɢ), ɧɚɯɨɞɢɦ ɩɨ ɮɨɪɦɭɥɟ (7)
݈ ҧ ൌ ʹǡ͸͹ ൅ ͲǡͺͲ ൌ ͵ǡͶ͹.
ȼɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɨɬɞɟɥɶɧɨ ɜɡɹɬɵɣ ɫɚɦɨɥɺɬ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɧɚɯɨɞɢɦ
ɩɨ ɮɨɪɦɭɥɟ (8)
ଷǡସ଻
ߦ ൌͳെ
ൌ Ͳǡͺ͵,
ଶ଴
ɬ.ɟ. ɨɤɨɥɨ 83% ȼɋ ɛɭɞɭɬ ɷɤɫɩɥɭɚɬɢɪɨɜɚɬɶɫɹ, ɚ 17% - ɨɠɢɞɚɬɶ ɌɈ ɢɥɢ ɧɚɯɨɞɢɬɶɫɹ ɧɚ ɌɈ.
ɋɪɟɞɧɟɟ ɜɪɟɦɹ ɩɪɨɫɬɨɹ ȼɋ ɧɚɣɞɺɦ ɩɨ ɮɨɪɦɭɥɟ (9)
ଵିక
ଵ
‫ݐ‬ഥɩ ൌ ‫ݐ‬ഥɪ
ൌ ൈ ͲǡʹͲ ൌ ͳɫɭɬɨɤ.
క
ఒ
ɋɪɟɞɧɟɟ ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɧɚɣɞɺɦ ɩɨ ɮɨɪɦɭɥɚɦ (10), (11).
ɋɥɟɞɭɟɬ ɨɛɪɚɬɢɬɶ ɜɧɢɦɚɧɢɟ ɧɚ ɬɨ, ɱɬɨ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɜɵɪɚɠɟɧɢɹ (11) ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ
ɨɩɪɟɞɟɥɹɸɬɫɹ ɡɧɚɱɟɧɢɹ ɫɥɟɞɭɸɳɢɯ ɮɭɧɤɰɢɣ: Į, p, q, ‫݌‬଴ ‫ כ‬, ɢ ɞɚɥɟɟ ݇ത, ‫ݎ‬ҧ , ݈‫כ‬ҧ , ߦ ‫ כ‬:
ఒ
ఈ
ൌ Ͳǡͳ͸͹Ǣ ‫ ݍ‬ൌ ͳ െ ‫ ݌‬ൌ Ͳǡͺ͵͵;
ߙ ൌ ൌ ͲǡʹǢ ‫ ݌‬ൌ
ఓ
ଵାఈ
‫כ‬
‫݌‬଴ ൌ ೃሺ೘ǡ೙ǡ೛ሻ
ோሺ௠ǡ௡ǡ௣ሻ
ɝɞɟ
௤೘
ோሺ௠ǡ௡ǡ௣ሻ
೜೘
ଵ
ುሺ೙ǡ೙ሻೃሺ೘ష೙షభǡഖሻ
ା
ುሺ೚ǡ೙ሻುሺ೘ǡഖሻ
଴ ଴
ଷ ଷ
ଵ ଵ
ଶ ଶ
ସ ସ
௞ ௞
ൌ σ௡௞ୀ଴ ‫ܥ‬௠
ߙ ൌ ‫ܥ‬ଶ଴
ߙ ൅ ‫ܥ‬ଶ଴
ߙ ൅ ‫ܥ‬ଶ଴
ߙ ൅ ‫ܥ‬ଶ଴
ߙ ൅ ‫ܥ‬ଶ଴
ߙ ,
ൌ ͳ ൅ ʹͲ ൈ Ͳǡʹ ൅ ͳͻͲ ൈ ͲǡͲͶ ൅ ͳͳͶͲ ൈ ͲǡͲͲͺ ൅ ͶͺͶͷ ൈ ͲǡͲͲͳ͸ ൌ ʹͻǡͶ͹;
ܲሺͲǡ ݊ሻ ൌ ܲሺͲǡͶሻ ൌ ͳ െ ܴതሺͲǡͶሻ ൌ ͳ െ Ͳǡͻͺʹ ൌ ͲǡͲͳͺ;
ܲሺ݊ǡ ݊ሻ ൌ ܲሺͶǡͶሻ ൌ ܴതሺ͵ǡͶሻ െ ܴതሺͶǡͶሻ ൌ Ͳǡͷ͸͸ െ Ͳǡ͵͹ͳ ൌ Ͳǡͳͻͷ;
ܴሺ݉ െ ݊ െ ͳǡ ߯ሻ ൌ ܴሺʹͲ െ Ͷ െ ͳǡʹͲሻ ൌ ͳ െ ܴതሺͳͷǡʹͲሻ ൌ ͳ െ ͲǡͺͶ͵ ൌ Ͳǡͳͷ͹;
ܲሺ݉ǡ ߯ሻ ൌ ܲሺʹͲǡʹͲሻ ൌ ܴത ሺͳͻǡʹͲሻ െ ܴതሺʹͲǡʹͲሻ ൌ Ͳǡͷʹͻ െ ͲǡͶͶͳ ൌ ͲǡͲͺͺͺ.
