Статистические методы контроля качества теоретические основы статистических методов качества. Практикум. Учебное пособие
.pdfȼɵɩɨɥɧɹɟɬɫɹ ɥɚɡɟɪɧɚɹ ɪɟɡɤɚ ɥɢɫɬɨɜɨɝɨ ɦɟɬɚɥɥɚ ɇɟɨɛɯɨɞɢɦɨ
ɨɩɪɟɞɟɥɢɬɶ ɧɚɥɢɱɢɟ ɢ ɫɬɟɩɟɧɶ ɜɡɚɢɦɨɫɜɹɡɢ ɦɟɠɞɭ ɭɤɚɡɚɧɧɵɦɢ ɩɚɪɚ ɦɟɬɪɚɦɢ ɢ ɤɚɱɟɫɬɜɟɧɧɵɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ ɬɚɛɥ
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Ɍɚɛɥɢɰɚ |
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Ɋɟɡɭɥɶɬɚɬɵ ɤɨɧɬɪɨɥɹ ɤɚɱɟɫɬɜɚ |
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ɉɚɪɚɦɟɬɪɵ |
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Ʉɚɱɟɫɬɜɟɧɧɵɟ ɩɨɤɚɡɚɬɟɥɢ |
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ɋɤɨɪɨɫɬɶɪɟɡɚɧɢɹ ɦɦɢɧ |
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Ɇɨɳɧɨɫɬɶɪɟɡɚɧɢɹ ɤȼɬ |
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ȼɪɟɦɹɪɚɛɨɬɵ ɥɚɡɟɪɧɨɣɝɨɥɨɜɤɢ ɦɢɧ |
ɉɨɹɜɥɟɧɢɟɬɪɟɳɢɧ ɲɬ |
Ɇɚɤɫɨɬɤɥɨɧɟɧɢɟ ɪɚɡɦɟɪɚɦɦ |
Ʉɨɥɢɱɟɫɬɜɨɛɪɚɤ ɞɟɬɚɥɟɣɲɬ |
ɩ ɩ |
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2. Факторный анализ
Ɏɚɤɬɨɪɧɵɣ ɚɧɚɥɢɡ – ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɦɟɬɨɞ ɢɫɩɨɥɶɡɭɟɦɵɣ ɩɪɢ ɨɛ ɪɚɛɨɬɤɟ ɛɨɥɶɲɢɯ ɦɚɫɫɢɜɨɜ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ
ɐɟɥɶɸ ɮɚɤɬɨɪɧɨɝɨ ɚɧɚɥɢɡɚ ɹɜɥɹɟɬɫɹ ɫɨɤɪɚɳɟɧɢɟ ɱɢɫɥɚ ɩɟɪɟɦɟɧ ɧɵɯ ɪɟɞɭɤɰɢɹ ɞɚɧɧɵɯ ɢ ɨɩɪɟɞɟɥɟɧɢɟ ɫɬɪɭɤɬɭɪɵ ɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ ɜɡɚɢɦɨɫɜɹɡɟɣ ɦɟɠɞɭ ɧɢɦɢ
11
ɋɭɳɟɫɬɜɟɧɧɵɦ ɨɬɥɢɱɢɟɦ ɮɚɤɬɨɪɧɨɝɨ ɚɧɚɥɢɡɚ ɨɬ ɞɪɭɝɢɯ ɫɬɚɬɢ ɫɬɢɱɟɫɤɢɯ ɦɟɬɨɞɨɜ ɹɜɥɹɟɬɫɹ ɜ ɬɨɦ ɱɬɨ ɟɝɨ ɧɟ ɢɫɩɨɥɶɡɭɸɬ ɩɪɢ ɨɛɪɚ ɛɨɬɤɟ ɩɟɪɜɢɱɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɬ ɟ ɩɨɥɭɱɟɧɧɵɯ ɧɟ-
ɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɨɫɥɟ ɢɫɩɵɬɚɧɢɣ ɢɥɢ ɤɨɧɬɪɨɥɹ > @ Ɉɫɧɨɜɨɣ ɮɚɤɬɨɪɧɨɝɨ ɚɧɚɥɢɡɚ ɫɥɭɠɚɬ ɤɨɪɪɟɥɹɰɢɨɧɧɵɟ ɫɜɹɡɢ ɚ
ɢɦɟɧɧɨ ɤɨɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ ɉɢɪɫɨɧɚ r ɤɨɬɨɪɵɟ ɜɵɱɢɫɥɹ-
ɸɬɫɹ ɦɟɠɞɭ ɩɟɪɟɦɟɧɧɵɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɜɤɥɸɱɟɧɧɵɦɢ ɜ ɢɫɫɥɟɞɨɜɚɧɢɟ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɮɚɤɬɨɪɧɨɦɭ ɚɧɚɥɢɡɭ ɩɨɞɜɟɪɝɚɸɬɫɹ ɤɨɪɪɟɥɹɰɢɨɧ ɧɵɟ ɦɚɬɪɢɰɵ ɢɥɢ ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɦɚɬɪɢɰɵ ɢɧɬɟɪɤɨɪɪɟɥɹɰɢɣ ɇɚɢ-
