Систематична похибка опосередкованих вимірювань

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Систематична похибка опосередкованих вимірювань при нелінійній
залежності

Підкреслимо одну важливу особливість результатів опосередкованих
вимірювань при нелінійній залежності у порівнянні з результатами прямих
багаторазових вимірювань. Якщо в результатах одноразових спостережень
систематичні похибки вилучені, то математичне сподівання середнього
арифметичного ряду прямих рівнорозсіяних спостережень дорівнює істинному
значенню вимірюваної величини, тобто результати прямих виправлених
спостережень вільні від систематичних похибок. На відміну від цього,
математичне сподівання похибки результату опосередкованих вимірювань при
нелінійній залежності, яка визначається певною формулою, не дорівнює
нулю, тобто похибка результату такого опосередкованого вимірювання,
поряд з випадковою складовою, має і систематичну складову. А це означає,
що математичне сподівання результату опосередкованих вимірювань при
нелінійній залежності не дорівнює істинному значенню вимірюваної
величини, або інакше, що оцінка є зміщеною, якщо хоча будь-яка одна
серед других похідних в не дорівнює нулю. Покажемо це.

Обчислимо математичне сподівання абсолютної похибки опосередкованих
вимірювань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 з урахуванням:

picscalex1000100090000033c0300000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02e005e0271200000026060f001a00ffffffff00001000
0000c0ffffffaeffffffa02700008e0500000b00000026060f000c004d61746854797065
0000400109000000fa02000010000000000000002200040000002d010000050000001402
f002980b050000001302f002990e050000001402f002e613050000001302f002e9140500
00001402f002f017050000001302f002ee1d10000000fb0240fe00000000000090010000
00020002001053796d626f6c0002040000002d01010008000000320a6003a42601000000
3d0008000000320a1e057c2501000000fa0008000000320a9f037c2501000000fa000800
0000320a6b057c2501000000fb0008000000320aef017c2501000000f90008000000320a
1e05020901000000ea0008000000320a9f03020901000000ea0008000000320a6b050209
01000000eb0008000000320aef01020901000000e90008000000320a6003d72101000000
440008000000320a60033c1e01000000440008000000320ab9049c1b0100000043000800
0000320ab904c31a01000000b60008000000320ab904db1801000000430008000000320a
b904021801000000b60008000000320a4c02971901000000b60008000000320a60039312
010000002b0008000000320a6003e70e01000000440008000000320ab904830c01000000
430008000000320ab904aa0b01000000b60008000000320a4c02350c01000000b6000800
0000320a6003f105010000003d0008000000320a6003590201000000440010000000fb02
c0fd0000000000009001000000020002001053796d626f6c0002040000002d0102000400
0000f001010008000000320aa803891501000000e50008000000320aa803b80901000000
e50010000000fb02c0fe0000000000009001000000020002001053796d626f6c00020400
00002d01010004000000f001020008000000320a1e058616010000003d0008000000320a
1e05310a010000003d0015000000fb02c0fe000000000000900100000000040200105469
6d6573204e657720526f6d616e0000a5040000002d01020004000000f001010008000000
320ae001d915010000006d0008000000320a1e05241701000000310008000000320a1e05
ce1501000000710008000000320a1e057515010000002c0008000000320a1e0525150100
00006a0008000000320ad003922401000000710008000000320ae2010f22010000006f00
08000000320ad0031a21010000006a0008000000320ae201741e010000006f0008000000
320a2905001d01000000710008000000320a2905621a010000006a0008000000320a9901
9e1a01000000320008000000320ae001080a010000006d0008000000320a1e05cf0a0100
0000310008000000320a1e05d809010000006a0008000000320ad003c511010000006a00
08000000320ae2011f0f010000006f0008000000320a29050a0e010000006a0008000000
320ae2019102010000006f0015000000fb0240fe0000000000009001000000cc04020010
54696d6573204e657720526f6d616e00cca5040000002d01010004000000f00102000800
0000320a60032e2301000000d50008000000320a6003931f01000000d50015000000fb02
40fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a5
040000002d01020004000000f001010008000000320a4c025a1b01000000460008000000
320ab904ff1301000000320008000000320a4c02f81301000000310015000000fb0240fe
0000000000009001000000cc0402001054696d6573204e657720526f6d616e00cca50400
00002d01010004000000f001020008000000320a60033e1001000000d50015000000fb02
40fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a5
040000002d01020004000000f001010008000000320a4c020e0d01000000460008000000
320a60035807010000004d0008000000320a60030005010000005d0008000000320a6003
b00301000000590008000000320a6003b901010000005b0008000000320a600339000100
00004d000a00000026060f000a00ffffffff01000000000010000000fb02100007000000
0000bc02000000cc0102022253797374656d00cc040000002d01010004000000f0010200
030000000000

picscalex100010009000003090300000300150000000000050000000902000000000400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.