௤೘
(13)
ɉɨɫɬɪɨɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɩɪɨɰɟɫɫɨɜ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ…
ɋɥɟɞɨɜɚɬɟɥɶɧɨ,
‫݌‬଴ ‫ כ‬ൌ
‫כ‬
ଵ
௡
௤
ൌ ͲǡͲʹͲ;
బǡభవఱൈబǡభఱళ
ଶଽǡସ଻ା
బǡబభఴൈబǡబఴఴఴ
௡௣బ ‫ כ‬௉ሺ௡ǡ௡ሻ
௣
݇ത ൌ బ೘ σ௡௞ୀ଴ ݇‫ܤ‬ሺ݉ǡ ݇ǡ ‫݌‬ሻ ൅
ସ
51
௉ሺ଴ǡ௡ሻ௉ሺ௠ǡఞሻ
ܴሺ݉ െ ݊ െ ͳǡ ߯ሻ;
(14)
෍ ݇‫ܤ‬ሺ݉ǡ ݇ǡ ‫݌‬ሻ ൌ ෍ ݇‫ܤ‬ሺʹͲǢ ݇Ǣ Ͳǡͳ͸͹ሻ ൌ ‫ܤ‬ሺʹͲǢ ͳǢ Ͳǡͳ͸͹ሻ ൅ ʹ‫ܤ‬ሺʹͲǢ ʹǢ Ͳǡͳ͸͹ሻ ൅
௞ୀ଴
௞ୀ଴
൅͵‫ܤ‬ሺʹͲǢ ͵Ǣ Ͳǡͳ͸͹ሻ ൅ Ͷ‫ܤ‬ሺʹͲǢ ʹǢ Ͳǡͳ͸͹ሻ ൌ ͲǡͳͲ͵ ൅ Ͳǡ͵ͻͶ ൅ Ͳǡ͹ʹ͵ ൅ Ͳǡͺͳ͸ ൌ ʹǡͲͶ;
௠ି௜
௜ ௜
‫ܤ‬൫݉ǡ ݅ǡ ‫݌‬ሺ௟ሻ ൯ ൌ ‫ܥ‬௠
‫݌‬ሺ௟ሻ ‫ݍ‬ሺ௟ሻ
;
ଵ
ଵ
ଵଽ
‫ܤ‬ሺʹͲǢ ͳǢ Ͳǡͳ͸͹ሻ ൌ ‫ܥ‬ଶ଴ Ͳǡͳ͸͹ Ͳǡͺ͵͵ ൌ ʹͲ ൈ Ͳǡͳ͸͹ ൈ ͲǡͲ͵ͳ ൌ ͲǡͳͲ͵;
ଶ
‫ܤ‬ሺʹͲǢ ʹǢ Ͳǡͳ͸͹ሻ ൌ ‫ܥ‬ଶ଴
Ͳǡͳ͸͹ଶ Ͳǡͺ͵͵ଵ଼ ൌ ͳͻͲ ൈ ͲǡͲʹͺ ൈ ͲǡͲ͵͹ ൌ Ͳǡͳͻ͹;
ଷ
‫ܤ‬ሺʹͲǢ ͵Ǣ Ͳǡͳ͸͹ሻ ൌ ‫ܥ‬ଶ଴ Ͳǡͳ͸͹ଷ Ͳǡͺ͵͵ଵ଻ ൌ ͳͳͶͲ ൈ ͲǡͲͲͶ͹ ൈ ͲǡͲͶͷ ൌ ͲǡʹͶͳ;
ସ
‫ܤ‬ሺʹͲǢ ͶǢ Ͳǡͳ͸͹ሻ ൌ ‫ܥ‬ଶ଴
Ͳǡͳ͸͹ସ Ͳǡͺ͵͵ଵ଺ ൌ ͶͺͶͷ ൈ ͲǡͲͲͲ͹ͺ ൈ ͲǡͲͷͶ ൌ ͲǡʹͲͶ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ,
଴ǡ଴ଶ଴
ସൈ଴ǡ଴ଶ଴ൈ଴ǡଵଽହ
݇ത ൌ
ൈ ʹǡͲͶ ൅
ൈ Ͳǡͳͷ͹ ൌ ͵ǡͳ;
‫ݎ‬ҧ ൌ
଴ǡ଴ଶ଺
௣బ ‫ כ‬௉ሺ௡ǡ௡ሻ
௉ሺ଴ǡ௡ሻ௉ሺ௠ǡఞሻ
଴ǡ଴ଵ଼ൈ଴ǡ଴଼଼଼
ൈ ሾሺ݉ െ ݊ሻܴ ሺ݉ െ ݊ǡ ߯ሻ െ ܴ߯ ሺ݉ െ ݊ െ ͳǡ ߯ሻሿ,
(15)
ܴሺ݉ െ ݊ǡ ߯ሻ ൌ ܴሺͳ͸ǡʹͲሻ ൌ ͳ െ ܴതሺͳ͸ǡʹͲሻ ൌ ͳ െ Ͳǡ͹͹ͻ ൌ ͲǡʹʹͳǤ
ɋɥɟɞɨɜɚɬɟɥɶɧɨ,
‫ݎ‬ҧ ൌ
଴ǡ଴ଶ଴ൈ଴ǡଵଽହ
ൈ ሾሺʹͲ െ Ͷሻ ൈ Ͳǡʹʹͳ െ ʹͲ ൈ Ͳǡͳͷ͹ሿ ൌ ͲǡͻͶ;