ɦɟɧɨɜɚɧɢɹ ɫɬɨɥɛɰɨɜ ɢ ɫɬɪɨɤ ɜ ɷɬɢɯ ɦɚɬɪɢɰɚɯ ɨɞɢɧɚɤɨɜɵ ɬɚɤ ɤɚɤ ɨɧɢ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɧɚɛɨɪ ɩɟɪɟɦɟɧɧɵɯ ɜɤɥɸɱɟɧɧɵɯ ɜ ɚɧɚɥɢɡ ȼ ɦɚɬ-
ɪɢɰɚɯ ɢɧɬɟɪɤɨɪɪɟɥɹɰɢɣ ɱɢɫɥɨ ɫɬɪɨɤ ɪɚɜɧɨ ɱɢɫɥɭ ɫɬɨɥɛɰɨɜ ɢ ɫɢɦɦɟɬ ɪɢɱɧɵɟ ɬɨ ɟɫɬɶ ɧɚ ɝɥɚɜɧɨɣ ɞɢɚɝɨɧɚɥɢ ɦɚɬɪɢɰɵ ɫɬɨɹɬ ɨɞɧɢ ɢ ɬɟ ɠɟ ɤɨ ɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ ȼɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧ ɩɪɢɦɟɪ ɬɚɤɨɣ ɦɚɬɪɢɰɵ
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Ɍɚɛɥɢɰɚ |
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Ɉɛɳɢɣ ɜɢɞ ɦɚɬɪɢɰɵ ɢɧɬɟɪɤɨɪɪɟɥɹɰɢɣ |
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ɉɨɤɚɡɚɬɟɥɶ – |
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ɉɨɤɚɡɚɬɟɥɶ – |
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ɉɨɤɚɡɚɬɟɥɶ – |
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ɉɨɤɚɡɚɬɟɥɶ – |
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ɉɨɤɚɡɚɬɟɥɶ – |
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ɉɨɤɚɡɚɬɟɥɶ – |
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ɉɨɤɚɡɚɬɟɥɶ – |
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ɉɨɤɚɡɚɬɟɥɶ – |
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Ⱦɥɹ ɨɰɟɧɤɢ ɫɢɥɵ ɜɡɚɢɦɨɫɜɹɡɢ r ɜ ɬɟɨɪɢɢ ɤɨɪɪɟɥɹɰɢɢ ɩɪɢɦɟɧɹ ɟɬɫɹ ɲɤɚɥɚ ɚɧɝɥɢɣɫɤɨɝɨ ɫɬɚɬɢɫɬɢɤɚ ɑɟɞɞɨɤɚ ɫɥɚɛɚɹ ɨɬ ɞɨ
12
ɭɦɟɪɟɧɧɚɹ ɨɬ ɞɨ ɡɚɦɟɬɧɚɹ ɨɬ ɞɨ ɜɵɫɨɤɚɹ ɨɬ ɞɨ ɜɟɫɶɦɚ ɜɵɫɨɤɚɹ ɫɢɥɶɧɚɹ ɨɬ ɞɨ
ȼɚɠɧɨ Ɉɬɪɢɰɚɬɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɤɨɪɪɟɥɹɰɢɢ ɝɨ ɜɨɪɹɬ ɬɨɥɶɤɨ ɨɛ ɨɛɪɚɬɧɨɣ ɜɡɚɢɦɨɫɜɹɡɢ ɉɨɷɬɨɦɭ ɡɧɚɤ ©–ª ɧɟ ɭɱɢɬɵɜɚ ɟɬɫɹ ɬɨ ɟɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ ɛɟɪɟɬɫɹ ɩɨ ɦɨɞɭɥɸ ɩɪɢ ɨɰɟɧɤɟ ɜɡɚɢɦɨɫɜɹɡɢ
Ƚɥɚɜɧɨɟ ɩɨɧɹɬɢɟ ɮɚɤɬɨɪɧɨɝɨ ɚɧɚɥɢɡɚ í ɮɚɤɬɨɪ ɗɬɨ ɢɫɤɭɫɫɬɜɟɧ-
ɧɵɣ ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɩɨɤɚɡɚɬɟɥɶ ɜɨɡɧɢɤɚɸɳɢɣ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɩɟɰɢɚɥɶ ɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɬɚɛɥɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɤɨɪɪɟɥɹɰɢɣ ɉɪɨɰɟɞɭɪɚ ɢɡɜɥɟɱɟɧɢɹ ɮɚɤɬɨɪɨɜ ɢɡ ɦɚɬɪɢɰɵ ɢɧɬɟɪɤɨɪɪɟɥɹɰɢɣ ɧɚɡɵɜɚɟɬɫɹ ɮɚɤɬɨɪɢɡɚɰɢɟɣ ɦɚɬɪɢɰɵ ȼ ɪɟɡɭɥɶɬɚɬɟ ɮɚɤɬɨɪɢɡɚɰɢɢ ɢɡ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɦɚɬɪɢɰɵ ɦɨɠɟɬ ɛɵɬɶ ɢɡɜɥɟɱɟɧɨ ɪɚɡɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɮɚɤɬɨɪɨɜ ɧɨ ɧɟ ɩɪɟ ɜɵɲɚɸɳɟɟ ɱɢɫɥɚ ɩɨɤɚɡɚɬɟɥɟɣ ɫɬɪɨɤ ɢɥɢ ɫɬɨɥɛɰɨɜ ɦɚɬɪɢɰɵ Ɉɞɧɚɤɨ ɮɚɤɬɨɪɵ ɜɵɹɜɥɹɟɦɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɮɚɤɬɨɪɢɡɚɰɢɢ ɤɚɤ ɩɪɚɜɢɥɨ ɧɟɪɚɜ ɧɨɰɟɧɧɵ ɩɨ ɫɜɨɟɦɭ ɡɧɚɱɟɧɢɸ ɗɥɟɦɟɧɬɵ ɮɚɤɬɨɪɧɨɣ ɦɚɬɪɢɰɵ – ɤɨɷɮ-
ɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ – ɱɚɫɬɨ ɧɚɡɵɜɚɸɬɫɹ ©ɮɚɤɬɨɪɧɵɦɢ ɧɚɝɪɭɡɤɚɦɢª ɢɥɢ ©ɮɚɤɬɨɪɧɵɦɢ ɜɟɫɚɦɢª
ȼɵɩɨɥɧɟɧɢɟ ɜɫɟɯ ɷɬɚɩɨɜ ɮɚɤɬɨɪɧɨɝɨ ɚɧɚɥɢɡɚ ɪɚɫɫɦɨɬɪɢɦ ɧɚ ɩɪɨ ɫɬɨɦ ɩɪɚɤɬɢɱɟɫɤɨɦ ɩɪɢɦɟɪɟ
ɉɪɟɞɩɪɢɹɬɢɟ ɡɚɧɢɦɚɟɬɫɹ ɜɵɩɟɱɤɨɣ ɯɥɟɛɨɛɭɥɨɱɧɵɯ ɢɡɞɟɥɢɣ ɇɚ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɩɟɪɟɞ ɩɪɟɞɩɪɢɹɬɢɟɦ ɜɫɬɚɥɚ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɜɵɩɨɥɧɢɬɶ ɢɫɫɥɟɞɨɜɚɧɢɹ ɤɚɱɟɫɬɜɚ ɩɪɨɞɭɤɰɢɢ ɢ ɩɪɢɱɢɧ ɜɥɢɹɸɳɢɯ ɧɚ ɨɛɪɚɡɨɜɚ-
ɧɢɟ ɛɪɚɤɚ ȼ ɪɟɡɭɥɶɬɚɬɟ ɫɩɥɨɲɧɨɝɨ ɤɨɧɬɪɨɥɹ ɛɵɥɢ ɫɨɛɪɚɧɵ ɞɚɧɧɵɟ ɩɨ ɛɪɚɤɭ ɡɚ ɨɞɧɭ ɪɚɛɨɱɭɸ ɧɟɞɟɥɸ ɬɚɛɥ ȼɵɹɜɥɟɧɵ ɫɥɟɞɭɸɳɢɟ ɪɚɡ ɧɨɜɢɞɧɨɫɬɢ ɛɪɚɤɚ ɩɟɪɟɠɨɝ ɧɟɩɪɨɩɟɤɚɧɢɟ ɩɨɫɬɨɪɨɧɧɢɟ ɡɚɩɚɯ ɢ ɜɤɭɫ ɧɟɫɨɨɬɜɟɬɫɬɜɢɟ ɦɚɫɫɵ
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Ɍɚɛɥɢɰɚ |
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Ʉɨɥɢɱɟɫɬɜɨ ɛɪɚɤɨɜɚɧɧɵɯ ɢɡɞɟɥɢɣ |
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Ʉɨɥɢɱɟɫɬɜɨ ɢɡɞɟɥɢɣ ɫ ɭɤɚɡɚɧɧɵɦ ɛɪɚɤɨɦ ɲɬ |
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Ⱦɟɧɶ ɧɟɞɟɥɢ |
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ɇɟɩɪɨ- |
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ɇɟɫɨɨɬɜɟɬ |
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ɉɟɪɟɠɨɝ |
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ɩɟɤɚɧɢɟ |
ɡɚɩɚɯ ɢ ɜɤɭɫ |
ɫɬɜɢɟ ɦɚɫɫɵ |
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ɉɨɧɟɞɟɥɶɧɢɤ |
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ɋɪɟɞɚ |
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ɑɟɬɜɟɪɝ |
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ɉɹɬɧɢɰɚ |
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ɋ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɬɨɞɢɤɢ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɜɡɚɢ-
ɦɨɫɜɹɡɢ ɢɥɢ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɵ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɩɚɪɧɵɯ ɤɨɪɪɟɥɹɰɢɣ
