Планирование эксперимента. Учебное пособие-1
.pdfɊɚɫɫɱɢɬɚɟɦ ɩɨ ɦɨɞɟɥɢ ɡɧɚɱɟɧɢɹ ɬɨɤɚ ɛɟɡ ɭɱɟɬɚ ɞɜɨɣɧɵɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ
ɮɚɤɬɨɪɨɜ
yc b b x b x x x
ɢ ɫ ɭɱɟɬɨɦ ɞɜɨɣɧɵɯ ɫɨɱɟɬɚɧɢɣ ɮɚɤɬɨɪɨɜ
ycc b b x b x b x x x x x x
ɉɨɥɭɱɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ Ʉɚɤ ɜɢɞɧɨ ɢɡ ɬɚɛɥɢɰɵ
ɡɧɚɱɟɧɢɹ ɬɨɤɚ ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɦɨɞɟɥɢ ɫ ɭɱɟɬɨɦ ɞɜɨɣɧɵɯ ɫɨɱɟɬɚɧɢɣ ɮɚɤɬɨɪɨɜ
ɩɨɥɧɨɫɬɶɸ ɫɨɜɩɚɞɚɸɬ ɫ ɢɡɦɟɪɟɧɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɜ ɬɟɯ ɬɨɱɤɚɯ ɜ ɤɨɬɨɪɵɯ ɩɪɨ
ɜɨɞɢɥɢɫɶ ɢɡɦɟɪɟɧɢɹ
ɉɪɨɜɟɪɢɦ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɜ ɩɪɨɢɡɜɨɥɶɧɨɣ ɬɨɱɤɟ ɧɚɩɪɢɦɟɪ ɩɪɢ ɧɚɩɪɹɠɟɧɢɢ
ȼx |
ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɢ Ɉɦx ɋɪɚɜɧɢɦ ɡɧɚɱɟɧɢɟ ɧɚɣɞɟɧ |
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ɧɨɟ ɩɨ ɦɨɞɟɥɢ ɫ ɢɡɦɟɪɟɧɧɵɦ ɡɧɚɱɟɧɢɟɦ ɧɚɣɞɟɧɧɵɦ ɩɨ ɮɨɪɦɭɥɟ |
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Ɂɧɚɱɟɧɢɟ ɬɨɤɚ ɩɨ ɦɨɞɟɥɢ ɫ ɭɱɟɬɨɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɮɚɤɬɨɪɨɜ ɫɨɫɬɚɜɥɹɟɬ |
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ycc |
b b x b x b x x |
x x x x |
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ɢ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɢɡɦɟɪɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɧɚ ɜɟɥɢɱɢɧɭ ± ɱɬɨ ɫɨɫɬɚɜɥɹɟɬ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɜ ɬɨɱɤɟ ɫ ɧɚɩɪɹɠɟɧɢɟɦ ȼ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ Ɉɦ ɬɚɤɠɟ ɤɚɤ ɢ ɜ ɰɟɧɬɪɚɥɶɧɨɣ ɬɨɱɤɟ ɢɦɟɟɬɫɹ ɪɚɫɯɨɠɞɟɧɢɟ ɦɟɠɞɭ ɬɨɤɨɦ ɧɚɣɞɟɧɧɵɦ ɩɨ ɦɨɞɟɥɢ ɢ ɢɡɦɟɪɟɧɧɵɦ ɢɞɟɚɥɶɧɵɦ ɡɧɚɱɟɧɢɟɦ ɗɬɨ ɝɨɜɨɪɢɬ ɨ ɧɚɥɢɱɢɢ ɧɟɥɢɧɟɣɧɨɫɬɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢI f U R Ɍɨɤ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɥɢɧɟɣɧɨ ɬɨɥɶɤɨ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɡɧɚɱɟɧɢɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ȿɫɥɢ ɡɧɚɱɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɬɚɤɠɟ ɢɡɦɟɧɹɟɬɫɹ ɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɫɬɚɧɨɜɢɬɫɹ ɧɟɥɢɧɟɣɧɨɣ