݈ ൌ ݇ത ൅ ‫ݎ‬ҧ ൌ ͵ǡͳ ൅ ͲǡͻͶ ൌ ͶǡͲͶ;
଴ǡ଴ଵ଼ൈ଴ǡ଴଼଼଼
‫כ‬ҧ
௟ ‫כ‬ҧ
ߦ‫ כ‬ൌ ͳ െ ൌ ͳ െ
௠
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨ ɜɵɪɚɠɟɧɢɸ (11)
௠ି௡ିଵ
෍ ܲሺ݉ െ ሺ݊ ൅ ‫ݎ‬ሻǡ ߯ሻ߮ሺ݊ߤǡ ‫ݎ‬ሻ ൌ
௥ୀ଴
ସǡ଴ସ
ଶ଴
ൌ ͲǡͺͲ.
ͲǡͲͳͺ ൈ ͲǡͲͺͺͺ
ͳ െ ͲǡͺͲ
ൈ ൤ͷ ൈ
െ ͳ൨ ൌ ͲǡͳͲǤ
Ͳǡͳͻͷ ൈ ͲǡͲʹͲ
ͲǡͺͲ
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɧɚɯɨɞɢɦ ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ (10)
Ͳǡʹ͹ͳ ൈ ͲǡͲͺ͸
ത‫ݐ‬തɨɱ
തത ൌ
ൈ ͲǡͳͲ ൌ ͲǡͳͻɫɭɬɨɤǤ
Ͳǡͳ͵ͷ ൈ ͲǡͲͺͺͺ
Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɫɪɟɞɧɟɝɨ ɜɪɟɦɟɧɢ ɌɈ ɨɞɧɨɝɨ ȼɋ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɪɚɜɟɧɫɬɜɨɦ (12)
‫ݐ‬തതതതത
ɨɛɫ ൌ ͳ െ Ͳǡͳͻ ൌ Ͳǡͺͳɫɭɬɨɤ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɉɌɗ ɩɨɡɜɨɥɹɟɬ ɜɵɩɨɥɧɹɬɶ ɜɟɪɨɹɬɧɨɫɬɧɵɟ
ɪɚɫɱɺɬɵ ɢ ɨɩɪɟɞɟɥɹɬɶ ɬɚɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɋɆɈ, ɤɚɤ ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɨɛɫɥɭɠɢɜɚɟɦɵɯ ɡɚɹɜɨɤ,
ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɡɚɹɜɨɤ, ɨɠɢɞɚɸɳɢɯ ɨɛɫɥɭɠɢɜɚɧɢɟ, ɫɪɟɞɧɟɟ ɱɢɫɥɨ ɡɚɹɜɨɤ, ɨɠɢɞɚɸɳɢɯ ɢ ɩɪɨɯɨɞɹɳɢɯ ɨɛɫɥɭɠɢɜɚɧɢɟ, ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɩɪɨɫɬɨɹ, ɫɪɟɞɧɟɟ ɜɪɟɦɹ ɨɠɢɞɚɧɢɹ ɨɛɫɥɭɠɢɜɚɧɢɹ, ɫɪɟɞɧɟɟ
ɜɪɟɦɹ ɨɛɫɥɭɠɢɜɚɧɢɹ ɨɞɧɨɣ ɡɚɹɜɤɢ.