r12 – ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ ɦɟɠɞɭ ɛɪɚɤɨɦ ©ɉɟɪɟɠɨɝª ɢ ©ɇɟɩɪɨ ɩɟɤɚɧɢɟª
r13 ; r14 = – r23 ; r24 = – r34 =
ȼɷɬɨɦɫɥɭɱɚɟɦɚɬɪɢɰɚɢɧɬɟɪɤɨɪɪɟɥɹɰɢɣɩɪɟɞɫɬɚɜɥɟɧɚɜɬɚɛɥɢɰɟ
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Ɍɚɛɥɢɰɚ |
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Ɇɚɬɪɢɰɚ ɢɧɬɟɪɤɨɪɪɟɥɹɰɢɣ |
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ɉɨɤɚɡɚɬɟɥɢ ɛɪɚɤɚ |
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ɉɟɪɟɠɨɝ |
ɇɟɩɪɨ- |
ɉɨɫɬɨɪɨɧɧɢɟ |
ɇɟɫɨɨɬɜɟɬ- |
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ɩɟɤɚɧɢɟ |
ɡɚɩɚɯ ɢɜɤɭɫ |
ɫɬɜɢɟ ɦɚɫɫɵ |
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ɉɟɪɟɠɨɝ |
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ɇɟɩɪɨɩɟɤɚɧɢɟ |
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ɉɨɫɬɨɪɨɧɧɢɟ |
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ɡɚɩɚɯ ɢ ɜɤɭɫ |
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ɇɟɫɨɨɬɜɟɬɫɬɜɢɟ ɦɚɫɫɵ |
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14
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ ɨɬɪɚɠɚɸɬ ɫɪɨɞɫɬɜɨ ɦɟɠɞɭ ɫɨɛɨɣ ɛɪɚɤɚ ɢɥɢ ɩɨɬɪɟɛɢɬɟɥɶɫɤɢɯ ɬɪɟɛɨɜɚɧɢɣ
ɉɪɢ ɚɧɚɥɢɡɟ ɜɟɥɢɱɢɧ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɤɨɪɪɟɥɹɰɢɢ r ɥɟɝɤɨ ɜɵɞɟ ɥɢɬɶ ɝɪɭɩɩɵ ɩɨ ɛɪɚɤɭ ɢɥɢ ɬɪɟɛɨɜɚɧɢɣ ɯɨɪɨɲɨ ɜɡɚɢɦɨɭɜɹɡɚɧɧɵɯ ɬ ɟ ɢɦɟɸɳɢɯ ɨɛɳɭɸ ɩɪɢɪɨɞɭ ɢɥɢ ɩɪɟɞɧɚɡɧɚɱɟɧɢɟ
ɇɚɢɛɨɥɟɟ ɨɱɟɜɢɞɧɵɦɢ ɝɪɭɩɩɚɦɢ ɩɪɢɱɢɧ ɮɚɤɬɨɪɚɦɢ ɹɜɥɹɸɬɫɹ Ⱥ – ɧɟɩɪɚɜɢɥɶɧɚɹ ɧɟɤɨɪɪɟɤɬɧɚɹ ɪɚɛɨɬɚ ɞɭɯɨɜɨɝɨ ɲɤɚɮɚ ɢɥɢ ɧɚ-
ɪɭɲɟɧɢɟ ɬɟɯɧɨɥɨɝɢɢ Ȼ – ɨɲɢɛɤɢ ɩɟɤɚɪɹ ɩɪɢ ɩɨɞɝɨɬɨɜɤɟ ɬɟɫɬɚ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɤ ɮɚɤɬɨɪɭ Ⱥ ɨɬɧɟɫɟɦ ©ɉɟɪɟɠɨɝª ɢ ©ɇɟɩɪɨɩɟɤɚ ɧɢɟª ɚ ɤ ɮɚɤɬɨɪɭ Ȼ – «ɉɨɫɬɨɪɨɧɧɢɟ ɡɚɩɚɯ ɢ ɜɤɭɫª ɢ ©ɇɟɫɨɨɬɜɟɬɫɬɜɢɟ ɦɚɫɫɵª
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ ɋɨɨɬɧɟɫɟɧɢɟ ɭɫɬɚɧɨɜɥɟɧɧɵɯ ɮɚɤɬɨɪɨɜ ɫ ɩɨ ɤɚɡɚɬɟɥɹɦɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɢɫɯɨɞɹ ɢɡ ɥɢɱɧɵɯ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɵɯ ɡɧɚ ɧɢɣ ɩɪɚɤɬɢɱɟɫɤɨɝɨ ɨɩɵɬɚ ɠɢɡɧɟɧɧɵɯ ɧɚɛɥɸɞɟɧɢɣ ɨɩɪɨɫɚ ɫɩɟɰɢɚɥɢ ɫɬɨɜ ɢɡ ɞɚɧɧɨɣ ɨɛɥɚɫɬɢ ɢɥɢ ɦɟɬɨɞɨɦ ©ɦɨɡɝɨɜɨɝɨ ɲɬɭɪɦɚª ɉɨɷɬɨɦɭ ɩɨɤɚɡɚɬɟɥɢ ɧɟ ɜɫɟɝɞɚ ɦɨɝɭɬ ɛɵɬɶ ɪɚɫɩɪɟɞɟɥɟɧɵ ɩɨ ɮɚɤɬɨɪɚɦ ɪɚɜɧɨ ɦɟɪɧɨ ɩɨ ɞɜɚ ɢɥɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɢ – ɤ ɮɚɤɬɨɪɭ Ⱥ ɢ – ɤ ɮɚɤ ɬɨɪɭ Ȼ ɤɚɤ ɜ ɞɚɧɧɨɦ ɩɪɢɦɟɪɟ