ɉɪɢɦɟɪ ɩɨɤɚɡɵɜɚɟɬ ɱɬɨ ɩɨɜɟɪɯɧɨɫɬɶ ɩɥɚɧɚ ɉɎɗ ɫɨɜɩɚɞɚɹ ɫ ɪɟɚɥɶɧɨɣ ɩɨ
ɜɟɪɯɧɨɫɬɶɸ ɜ ɝɪɚɧɢɱɧɵɯ ɬɨɱɤɚɯ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɪɟɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɞɪɭɝɢɯ
ɬɨɱɤɚɯ ɮɚɤɬɨɪɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɜ ɱɚɫɬɧɨɫɬɢ ɜ ɰɟɧɬɪɟ ɩɥɚɧɚ ɚ ɬɚɤɠɟ ɜ ɬɨɱɤɟ ɯ ɢɯ
ȼ ɪɚɫɫɦɨɬɪɟɧɧɨɦ ɩɪɢɦɟɪɟ ɜɵɛɪɚɧ ɛɨɥɶɲɨɣ ɞɢɚɩɚɡɨɧ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɚɤɫɢɦɚɥɶɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɞɜɚ ɪɚɡɚ ɛɨɥɶɲɟ ɦɢɧɢɦɚɥɶɧɨɝɨ
ɱɬɨ ɧɟ ɞɚɟɬ ɩɨɥɭɱɢɬɶ ɜɵɫɨɤɭɸ ɬɨɱɧɨɫɬɶ ɦɨɞɟɥɢ Ⱦɥɹ ɩɨɜɵɲɟɧɢɹ ɬɨɱɧɨɫɬɢ ɦɨ
ɞɟɥɢ ɧɟɨɛɯɨɞɢɦɨ ɭɦɟɧɶɲɚɬɶ ɞɢɚɩɚɡɨɧɵ ɜɚɪɶɢɪɨɜɚɧɢɹ ɮɚɤɬɨɪɨɜ Ɍɚɤ ɟɫɥɢ ɭɦɟɧɶɲɢɬɶ ɞɢɚɩɚɡɨɧ ɢɡɦɟɧɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɨ Ɉɦ ɬɨ
ɢɡɦɟɪɟɧɧɚɹ ɜɟɥɢɱɢɧɚ ɬɨɤɚ ɜ ɧɭɥɟɜɨɣ ɬɨɱɤɟ I Ⱥ ɂɡɦɟɪɟɧɧɵɟ
ɡɧɚɱɟɧɢɹ ɜ ɱɟɬɵɪɟɯ ɨɩɵɬɚɯ ɛɭɞɭɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
Ⱥ
ȼɟɥɢɱɢɧɚ ɬɨɤɚ ɜ ɧɭɥɟɜɨɣ ɬɨɱɤɟ ɨɩɪɟɞɟɥɢɬɫɹ ɩɨ ɤɨɷɮɮɢɰɢɟɧɬɭ
b |
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ɢ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɢɡɦɟɪɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɜɫɟɝɨ ɧɚ Ⱥ ɱɬɨ ɫɨɫɬɚɜɥɹɟɬ
ɍɦɟɧɶɲɟɧɢɟ ɞɢɚɩɚɡɨɧɨɜ ɜɚɪɶɢɪɨɜɚɧɢɹ ɮɚɤɬɨɪɨɜ ± ɷɬɨ ɨɞɢɧ ɢɡ ɩɭɬɟɣ ɩɨ
ɜɵɲɟɧɢɹ ɬɨɱɧɨɫɬɢ ɩɨɥɢɧɨɦɨɜ ȿɫɥɢ ɢɧɬɟɪɟɫ ɩɪɟɞɫɬɚɜɥɹɟɬ ɜɟɫɶ ɞɢɚɩɚɡɨɧ ɢɡɦɟ
ɧɟɧɢɹ ɮɚɤɬɨɪɚ ɬɨ ɦɨɠɧɨ ɪɚɡɛɢɬɶ ɜɟɫɶ ɞɢɚɩɚɡɨɧ ɧɚ ɩɨɞɞɢɚɩɚɡɨɧɵ ɧɚɩɪɢɦɟɪ