У цьому виразі перша сума дорівнює нулю, оскільки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 за умовою
проведення експерименту, а друга сума визначає систематичну похибку.
Отже, якщо вимірювані величини корельовані між собою, то, враховуючи
рівність
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,

для систематичної похибки результату опосередкованих вимірювань дістаємо
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Оцінку коефіцієнта кореляції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 або визначають за
експериментальними даними, або задають функціональною залежністю чи у
вигляді матриці.

За умови, що вимірювані величини не корельовані, маємо
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Тоді систематична похибка результату опосередкованих вимірювань
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.

Отже, опосередковані вимірювання при нелінійній залежності мають
специфічну систематичну похибку, яка обумовлена ненульовими частинними
похідними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.

Щоб вилучити цю систематичну похибку, треба в результат опосередкованих
вимірювань, обчислений за формулою, ввести поправку П, яка дорівнює
систематичній похибці за значенням і обернена їй за знаком, тобто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.

Опосередковані вимірювання при лінійній залежності вказаної вище
специфічної систематичної похибки не мають, тому що для них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.

Результат і похибка опосередкованих вимірювань

Довірчі границі випадкової похибки і границі не вилученої систематичної
похибки результату опосередкованого вимірювання з нелінійною залежністю
визначають за певними формулами, підставляючи в останні замість
коефіцієнтів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 відповідно перші похідні
picscalex100010009000003f90000000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a002c0051200000026060f001a00ffffffff00001000
0000c0ffffffb7ffffff80050000570200000b00000026060f000c004d61746854797065
0000800009000000fa02000010000000000000002200040000002d010000050000001402
490085020500000013025602dd0115000000fb02c0fe0000000000009001000000000402
001054696d6573204e657720526f6d616e0000b4040000002d01010008000000320a1002
fc04010000006a0015000000fb0240fe0000000000009001000000000402001054696d65
73204e657720526f6d616e0000b4040000002d01020004000000f001010008000000320a
a0010a0101000000460010000000fb0240fe000000000000900100000002000200105379
6d626f6c0002040000002d01010004000000f001020008000000320aa0017a0301000000
430008000000320aa001a20201000000b60008000000320aa001320001000000b6000a00
000026060f000a00ffffffff01000000000010000000fb021000070000000000bc020000
00cc0102022253797374656d00cc040000002d01020004000000f0010100030000000000
.

Довірчу повну похибку результату опосередкованого вимірювання обчислюють
певним чином.

Остаточний результат опосередкованих вимірювань записується у вигляді
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 при , (4.35)

деpicscalex1000100090000034301000003001500000000000500000009020000000004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 границі допустимої випадкової похибки опосередкованих
вимірювань.

Формули для оцінки СКВ і результату опосередкованих вимірювань
справедливі за умови, що відомі оцінки дисперсії (і СКВ) початкових
величин. Значення коефіцієнта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 визначається
для заданої довірчої ймовірності P, виходячи із закону розподілу
результату опосередкованого вимірювання. Якщо закон розподілу
результату опосередкованих вимірювань можна вважати нормальним, то для
визначення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(і довірчих границь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) використовується інтегральна функція нормованого нормального
розподілу при великому числі вимірювань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. При малому числі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 нормально розподілених результатів спостережень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 слід
користуватися розподілом Стьюдента з “ефективним” числом степенів
вільності, що визначається виразом
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.

Якщо числа спостережень усіх аргументів однакові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, то
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.

При лінійній функціональній залежності опосередкованих вимірювань маємо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 і одержуємо приведені раніше формули для
ефективного числа степенів вільності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.