ɅɂɌȿɊȺɌɍɊȺ
1. Ⱥɥɟɤɫɚɧɹɧ Ⱥ.Ɋ., ɂɰɤɨɜɢɱ Ⱥ.Ⱥ. Ɏɚɣɧɛɭɪɝ ɂ.Ⱥ. Ɇɨɧɢɬɨɪɢɧɝ ɩɪɨɰɟɫɫɨɜ ɩɨɞɞɟɪɠɚɧɢɹ ɥɺɬɧɨɣ ɝɨɞɧɨɫɬɢ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ ɧɚ ɨɫɧɨɜɟ ɩɪɢɦɟɧɟɧɢɹ ɦɟɬɨɞɨɜ ɦɨɞɟɥɢɪɨɜɚɧɢɹ IDEF0// ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ. 2010. ʋ 162.
ɋ. 51 - 58.
2. Ⱥɥɟɤɫɚɧɹɧ Ⱥ.Ɋ. Ɏɨɪɦɢɪɨɜɚɧɢɟ ɩɪɨɰɟɞɭɪ ɩɨɞɞɟɪɠɚɧɢɹ ɥɺɬɧɨɣ ɝɨɞɧɨɫɬɢ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ // ɇɚɭɱɧɵɣ
ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ. 2011. ʋ 173. ɋ. 52 - 60.
3. Ⱥɥɟɤɫɚɧɹɧ Ⱥ.Ɋ., Ʉɢɫɟɥɺɜ Ⱦ.ɘ., Ɏɚɣɧɛɭɪɝ ɂ.Ⱥ. Ɏɨɪɦɢɪɨɜɚɧɢɟ ɩɪɨɰɟɞɭɪ ɜɵɩɨɥɧɟɧɢɹ ɪɟɝɥɚɦɟɧɬɧɵɯ ɪɚɛɨɬ
ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɬɟɯɧɨɥɨɝɢɣ ɢɦɢɬɚɰɢɨɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ // ɇɚɭɱɧɵɣ ȼɟɫɬɧɢɤ ɆȽɌɍ ȽȺ. 2011.
ʋ 173. ɋ. 98 - 108.
52
Ⱥ.Ɋ. Ⱥɥɟɤɫɚɧɹɧ, Ⱥ.Ⱥ. ɂɰɤɨɜɢɱ, ɂ.Ⱥ. Ɏɚɣɧɛɭɪɝ
4. ȼɟɧɬɰɟɥɶ ȿ.ɋ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɨɩɟɪɚɰɢɣ. Ɇ.: ɋɨɜɟɬɫɤɨɟ ɪɚɞɢɨ, 1972. 552 ɫ.
5. ȼɟɧɬɰɟɥɶ ȿ.ɋ. Ɍɟɨɪɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɢ ɟɟ ɬɟɯɧɢɱɟɫɤɢɟ ɩɪɢɥɨɠɟɧɢɹ: ɭɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɜɭɡɨɜ / Ɇ.:
ɂɡɞɚɬɟɥɶɫɤɢɣ ɰɟɧɬɪ «Ⱥɤɚɞɟɦɢɹ», 2003. 464 ɫ.
6. Ɉɜɱɚɪɨɜ Ʌ.Ⱥ. ɉɪɢɤɥɚɞɧɵɟ ɡɚɞɚɱɢ ɬɟɨɪɢɢ ɦɚɫɫɨɜɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ. Ɇ.: Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, 1969. 324 ɫ.
THE CONSTRUCTION OF MATHEMATICAL MODEL
OF PROCESSES OF MAINTENANCE OF AIRCRAFT ENGINEERING
AS A CLOSED SERVICE SYSTEM
Aleksanyan A.R., Itskovich A.A., Faynburg I.A.
A mathematical model of the processes of maintenance of aircraft engineering as a closed service system shoving
their probability-statistic characteristics is constructed.
Keywords: the processes of maintenance, the model of processes of maintenance, a closed service system.
REFERENCES
1. Aleksanyan A.R., Itskovich A.A. Faynburg I.A. Monitoring protsessov podderzhaniya ljotnoj godnosti vozdushnykh sudov na osnove primeneniya metodov modelirovaniya IDEF0. Nauchnyy Vestnik MGTU GA. 2010. ʋ 162. Pp. 51 58. (In Russian).
2. Aleksanyan A.R. Formirovanie protsedur podderzhaniya ljotnoi godnosti vozdushnykh sudov. Nauchnyy Vestnik
MGTU GA. 2011. ʋ 173. Pp. 52 - 60. (In Russian).