ɧɚ ɩɨɞɞɢɚɩɚɡɨɧɨɜ ɞɥɹ ɧɚɲɟɝɨ ɩɪɢɦɟɪɚ ɢ ɞɥɹ ɤɚɠɞɨɝɨ ɩɨɞɞɢɚɩɚɡɨɧɚ ɩɨɫɬɪɨ ɢɬɶ ɫɜɨɣ ɩɥɚɧ ɉɎɗ ɗɬɨ ɧɟ ɱɬɨ ɢɧɨɟ ɤɚɤ ɥɢɧɟɚɪɢɡɚɰɢɹ ɬɨ ɟɫɬɶ ɩɪɟɞɫɬɚɜɥɟ ɧɢɟ ɧɟɥɢɧɟɣɧɨɣ ɦɨɞɟɥɢ ɧɟɫɤɨɥɶɤɢɦɢ ɥɢɧɟɣɧɵɦɢ Ɍɚɤɨɣ ɩɭɬɶ ɩɨɜɵɲɟɧɢɹ ɬɨɱ ɧɨɫɬɢ ɨɬɥɢɱɚɟɬɫɹ ɜɵɫɨɤɨɣ ɬɪɭɞɨɟɦɤɨɫɬɶɸ ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɩɪɢɞɟɬɫɹ ɩɪɨɞɟ ɥɚɬɶ ɨɩɵɬɨɜ ɜɦɟɫɬɨ ɯ Ɍɪɭɞɨɟɦɤɨɫɬɶ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɨɫɨɛɟɧɧɨ ɤɨɝɞɚ ɧɟ ɨɞɢɧ ɮɚɤɬɨɪ ɪɚɡɛɢɜɚɟɬɫɹ ɧɚ ɩɨɞɞɢɚɩɚɡɨɧɵ ɚ ɧɟɫɤɨɥɶɤɨ
ɂ ɡɞɟɫɶ ɜɚɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɚɤɨɣ ɢɦɟɧɧɨ ɮɚɤɬɨɪ ɢɥɢ ɮɚɤɬɨɪɵ ɩɨɪɨɠɞɚɸɬ ɧɟɥɢɧɟɣɧɨɫɬɶ ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɬɚɤɢɦ ɮɚɤɬɨɪɨɦ ɹɜɥɹɟɬɫɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɂ ɢɦɟɧɧɨ ɞɢɚɩɚɡɨɧ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɚɡɛɢɜɚɟɬɫɹ ɧɚ ɩɨɞɞɢɚɩɚɡɨɧɵ
ɇɨ ɟɫɥɢ ɜɡɹɬɶ ɞɢɚɩɚɡɨɧ ɢɡɦɟɧɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɮɚɤɬɨɪɚ ɤɨɬɨɪɵɣ ɧɟ ɜɵ
ɡɵɜɚɟɬ ɧɟɥɢɧɟɣɧɨɫɬɶ ɛɨɥɶɲɨɣ ɧɚɩɪɢɦɟɪ ɨɬ ɞɨ ȼ ɚ ɞɢɚɩɚɡɨɧ ɢɡɦɟɧɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɮɚɤɬɨɪɚ ɩɨɪɨɠɞɚɸɳɟɝɨ ɧɟɥɢɧɟɣɧɨɫɬɶ ɦɚɥɵɦ ɧɚɩɪɢɦɟɪ ɨɬ ɞɨ Ɉɦ ɬɨ ɩɨɥɭɱɢɦ ɜɵɫɨɤɭɸ ɬɨɱɧɨɫɬɶ ɦɨɞɟɥɢ ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɢɡɦɟɪɟɧ ɧɵɟ ɡɧɚɱɟɧɢɹ ɨɬɤɥɢɤɚ ɜ ɱɟɬɵɪɟɯ ɨɩɵɬɚɯ ɛɭɞɭɬ ɫɨɫɬɚɜɥɹɬɶ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
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Ɍɨɝɞɚ ɤɨɷɮɮɢɰɢɟɧɬb |
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ɂɞɟɚɥɶɧɨɟ ɢɡɦɟɪɟɧɧɨɟ ɡɧɚ |
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ɱɟɧɢɟ ɬɨɤɚ ɜ ɰɟɧɬɪɟ ɩɥɚɧɚ ɩɪɢ ɧɭɥɟɜɵɯ ɩɪɢɜɟɞɟɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɮɚɤɬɨɪɨɜ
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Ⱥ Ɋɚɫɯɨɠɞɟɧɢɟ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦb ɜɫɟɝɨ ɩɨ |
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ɨɩɪɟɞɟɥɢɬɫɹ ɤɚɤ |
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ɝɪɟɲɧɨɫɬɶ ɪɚɜɧɚ ɢ ɜɢɞɧɨ ɱɬɨ ɬɨɱɧɨɫɬɶ ɦɨɞɟɥɢ ɧɟ ɭɯɭɞɲɢɥɚɫɶ