Ɍɚɤɠɟ ɜ ɧɟɤɨɬɨɪɵɯ ɫɥɭɱɚɹ ɩɨɤɚɡɚɬɟɥɶ ɥɢ ɦɨɝɭɬ ɧɟ ɨɬɧɨɫɢɬɫɹ ɤ ɤɚɤɨɦɭ-ɥɢɛɨ ɢɡ ɨɩɪɟɞɟɥɟɧɧɵɯ ɮɚɤɬɨɪɨɜ Ɂɞɟɫɶ ɫɥɟɞɭɟɬ ɜɵɞɟɥɢɬɶ ɢɯ ɜ ɨɬɞɟɥɶɧɭɸ ɝɝɪɭɩɩɭ ɵ ɢ ɢɫɤɥɸɱɢɬɶ ɢɡ ɩɨɫɥɟɞɭɸɳɢɯ ɪɚɫɱɟɬɨɜ
ɋɥɟɞɭɸɳɢɦ ɲɚɝɨɦ ɹɜɥɹɟɬɫɹ ɮɚɤɬɨɪɢɡɚɰɢɹ ȼ ɬɚɛɥɢɰɟ ɭɤɚɡɚɧɵ ɞɜɚ ɮɚɤɬɨɪɚ Ⱥ ɢ Ȼ ɜ ɜɢɞɟ ɫɬɨɥɛɰɨɜ ɚ ɩɟɪɟɦɟɧɧɵɟ ɩɨɤɚɡɚɬɟɥɢ ɛɪɚɤɚ – ɜ ɜɢɞɟ ɫɬɪɨɤ ɉɪɢ ɷɬɨɦ ɤɚɠɞɨɦɭ ɮɚɤɬɨɪɭ ɜ ɫɬɪɨɤɟ ɛɭɞɟɬ ɫɨɨɬɜɟɬ-
15
ɫɬɜɨɜɚɬɶ ɫɪɟɞɧɟɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɤɨɪɪɟɥɹ-
ɰɢɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɟɪɟɦɟɧɧɵɯ ɩɨ ɷɬɨɦɭ ɮɚɤɬɨɪɭ
Ɏ x |
rx1 rx2 rxn |
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Ʉɚɤ ɛɵɥɨ ɨɬɦɟɱɟɧɨ ɜɵɲɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ ɜ ɮɚɤɬɨɪ ɧɨɣ ɦɚɬɪɢɰɟ ɬɚɛɥ ɧɚɡɵɜɚɸɬɫɹ ɮɚɤɬɨɪɧɵɦɢ ɧɚɝɪɭɡɤɚɦɢ ɜɟɫɚɦɢ
Ɍɚɛɥɢɰɚ
Ɍɚɛɥɢɰɚ ɮɚɤɬɨɪɢɡɚɰɢɢ
ɉɨɤɚɡɚɬɟɥɢ ɛɪɚɤɚ |
Ɏɚɤɬɨɪ Ⱥ |
Ɏɚɤɬɨɪ Ȼ |
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ɉɟɪɟɠɨɝ |
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ɇɟɩɪɨɩɟɤɚɧɢɟ |
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ɉɨɫɬɨɪɨɧɧɢɟ ɡɚɩɚɯ ɢ ɜɤɭɫ |
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ɇɟɫɨɨɬɜɟɬɫɬɜɢɟ ɦɚɫɫɵ |
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Ɏɚɤɬɨɪ Ⱥ ɩɟɪɟɠɨɝ |
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Ɏɚɤɬɨɪ Ȼ ɩɟɪɟɠɨɝ |
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Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɜɵɜɨɞ ɨ ɬɨɦ ɱɬɨ ɤɚɤ ɢ ɩɪɟɞɩɨɥɚ |
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ɝɚɥɨɫɶ ɧɟɩɪɚɜɢɥɶɧɚɹ ɧɟɤɨɪɪɟɤɬɧɚɹ ɪɚɛɨɬɚ ɞɭɯɨɜɨɝɨ ɲɤɚɮɚ ɢɥɢ ɧɚ-
ɪɭɲɟɧɢɟ ɬɟɯɧɨɥɨɝɢɢ ɮɚɤɬɨɪ Ⱥ ɡɚɦɟɬɧɭɸ ɢɥɢ ɡɧɚɱɢɦɭɸ ɜɡɚɢɦɨɫɜɹɡɶ ɫ ɬɚɤɢɦ ɛɪɚɤɨɦ ɤɚɤ ©ɉɟɪɟɠɨɝª ɢ ©ɇɟɩɪɨɩɟɤɚɧɢɟª ɚ ɨɲɢɛɤɢ ɩɟɤɚɪɹ ɩɪɢ ɩɨɞɝɨɬɨɜɤɟ ɬɟɫɬɚ ɮɚɤɬɨɪ Ȼ ɫ ©ɉɨɫɬɨɪɨɧɧɢɟ ɡɚɩɚɯ ɢ ɜɤɭɫª ɢ ©ɇɟɫɨ ɨɬɜɟɬɫɬɜɢɟ ɦɚɫɫɵª ɗɬɨ ɬɚɤɠɟ ɩɨɡɜɨɥɹɟɬ ɧɚɦ ɜ ɬɨɣ ɠɟ ɩɪɢɧɚɞɥɟɠɧɨɫɬɢ ɫɱɢɬɚɬɶ ɞɚɧɧɵɟ ɮɚɤɬɨɪɵ ɨɫɧɨɜɧɵɦɢ ɩɪɢɱɢɧɚɦɢ ɨɛɪɚɡɨɜɚɧɢɹ ɜɵɹɜɥɟɧ ɧɵɯ ɪɚɡɧɨɜɢɞɧɨɫɬɟɣ ɛɪɚɤɚ Ɉɞɧɚɤɨ ɫ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ ɩɨɤɚɡɚɬɟɥɢ ɯɨɬɶ ɢ ɡɧɚɱɢɦɵɟ ɧɨ ɧɟɜɵɫɨɤɢɟ ɗɬɨ ɝɨɜɨɪɢɬ ɨ ɬɨɦ ɱɬɨ ɢ ɞɪɭɝɢɟ ɮɚɤɬɨɪɵ ɦɨɝɭɬ ɨɤɚɡɵɜɚɬɶ ɜɥɢɹɧɢɟ ɧɚ ɨɛɪɚɡɨɜɚɧɢɹ ɛɪɚɤɚ ɇɚɩɪɢɦɟɪ ɮɚɤɬɨɪɧɵɟ