3. Aleksanyan A.R., Kiseljov D.Ju., Faynburg I.A. Formirovanie protsedur vypolneniya reglamentnykh rabot s
primeneniem informacionnykh tekhnologiy imitatsionnogo modelirovaniya. Nauchnyy Vestnik MGTU GA. 2011. ʋ 173.
Pp. 98 - 108. (In Russian).
4. Ventcel' E.S. Issledovanie operatsiyy. M.: Sovetskoe radio. 1972. 552 p. (In Russian).
5. Ventcel' E.S. Teoriya veroyatnostey i ee tekhnicheskie prilozheniya: ucheb. posobie dlya studentov vuzov. M.: Izdatel'skij tsentr «Akademiya». 2003. 464 p . (In Russian).
6. Ovcharov L.A. Prikladnye zadachi teorii massovogo obsluzhivaniya. M.: Mashinostroenie. 1969, 324 p. (In Russian).
ɋɜɟɞɟɧɢɹ ɨɛ ɚɜɬɨɪɚɯ
Ⱥɥɟɤɫɚɧɹɧ Ⱥɪɦɟɧ Ɋɚɡɦɢɤɨɜɢɱ, 1976 ɝ.ɪ., ɨɤɨɧɱɢɥ ɆȺɂ (2007), ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɫɩɟɰɢɚɥɢɫɬ ɞɟɩɚɪɬɚɦɟɧɬɚ ɩɨɫɥɟɩɪɨɞɚɠɧɨɝɨ ɨɛɫɥɭɠɢɜɚɧɢɹ ɝɪɚɠɞɚɧɫɤɨɣ ȺɌ ɈȺɈ «Ɉɛɴɟɞɢɧɺɧɧɚɹ ɚɜɢɚɫɬɪɨɢɬɟɥɶɧɚɹ ɤɨɪɩɨɪɚɰɢɹ (ɈȺɄ)», ɚɜɬɨɪ 19 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ – ɩɨɞɞɟɪɠɚɧɢɟ ɥɺɬɧɨɣ ɝɨɞɧɨɫɬɢ ɜɨɡɞɭɲɧɵɯ ɫɭɞɨɜ.
ɂɰɤɨɜɢɱ Ⱥɥɟɤɫɚɧɞɪ Ⱥɛɪɚɦɨɜɢɱ, 1934 ɝ.ɪ., ɨɤɨɧɱɢɥ ɍȺɂ (1957), ɩɪɨɮɟɫɫɨɪ, ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ
ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ ɤɚɮɟɞɪɵ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ ɢ ɚɜɢɚɞɜɢɝɚɬɟɥɟɣ ɆȽɌɍ
ȽȺ, ɚɜɬɨɪ ɛɨɥɟɟ 280 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ - ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɚɹ ɧɚɞɟɠɧɨɫɬɶ ɢ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɷɤɫɩɥɭɚɬɚɰɢɢ ɚɜɢɚɰɢɨɧɧɨɣ ɬɟɯɧɢɤɢ, ɭɩɪɚɜɥɟɧɢɟ ɩɪɨɰɟɫɫɚɦɢ ɩɨɞɞɟɪɠɚɧɢɹ ɥɟɬɧɨɣ ɝɨɞɧɨɫɬɢ
ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ, ɢɧɬɟɝɪɢɪɨɜɚɧɧɚɹ ɥɨɝɢɫɬɢɱɟɫɤɚɹ ɩɨɞɞɟɪɠɤɚ.
Ɏɚɣɧɛɭɪɝ ɂɧɧɚ Ⱥɥɟɤɫɚɧɞɪɨɜɧɚ, ɨɤɨɧɱɢɥɚ ɆɂɂȼɌ (1989), ɞɨɰɟɧɬ, ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ,
ɞɨɰɟɧɬ ɤɚɮɟɞɪɵ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ ɢ ɚɜɢɚɞɜɢɝɚɬɟɥɟɣ ɆȽɌɍ ȽȺ, ɚɜɬɨɪ
ɛɨɥɟɟ 60 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ - ɭɩɪɚɜɥɟɧɢɟ ɩɪɨɰɟɫɫɚɦɢ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɢ ɩɨɞɞɟɪɠɚɧɢɹ ɥɟɬɧɨɣ ɝɨɞɧɨɫɬɢ ɥɟɬɚɬɟɥɶɧɵɯ ɚɩɩɚɪɚɬɨɜ, ɢɧɬɟɝɪɢɪɨɜɚɧɧɚɹ ɥɨɝɢɫɬɢɱɟɫɤɚɹ ɩɨɞɞɟɪɠɤɚ.
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