Ⱦɪɭɝɨɣ ɩɭɬɶ ɩɨɜɵɲɟɧɢɹ ɬɨɱɧɨɫɬɢ ɦɨɞɟɥɢ ± ɟɟ ɭɫɥɨɠɧɟɧɢɟ ɢ ɞɨɛɚɜɥɟɧɢɟ ɜ
ɩɨɥɢɧɨɦ ɤɜɚɞɪɚɬɨɜ ɮɚɤɬɨɪɨɜ Ⱦɨɫɬɪɨɢɦ ɩɥɚɧ ɉɎɗ ɞɨ ɈɐɄɉ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɢɫɩɨɥɶɡɭɹ ɩɪɢ ɷɬɨɦ ɜ
ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɧɰɢɩɨɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɩɥɚɧɢɪɨɜɚɧɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚ ɢɧɮɨɪɦɚɰɢɸ ɜ ɪɚɧɟɟ ɫɞɟɥɚɧɧɵɯ ɨɩɵɬɚɯ Ⱦɨɛɚɜɢɦ ɜ ɪɚɫɲɢɪɟɧɧɭɸ ɦɚɬɪɢɰɭ ɩɥɚ ɧɚ ɉɎɗ ɞɜɚ ɫɬɨɥɛɰɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɤɜɚɞɪɚɬɚɦ ɮɚɤɬɨɪɨɜ Ⱦɥɹ ɫɨɯɪɚɧɟ ɧɢɹ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɩɥɚɧɚ ɢɫɩɨɥɶɡɭɟɦ ɩɚɪɚɦɟɬɪ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɚɤɨɬɨɪɵɣ
ɞɥɹ ɩɥɚɧɚ ɫ ɞɜɭɦɹ ɮɚɤɬɨɪɚɦɢ ɪɚɜɟɧ
Ʉ ɜɵɩɨɥɧɟɧɧɵɦ ɱɟɬɵɪɟɦ ɨɩɵɬɚɦ ɞɨɛɚɜɢɦ ɟɳɟ ɩɹɬɶ ɨɩɵɬɨɜ ± ɱɟɬɵɪɟ ɨɩɵ ɬɚ ɡɜɟɡɞɧɨɝɨ ɩɥɚɧɚ ɩɨ ɞɜɚ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɢɡɦɟɪɟɧɢɣ ɧɚ ɤɚɠɞɵɣ ɮɚɤɬɨɪ ɢɨɞɢɧɨɩɵɬɜɰɟɧɬɪɟɩɥɚɧɚ©ɉɥɟɱɨªɡɜɟɡɞɧɵɯɬɨɱɟɤɚ ɞɥɹɞɜɭɯɮɚɤɬɨɪɧɨɝɨ ɩɥɚɧɚ ɪɚɜɧɨ ɉɨɥɭɱɢɦ ɬɚɛɥɢɰɭ ɜ ɤɨɬɨɪɭɸ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɜɧɟɫɟɦ ɪɟɡɭɥɶ ɬɚɬɵ ɢɡɦɟɪɟɧɢɣ ɢ ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɦɨɞɟɥɢ ɡɧɚɱɟɧɢɹ ɬɨɤɚ
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Ɍ ɚ ɛ ɥ ɢ ɰ ɚ |
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ɈɐɄɉ ɝɨ ɩɨɪɹɞɤɚ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɢɡɦɟɪɟɧɢɣ ɢ ɪɚɫɱɟɬɨɜ |
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ɂɡɦɟɪɟɧɧɵɟ |
Ɋɚɫɫɱɢɬɚɧɧɵɟ |
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ɇɨɦɟɪ |
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x |
x |
x |
ɯ ɯ |
ɯ ɚ |
ɯ ɚ |
ɡɧɚɱɟɧɢɹ |
ɡɧɚɱɟɧɢɹ |
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ɨɩɵɬɚ |
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Ɉɛɳɟɟ ɤɨɥɢɱɟɫɬɜɨ ɢɡɦɟɪɟɧɢɣ ɜ ɬɚɤɨɦ ɩɥɚɧɟ