ɧɚɝɪɭɡɤɢ ɩɨɤɚɡɚɥɢ ɹɜɧɨɟ ɧɚɥɢɱɢɟ ɜɡɚɢɦɨɫɜɹɡɢ ɦɟɠɞɭ ɨɲɢɛɤɚɦɢ ɩɟɤɚɪɹ ɢ ɩɟɪɟɠɨɝɨɦ ɚ ɬɚɤɠɟ ɦɟɠɞɭ ɧɟɩɪɚɜɢɥɶɧɨɣ ɧɟɤɨɪɪɟɤɬɧɨɣ ɪɚɛɨɬɨɣ ɞɭ ɯɨɜɨɝɨ ɲɤɚɮɚ ɢɥɢ ɧɚɪɭɲɟɧɢɟɦ ɬɟɯɧɨɥɨɝɢɢ ɢ ɩɨɹɜɥɟɧɢɟɦ ɩɨɫɬɨɪɨɧɧɟɝɨ ɡɚɩɚɯɚ ɢ ɜɤɭɫɚ
Ⱦɥɹ ɩɨɞɬɜɟɪɠɞɟɧɢɹ ɩɨɥɧɨɬɵ ɭɤɚɡɚɧɧɵɯ ɮɚɤɬɨɪɨɜ ɢɥɢ ɩɪɢɱɢɧ ɜɥɢɹɸɳɢɣ ɧɚ ɨɛɪɚɡɨɜɚɧɢɟ ɛɪɚɤɚ ɩɪɢɦɟɧɹɟɬɫɹ ɞɢɫɩɟɪɫɢɨɧɧɵɣ ɚɧɚɥɢɡ Ɉɧ ɬɚɤɠɟ ɩɪɢɦɟɧɢɦ ɞɥɹ ɪɚɧɠɢɪɨɜɚɧɢɹ ɮɚɤɬɨɪɨɜ ɩɨ ɡɧɚɱɢɦɨɫɬɢ
Ⱦɢɫɩɟɪɫɢɹɨɩɪɟɞɟɥɹɟɬɫɹɤɚɤɫɭɦɦɚɤɜɚɞɪɚɬɨɜɮɚɤɬɨɪɧɵɯɜɟɫɨɜ ɚ ɩɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɞɨɥɸ ɨɛɳɟɝɨ ɩɟɪɟɤɪɵɬɢɹ ɨɯɜɚɬɚ ɮɚɤɬɨɪɚɦɢ ɤɚɠɞɨɝɨ ɤɨɧɤɪɟɬɧɨɝɨ ɩɨɤɚɡɚɬɟɥɹ Ɍɨ ɟɫɬɶ ɩɪɨɫɬɵɦɢ ɫɥɨ ɜɚɦɢ ɩɪɢ ɡɧɚɱɟɧɢɢ ɩɟɪɟɤɪɵɬɢɟ ɭɤɚɡɚɧɧɵɯ ɮɚɤɬɨɪɨɜ ɩɨ ɩɨɤɚɡɚ-
ɬɟɥɸ ɫɨɫɬɚɜɥɹɟɬ ɗɬɨ ɜɵɫɨɤɨɟ ɡɧɚɱɟɧɢɟ ɱɬɨ ɝɨɜɨɪɢɬ ɨ ɛɨɥɶɲɨɣ ɨɛɥɚɫɬɢ ɨɯɜɚɬɚ ɉɪɢ ɷɬɨɦ ɨɫɬɚɟɬɫɹ ɧɟɛɨɥɶɲɚɹ ɞɨɥɹ ɪɚɜɧɚɹ ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɫɨɞɟɪɠɚɬɶ ɢɧɵɟ ɧɟ ɪɚɫɫɦɨɬɪɟɧɧɵɟ ɮɚɤɬɨɪɵ ɜɥɢɹɸɳɢɟ ɧɚ ɞɚɧ ɧɵɣ ɩɨɤɚɡɚɬɟɥɶ
D x y i Ɏ ɯ |
2 Ɏ \ |
2 ɎL |
2 |
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Ɂɧɚɱɢɦɨɫɬɶ ɤɚɠɞɨɝɨ ɨɬɞɟɥɶɧɨɝɨ ɮɚɤɬɨɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɫɭɦɦɚ ɤɜɚɞɪɚɬɨɜ ɮɚɤɬɨɪɧɵɯ ɜɟɫɨɜ ɩɨ ɜɫɟɦ ɩɨɤɚɡɚɬɟɥɹɦ
ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɞɨɥɹ ɨɛɳɟɝɨ ɩɟɪɟɤɪɵɬɢɹ ɩɨ ɩɨɤɚɡɚɬɟɥɹɦ ɛɭɞɟɬ ɪɚɜɧɚ
D |
2 2 |
ɩɟɪɟɠɨɝ |
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Dɧɟɩɪɨɩɟɤ |
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Dɩɨɫɬ ɡɚɩ |
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Dɧɟɫɨɨɬ ɦɚɫɫɵ
Ⱦɢɫɩɟɪɫɢɹ ɮɚɤɬɨɪɨɜ
D |
2 2 2 2 |
ɮɚɤɬɨɪȺ |
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DɮɚɤɬɨɪȻ
Ʉɚɤ ɜɢɞɧɨ ɞɢɫɩɟɪɫɢɹ ɮɚɤɬɨɪɚ Ȼ ɛɨɥɶɲɟ ɱɟɦ ɭ ɮɚɤɬɨɪɚ Ⱥ ɗɬɨ ɝɨ ɜɨɪɢɬ ɱɬɨ ɨɲɢɛɤɢ ɩɟɤɚɪɹ ɩɪɢ ɩɨɞɝɨɬɨɜɤɟ ɬɟɫɬɚ ɢɦɟɟɬ ɛɨɥɶɲɭɸ ɡɧɚɱɢ ɦɨɫɬɶ ɚ ɡɧɚɱɢɬ ɢ ɜɥɢɹɧɢɟ ɧɚ ɩɨɹɜɥɟɧɢɟ ɛɪɚɤɚ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɧɟɩɪɚ ɜɢɥɶɧɨɣ ɧɟɤɨɪɪɟɤɬɧɨɣ ɪɚɛɨɬɨɣ ɞɭɯɨɜɨɝɨ ɲɤɚɮɚ ɢɥɢ ɧɚɪɭɲɟɧɢɟɦ ɬɟɯ ɧɨɥɨɝɢɢ ɛɨɥɶɲɟ
Ɍɚɤɠɟ ɞɨɥɹ ɨɛɳɟɝɨ ɩɟɪɟɤɪɵɬɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɜɵɫɨɤɚɹ ɢ ɧɚɯɨ ɞɢɬɫɹ ɜ ɞɢɚɩɚɡɨɧɟ ɨɬ ɞɨ ɢɥɢ ɨɬ ɞɨ ɇɟɨɯɜɚɱɟɧɧɚɹɧɟɢɡɜɟɫɬɧɚɹ ɨɛɥɚɫɬɶ ɫɨɫɬɚɜɥɹɟɬ ɨɬ ɞɨ ɉɪɢ ɷɬɨɦ ɧɟɥɶɡɹ ɝɨ-
ɜɨɪɢɬɶ ɨ ɜɵɫɨɤɨɣ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɮɚɤɬɨɪɧɨɝɨ ɚɧɚɥɢɡɚ Ɂɞɟɫɶ ɫɥɟɞɭɟɬ ɪɚɫɲɢɪɢɬɶ ɤɨɥɢɱɟɫɬɜɨ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɮɚɤ-