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ɝɞɟN ± ɱɢɫɥɨ ɨɩɵɬɨɜ ɜ ɩɥɚɧɟ ɉɎɗ ɪɚɜɧɨɟ |
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ɉɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ b |
ɧɟ ɨɩɪɟɞɟɥɹɟɬ ɜɟɥɢɱɢɧɭ |
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ɬɨɤɚ ɜ ɰɟɧɬɪɟ ɩɥɚɧɚ ɢɡɦɟɪɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɪɚɜɧɨ Ⱥ Ʉɨɷɮɮɢ ɰɢɟɧɬb ɫɤɨɪɪɟɤɬɢɪɭɟɬɫɹ ɩɨɫɥɟ ɧɚɯɨɠɞɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜb ɢb Ɂɧɚɱɟ ɧɢɟ ɬɨɤɚ ɜ ɰɟɧɬɪɟ ɩɥɚɧɚ ɨɩɪɟɞɟɥɢɬɫɹ ɤɚɤ ɫɤɨɪɪɟɤɬɢɪɨɜɚɧɧɨɟ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢ ɰɢɟɧɬɚb
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ɱɬɨ ɝɨɜɨɪɢɬ ɨ ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɥɧɨɦ ɫɨɜɩɚɞɟɧɢɢ ɫ ɢɡɦɟɪɟɧɧɨɣ ɜɟɥɢɱɢɧɨɣ ɬɨɤɚ
ɜ ɰɟɧɬɪɟ ɩɥɚɧɚ ɪɚɜɧɨɣ Ⱥ
Ɋɚɫɫɱɢɬɚɟɦ ɡɧɚɱɟɧɢɹ ɬɨɤɚ ɜ ɬɨɱɤɚɯ ɢɡɦɟɪɟɧɢɹ ɩɨ ɦɨɞɟɥɢ ɜ ɜɢɞɟ ɩɨɥɢɧɨɦɚ
ɝɨ ɩɨɪɹɞɤɚ
yb b x b x b x x b x b x
x x x x x
Ɋɚɫɫɱɢɬɚɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ ɂɡ ɬɚɛɥɢɰɵ ɜɢɞɧɨ
ɱɬɨ ɪɚɫɯɨɠɞɟɧɢɣ ɫ ɢɡɦɟɪɟɧɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ
ɪɚɫɯɨɠɞɟɧɢɟ ɜ ɨɩɵɬɟ ɉɪɨɜɟɪɢɦ ɧɚɫɤɨɥɶɤɨ ɜɟɥɢɤɨ ɪɚɫɯɨɠɞɟɧɢɟ ɪɚɫɫɱɢɬɚɧɧɨɝɨ ɩɨ ɦɨɞɟɥɢ
ɝɨ ɩɨɪɹɞɤɚ ɡɧɚɱɟɧɢɹ ɬɨɤɚ ɜ ɬɨɱɤɟ ɫ ɧɚɩɪɹɠɟɧɢɟɦ ɜɨɥɶɬɯ ɢ ɫɨɩɪɨ ɬɢɜɥɟɧɢɟɦ ɨɦɯ ɫ ɢɡɦɟɪɟɧɧɵɦ ɡɧɚɱɟɧɢɟɦ ɜ ɷɬɨɣ ɬɨɱɤɟ ɂɡɦɟɪɟɧ ɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɞɚɧɧɨɣ ɬɨɱɤɟ ɫɨɫɬɚɜɥɹɟɬ Ⱥ Ɋɚɫɫɱɢɬɚɧɧɨɟ ɩɨ ɦɨɞɟɥɢ ɜ ɜɢɞɟ ɩɨɥɢɧɨɦɚ ɝɨ ɩɨɪɹɞɤɚ ɡɧɚɱɟɧɢɟ ɨɩɪɟɞɟɥɢɬɫɹ ɤɚɤ
y
Ɋɚɫɯɨɠɞɟɧɢɟ ɧɟɜɟɥɢɤɨ ± Ⱥ ɱɬɨ ɫɨɫɬɚɜɥɹɟɬ ɜɫɟɝɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɨ ɩɥɚɧɭ ɉɎɗ
ɌɚɤɢɦɨɛɪɚɡɨɦɩɪɢɦɟɧɟɧɢɟɈɐɄɉɢɩɟɪɟɯɨɞɤɩɨɥɢɧɨɦɭɝɨɩɨɪɹɞɤɚ ɩɨɡɜɨɥɹɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɭɜɟɥɢɱɢɬɶ ɬɨɱɧɨɫɬɶ ɦɨɞɟɥɢ
Ɂɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ D a N N ɈɐɄɉ ɩɪɢ ɪɚɡɥɢɱɧɨɦ ɱɢɫɥɟ ɮɚɤɬɨɪɨɜ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
Ɂɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜD a N N
ɩɪɢ ɪɚɡɥɢɱɧɨɦ ɱɢɫɥɟ ɮɚɤɬɨɪɨɜ
n |
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ɉɪɢ n ©ɡɜɟɡɞɧɵɟª ɬɨɱɤɢ ɈɐɄɉ ɥɟɠɚɬ ɧɚ ɝɪɚɧɢɰɚɯ ɜɚɪɶɢɪɨɜɚɧɢɹ ɮɚɤ ɬɨɪɨɜȿɫɥɢɬɨɱɤɢɩɥɚɧɚɉɎɗ n ɜɫɟɝɞɚɥɟɠɚɬɧɚɨɤɪɭɠɧɨɫɬɢɩɨɜɟɪɯɧɨɫɬɢ ɲɚɪɚ ɝɢɩɟɪɲɚɪɚ ɬɨ ɬɨɱɤɢ ɩɥɚɧɚ ɈɐɄɉ ɧɟ ɥɟɠɚɬ ɧɚ ɨɞɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɩɨ ɜɟɪɯɧɨɫɬɢ ɲɚɪɚ ɝɢɩɟɪɲɚɪɚ ɉɥɚɧ ɈɐɄɉ ɧɟ ɹɜɥɹɟɬɫɹ ɧɚɫɵɳɟɧɧɵɦ Ɍɚɤ ɧɚɩɪɢɦɟɪ ɞɥɹ n ɩɨɥɢɧɨɦ ɢɦɟɟɬ ɱɥɟɧɨɜ ɫɨ ɫɜɨɢɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɫɭɱɟɬɨɦɬɪɨɣɧɨɝɨɫɨɱɟɬɚɧɢɹɧɨɞɥɹɢɯɨɩɪɟɞɟɥɟɧɢɹɢɫɩɨɥɶɡɭɸɬɫɹɩɹɬɧɚ ɞɰɚɬɶ ɨɩɵɬɨɜ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɢɫɩɨɥɶɡɭɹ ɭɤɚɡɚɧɧɵɟ ɡɧɚɱɟɧɢɹDɢ a ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɨɪɬɨɝɨɧɚɥɶɧɵɣ ɩɥɚɧ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɫ ɞɢɚɝɨɧɚɥɶɧɨɣ ɦɚɬɪɢɰɟɣ& ;T ;
N
ɗɥɟɦɟɧɬɵ ɝɥɚɜɧɨɣ ɞɢɚɝɨɧɚɥɢ ɷɬɨɣ ɦɚɬɪɢɰɵ ɫɨɨɬɜɟɬɫɬɜɭɸɬ¦xiu ɨɫɬɚɥɶ u
ɧɵɟ ɷɥɟɦɟɧɬɵ ± ɧɭɥɢ
N
Ɂɧɚɱɟɧɢɹ¦xiu ɩɪɢɜɟɞɟɧɵ ɜ ɧɢɠɧɟɣ ɫɬɪɨɤɟ ɬɚɛɥɢɰɵ u
ȼɵɪɚɠɟɧɢɟ
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ɩɪɢɜɟɞɟɧɧɨɟ ɜ ɬɚɛɥɢɰɟ ɞɥɹ ɫɭɦɦɵ ɤɜɚɞɪɚɬɨɜ ɷɥɟɦɟɧɬɨɜ ɫɬɨɥɛɰɨɜ ɫɨɨɬɜɟɬ ɫɬɜɭɸɳɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɧɵɦ ɤɜɚɞɪɚɬɚɦ ɮɚɤɬɨɪɨɜ ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ
ȼɨɡɜɨɞɹ ɜ ɤɜɚɞɪɚɬ ɢ ɪɚɫɤɪɵɜɚɹ ɫɤɨɛɤɢ ɩɨɥɭɱɢɦ
n n a n a D D a a na a a
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n n a N a D D a n a n D Na D |
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ɉɪɢɦɟɪ.ɉɨɫɬɪɨɢɬɶ ɩɥɚɧ ɈɐɄɉ ɞɥɹn |
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ɉɚɪɚɦɟɬɪɵ ɩɥɚɧɚ |
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a D a