ɬɨɪɨɜ ɥɢɛɨ ɭɜɟɥɢɱɢɬɶ ɨɛɴɟɦ ɢɥɢ ɞɢɚɩɚɡɨɧ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ
Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ
Ɋɟɡɭɥɶɬɚɬɵ ɤɨɧɬɪɨɥɹ ɤɚɱɟɫɬɜɚ ɞɟɬɚɥɟɣ ɩɨɥɭɱɟɧɧɵɯ ɜ ɪɟɡɭɥɶ
ɬɚɬɟ ɬɨɤɚɪɧɨɣ ɨɛɪɚɛɨɬɤɢ
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Ɋɚɡɧɨɜɢɞɧɨɫɬɢ ɛɪɚɤɚ |
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ɇɟɫɨɨɬɜɟɬɫɬɜɢɟ ɲɟɪɨɯɨɜɚɬɨɫɬɢ |
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ɩɨɜɟɪɯɧɨɫɬɢ ɞɟɬɚɥɢ |
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ɇɟɫɨɨɬɜɟɬɫɬɜɢɟ ɞɢɚɦɟɬɪɚ ɞɟɬɚɥɢ |
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ɂɡɦɟɧɟɧɢɟ ɰɜɟɬɚ |
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Ɉɬɫɭɬɫɬɜɢɟ ɮɚɫɤɢ |
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ɐɚɪɚɩɢɧɵ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ |
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ɋɥɟɞɵ ɪɠɚɜɱɢɧɵ |
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ɇɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɮɚɤɬɨɪɵ ɩɪɢɱɢɧɵ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɛɪɚɤɚ ɢ ɢɯ ɜɥɢɹɧɢɟ ɧɚ ɤɨɧɤɪɟɬɧɵɟ ɩɨɤɚɡɚɬɟɥɢ ɛɪɚɤɚ Ɍɚɤɠɟ ɨɩɪɟɞɟɥɢɬɶɫɹ ɫ ɧɚɢɛɨɥɟɟ ɡɧɚɱɢɦɵɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ ɤɨɬɨɪɵɟ ɬɪɟɛɭɸɬ ɩɟɪɜɨɨɱɟɪɟɞ ɧɨɝɨ ɪɟɲɟɧɢɹ
Ɋɟɲɢɬɟ ɡɚɞɚɱɭ ɜ ɨɛɥɚɫɬɢ ɩɪɨɢɡɜɨɞɫɬɜɚ ɢ ɤɨɧɬɪɨɥɹ ɤɚɱɟɫɬɜɚ ɲɜɟɣɧɨɣ ɩɪɨɞɭɤɰɢɢ Ⱦɥɹ ɷɬɨɝɨ ɚɧɚɥɨɝɢɱɧɨ ɪɚɫɫɦɨɬɪɟɧɧɨɦɭ ɜɵɲɟ ɩɪɢ ɦɟɪɭ ɩɪɟɞɥɨɠɢɬɟ ɪɚɡɧɨɜɢɞɧɨɫɬɢ ɜɨɡɦɨɠɧɨɝɨ ɛɪɚɤɚ ɧɟ ɦɟɧɟɟ ɢ ɮɚɤ ɬɨɪɨɦ ɫɜɹɡɚɧɧɵɯ ɫ ɧɢɦɢ Ⱦɚɧɧɵɟ ɩɨ ɤɨɥɢɱɟɫɬɜɭ ɛɪɚɤɚ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɡɚɩɨɥɧɢɬɟ ɧɚ ɤɚɠɞɵɣ ɦɟɫɹɰ ɧɚ ɨɞɢɧ ɝɨɞ ɦɟɫɹɰɟɜ ȼ ɯɨɞɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɨɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɟɟ ɡɧɚɱɢɦɵɟ ɞɟɮɟɤɬɵ ɡɧɚɱɢɦɨɫɬɶ ɮɚɤɬɨɪɨɜ ɢ ɨɛɳɭɸ ɡɧɚɱɢɦɨɫɬɶ ɤɚɠɞɨɝɨ ɢɡ ɞɟɮɟɤɬɨɜ ɞɢɫɩɟɪɫɢɢ
3. Количественные методы прогнозирования
Ⱥɧɚɥɢɡ ɜɪɟɦɟɧɧɵɯ ɪɹɞɨɜ
Ʉ ɚɧɚɥɢɡɭ ɜɪɟɦɟɧɧɵɯ ɪɹɞɨɜ ɨɬɧɨɫɹɬɫɹ ɫɥɟɞɭɸɳɢɟ ɦɟɬɨɞɵɦɟɬɨɞ ɩɨɞɜɢɠɧɨɝɨ ɫɤɨɥɶɡɹɳɟɝɨ ɫɪɟɞɧɟɝɨɦɟɬɨɞ ɜɡɜɟɲɟɧɧɨɝɨ ɫɤɨɥɶɡɹɳɟɝɨ ɫɪɟɞɧɟɝɨɦɟɬɨɞ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɝɨ ɫɝɥɚɠɢɜɚɧɢɹɦɟɬɨɞ ɩɪɨɟɰɢɪɨɜɚɧɢɹ ɬɪɟɧɞɚ