ɂɫɩɨɥɶɡɭɟɦ ɩɥɚɧ ɉɎɗn ɫ ɞɨɛɚɜɥɟɧɧɵɦɢ ɨɩɵɬɚɦɢ ± Ɋɚɫɲɢɪɟɧɧɚɹ ɦɚɬɪɢɰɚ ɩɥɚɧɚ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɢɡɦɟɪɟɧɢɣ ɢ ɪɚɫɱɟɬɨɜ ɩɨ ɦɨ
ɞɟɥɢ ɩɪɢɜɟɞɟɧɚ ɜ ɬɚɛɥɢɰɟ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
ɈɐɄɉ ɞɥɹn ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɢɡɦɟɪɟɧɢɣ ɢ ɪɚɫɱɟɬɨɜ ɩɨ ɦɨɞɟɥɢ
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Ɉɤɨɧɱɚɧɢɟ ɬɚɛɥɢɰɵ
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ȿɫɥɢ ɨɝɪɚɧɢɱɢɬɶɫɹ ɩɨɫɬɪɨɟɧɢɟɦ ɬɨɥɶɤɨ ɩɥɚɧɚ ɉɎɗ ɬɨ ɤɨɷɮɮɢɰɢɟɧɬɵ ɨɩɪɟɞɟɥɹɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ
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ɢ ɛɭɞɟɬ ɫɮɨɪɦɢɪɨɜɚɧ ɩɨɥɢɧɨɦ |
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ɤɨɬɨɪɵɣ ɧɟ ɞɚɟɬ ɞɨɫɬɚɬɨɱɧɭɸ ɬɨɱɧɨɫɬɶ ɋɭɞɹ ɩɨ ɜɟɥɢɱɢɧɟ ɤɨɷɮɮɢɰɢɟɧɬɚb ɫɪɚ ɡɭ ɜɢɞɧɨ ɡɧɚɱɢɬɟɥɶɧɨɟ ɪɚɫɯɨɠɞɟɧɢɟ ɜ ɰɟɧɬɪɚɥɶɧɨɣ ɬɨɱɤɟ ɏɨɬɹ ɜ ɬɨɱɤɚɯ ɩɪɨɜɟ ɞɟɧɢɹɱɟɬɵɪɟɯɨɩɵɬɨɜɩɥɚɧɚɉɎɗ ɩɨɥɭɱɚɟɦɡɧɚɱɟɧɢɹ ɫɨɨɬɜɟɬ ɫɬɜɟɧɧɨ ɬɨ ɟɫɬɶ ɩɨɥɧɨɟ ɫɨɜɩɚɞɟɧɢɟ ɫ ɢɡɦɟɪɟɧɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ
ɉɨɥɭɱɟɧɧɵɟɡɧɚɱɟɧɢɹɨɬɤɥɢɤɚɪɚɫɫɱɢɬɚɧɧɵɟɩɨ ɦɨɞɟɥɢ ɫɭɱɟɬɨɦɤɜɚɞ ɪɚɬɨɜ ɮɚɤɬɨɪɨɜ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ ȼ ɷɬɨɣ ɠɟ ɬɚɛɥɢɰɟ ɬɚɤɠɟ ɩɪɢ ɜɟɞɟɧɵ ɢ ɨɬɤɥɨɧɟɧɢɹ ɨɬ ɢɡɦɟɪɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ayu yu ɩɨɞɬɜɟɪɠɞɚɸɳɢɟ ɞɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɭɸ ɬɨɱɧɨɫɬɶ ɩɨɥɢɧɨɦɚ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ Ɍɚɤ ɜ ɰɟɧɬɪɚɥɶ ɧɨɣ ɬɨɱɤɟ ɩɥɚɧɚ ɜ ɨɬɥɢɱɢɟɨɬ ɫɥɭɱɚɹ ɩɪɢɦɟɧɟɧɢɹ ɩɥɚɧɚɉɎɗ ɪɚɫɯɨɠɞɟ ɧɢɣ ɧɟɬ
ȼ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɵ ɜɨɡɦɨɠɧɵɟ ɜɚɪɢɚɧɬɵ ɹɞɪɚ ɈɐɄɉ ɩɪɢ ɪɚɡɥɢɱ
ɧɵɯ ɡɧɚɱɟɧɢɹɯ ɱɢɫɥɚ ɮɚɤɬɨɪɨɜ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
ȼɨɡɦɨɠɧɵɟ ɜɚɪɢɚɧɬɵ ɹɞɪɚ ɈɐɄɉ
ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɱɢɫɥɚ ɮɚɤɬɨɪɨɜ
ɑɢɫɥɨ |
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ɮɚɤɬɨɪɨɜn |