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ ɉɟɪɜɵɟ ɬɪɢ ɦɟɬɨɞɚ ɢɫɩɨɥɶɡɭɸɬɫɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ ɞɥɹ ɫɝɥɚɠɢɜɚɧɢɹ ɮɢɥɶɬɪɚɰɢɢ ɞɚɧɧɵɯ ɬɨ ɟɫɬɶ ɜ ɬɟɯ ɫɥɭɱɚɹɯ ɤɨɝɞɚ ɧɟɨɛɯɨɞɢɦɨ ɭɫɪɟɞɧɢɬɶ ɞɚɧɧɵɟ ɢ ɜɵɹɜɢɬɶ ɢɯ ɨɛɳɭɸ ɡɚɤɨɧɨɦɟɪ ɧɨɫɬɶ ɇɚɢɛɨɥɟɟ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɚɧɚɥɢɡɚ ɢ ɫɝɥɚɠɢɜɚɧɢɹ ɪɚɞɢɨ ɫɢɝɧɚɥɨɜ ɭɦɟɧɶɲɟɧɢɹ ɩɨɦɟɯ ɜɢɡɭɚɥɢɡɚɰɢɢ ɮɨɧɞɨɜɵɯ ɞɚɧɧɵɯ ɰɟɧɚ ɚɤɰɢɢ ɧɟɮɬɢ ɢ ɬ ɞ ɢ ɨɩɪɟɞɟɥɟɧɢɹ ɨɛɳɟɣ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ ɢɡɦɟɧɟɧɢɹ
Ɇɟɬɨɞ ɩɨɞɜɢɠɧɨɝɨ ɫɤɨɥɶɡɹɳɟɝɨ ɫɪɟɞɧɟɝɨ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ ɱɬɨ ɪɚɫɱɟɬ ɩɨɤɚɡɚɬɟɥɹ ɧɚ ɩɪɨɝɧɨɡɢɪɭɟɦɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɫɬɪɨɢɬɫɹ ɩɭɬɟɦ ɭɫɪɟɞɧɟɧɢɹ ɡɧɚɱɟɧɢɣ ɷɬɨɝɨ ɩɨɤɚɡɚɬɟɥɹ ɡɚ ɧɟɫɤɨɥɶɤɨ ɩɪɟɞɲɟ ɫɬɜɭɸɳɢɯ ɩɟɪɢɨɞɨɜ
Ɋɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪ ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɜɵɲɟ ɬɚɛɥ ɉɨ ɧɟɦɭ ɢɡ ɜɟɫɬɧɨ ɤɨɥɢɱɟɫɬɜɨ ɯɥɟɛɨɛɭɥɨɱɧɵɯ ɢɡɞɟɥɢɣ ɩɪɨɢɡɜɟɞɟɧɧɵɯ ɜ ɬɟɱɟɧɢɟ ɧɟɞɟɥɢ ɢ ɢɦɟɸɳɢɯ «ɉɟɪɟɠɨɝª ɫɦ ɬɚɛɥ 10
Ɍɚɛɥɢɰɚ 10
Ʉɨɥɢɱɟɫɬɜɨ ɯɥɟɛɨɛɭɥɨɱɧɵɯ ɢɡɞɟɥɢɣ ɢɦɟɸɳɢɯ ©ɉɟɪɟɠɨɝª
ɉɨɧɟɞɟɥɶɧɢɤ |
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ȼɬɨɪɧɢɤ |
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ɋɪɟɞɚ |
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ɑɟɬɜɟɪɝ |
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ɉɹɬɧɢɰɚ |
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ɋɭɛɛɨɬɚ |
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ȼɨɫɤɪɟɫɟɧɶɟ |
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ɉɪɟɞɫɬɚɜɢɦ ɟɟ ɜ ɜɢɞɟ ɜɪɟɦɟɧɧɨɝɨ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɹɞɚ ɞɚɧɧɵɯɬɚɛɥ 11
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Ɍɚɛɥɢɰɚ 11 |
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Ⱦɢɧɚɦɢɱɟɫɤɢɣ ɪɹɞ ɞɚɧɧɵɯ |
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ɉɪɢɦɟɱɚɧɢɟ t – ɭɫɥɨɜɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ x – ɤɨɥɢɱɟɫɬɜɨ ɢɡɞɟɥɢɣ ɲɬ
ɂɫɩɨɥɶɡɭɹ ɦɟɬɨɞ ɩɨɞɜɢɠɧɨɝɨ ɫɤɨɥɶɡɹɳɟɝɨ ɫɪɟɞɧɟɝɨ ɦɨɠɧɨ ɜɵ ɩɨɥɧɢɬɶ ɫɝɥɚɠɢɜɚɧɢɟ ɞɚɧɧɵɯ ɢ ɫɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɞɚɧɧɵɟ ɧɚ ɫɥɟɞɭɸɳɢɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ – ɧɚ ɞɟɧɶ ɢɥɢ ɧɚ ɫɥɟɞɭɸɳɢɣ ɩɨ-
ɧɟɞɟɥɶɧɢɤ
20