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Ɍɨɥɶɤɨ ɉɎɗ |
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ɉɎɗ ɢɥɢ ȾɎɗ |
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ɉɎɗ ɢɥɢ ȾɎɗ |
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ɉɎɗ ȾɎɗ |
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ɉɎɗ ȾɎɗ |
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ɉɎɗ ȾɎɗ |
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ɢɥɢ ȾɎɗ |
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ȼ ɤɚɱɟɫɬɜɟ ɹɞɪɚ ɩɥɚɧɚ ɜ ɈɐɄɉ ɦɨɠɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ ɢ ɞɪɨɛɧɚɹ ɪɟɩɥɢɤɚ
ɉɪɢ ɷɬɨɦ ɬɪɟɛɭɟɬɫɹ ɱɬɨɛɵ ɹɞɪɨ ɩɥɚɧɚ ɨɛɟɫɩɟɱɢɜɚɥɨ ɪɚɡɞɟɥɶɧɭɸ ɨɰɟɧɤɭ ɤɨɷɮ
ɮɢɰɢɟɧɬɨɜ ɦɨɞɟɥɢ ɜɤɥɸɱɚɸɳɢɯ ɥɢɧɟɣɧɵɟ ɷɮɮɟɤɬɵ ɢ ɷɮɮɟɤɬɵ ɞɜɨɣɧɵɯ ɜɡɚɢ ɦɨɞɟɣɫɬɜɢɣɗɬɨɬɪɟɛɨɜɚɧɢɟɧɚɤɥɚɞɵɜɚɟɬɨɝɪɚɧɢɱɟɧɢɹɧɚɫɬɟɩɟɧɶɞɪɨɛɧɨɫɬɢ ɢɫɩɨɥɶɡɭɟɦɨɝɨ ȾɎɗ
Ʉɨɥɢɱɟɫɬɜɨ ɨɩɵɬɨɜ ɜ ɐɄɉ ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɢɫɥɨɦ ɮɚɤɬɨɪɨɜ ɢ ɤɨɥɢɱɟɫɬɜɨɦ
ɨɩɵɬɨɜ ɜ ɹɞɪɟ ɩɥɚɧɚ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɩɥɚɧɨɜ ɝɨ ɩɨɪɹɞɤɚ ɩɪɢ
ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɜ ɹɞɪɟ ȾɎɗ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɞɟɪɠɢɜɚɬɶɫɹ ɬɟɯ ɠɟ ɩɪɢɧɰɢɩɨɜ ɩɪɢ
ɜɵɛɨɪɟ ɝɟɧɟɪɢɪɭɸɳɢɯ ɫɨɨɬɧɨɲɟɧɢɣ ɱɬɨ ɢ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɩɥɚɧɨɜ ɝɨ ɩɨɪɹɞɤɚ
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɤɨɥɢɱɟɫɬɜɨ ɬɨɱɟɤ ɹɞɪɚ ɈɐɄɉ ɫɨɫɬɚɜɥɹɟɬ
N n k
ɩɪɢ ɷɬɨɦk ɟɫɥɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɉɎɗ ɢk ! ɜ ɫɥɭɱɚɟ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ȾɎɗ ɜ ɤɚɱɟɫɬɜɟ ɹɞɪɚ ɩɥɚɧɚ ȼ ɥɸɛɨɦ ɫɥɭɱɚɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɨɥɢɧɨɦɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ
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