Оскільки число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 звичайно є дробовим, то для пошуку величини
picscalex100010009000003ad0000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c026002e0011200000026060f001a00ffffffff00001000
0000c0ffffffb7ffffffa0010000170200000b00000026060f000c004d61746854797065
0000600010000000fb02c0fe0000000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a1002e10001000000520015000000fb0240fe00000000
00009001000000000402001054696d6573204e657720526f6d616e0000ae040000002d01
010004000000f001000008000000320aa00140000100000074000a00000026060f000a00
ffffffff01000000000010000000fb021000070000000000bc02000000cc010202225379
7374656d00cc040000002d01000004000000f0010100030000000000 за таблицею
розподілу Стьюдента необхідно використовувати інтерполяцію.

Довірчі границі повної похибки опосередкованих вимірювань (з урахуванням
випадкової і не вилученої систематичної складових похибки вимірювань)
знаходять за відповідною методикою.

Отже, загальна методика статистичної обробки результатів опосередкованих
вимірювань передбачає такий алгоритм:

1) вилучення відомих (виявлених) систематичних похибок з результатів
вимірювань кожного аргументу;

2) перевірку відповідності реального розподілу результатів прямих
вимірювань кожного аргументу нормальному закону за одним із критеріїв
згоди. Якщо така відповідність підтверджується, то проводять перевірку
надмірних похибок і їх вилучення з результатів вимірювань;

3) обчислення оцінок аргументів та їх похибок;

4) перевірку відсутності кореляції між результатами вимірювань
аргументів попарно, при її наявності обчислюють відповідні коефіцієнти
кореляції;

5) обчислення результату опосередкованого вимірювання;

6) обчислення довірчої випадкової похибки і загальної похибки результату
опосередкованого вимірювання; при нелінійній залежності знаходять
систематичну похибку опосередкованих вимірювань, обумовлену перехресними
членами у рівнянні.

При прямих одноразових вимірюваннях початкових величин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 процедура
визначення результату Y опосередкованих вимірювань зберігається такою
самою, як і при багаторазових вимірюваннях. Проте при прямих одноразових
вимірюваннях початкових величин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 для оцінки
характеристик похибки опосередкованих вимірювань широко використовуються
абсолютні і відносні значення похибок. Для визначення абсолютної похибки
результату опосередкованих вимірювань використовують співвідношення,
аналогічне за формою виразу без залишкового члена, а за абсолютною
похибкою знаходять відповідні відносні похибки з рівності.

Формули обчислення абсолютних і відносних похибок опосередкованих
вимірювань для тих функціональних залежностей, які часто зустрічаються в
практиці, наведені в табл. 1. Якщо похибки є систематичними, то формули
в табл. 1. використовують з урахуванням знаків похибок. Для випадкових
похибок здійснюється підсумовування за модулем, тобто арифметичне
підсумовування, причому за величину беруть границі допустимих похибок
(максимальні значення).

Табл. 1. свідчить, що піднесення аргументу до цілого степеня значно
збільшує, а добування цілого степеня аргументу зменшує похибки
результату. Тому вимірювання величин, які у формулу входять у вигляді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 ціле додатне число), необхідно
виконувати з більшою точністю, а вимірювання величин, які входять у
формулу (1.6) у вигляді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, може здійснюватися з меншою точністю. Якщо
результат опосередкованих вимірювань виражається через степеневу функцію
аргументів, наприклад,
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,

то для відносної систематичної похибки одержимо
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,

а для оцінки “зверху”, тобто максимального значення відносної випадкової
похибки

picscalex100010009000003ca0100000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02e004e01b1200000026060f001a00ffffffff00001000
0000c0ffffffb3ffffffa01b0000930400000b00000026060f000c004d61746854797065
0000000110000000fb0240fe0000000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a0903031b01000000f70008000000320a7004031b0100
0000f80008000000320aea01031b01000000f60008000000320a0903680501000000e700
08000000320a7004680501000000e80008000000320aea01680501000000e60008000000
320ae002151801000000430008000000320ae002f61601000000640008000000320ae002
f91501000000670008000000320ae002e713010000002b0008000000320ae0029d100100
0000430008000000320ae0027e0f01000000640008000000320ae002570e010000006200
08000000320ae002610c010000002b0008000000320ae002530901000000430008000000
320ae002340801000000640008000000320ae002dd0601000000610008000000320ae002
6d0401000000b10008000000320ae0020603010000003d0008000000320ae0024a010100
0000550008000000320ae002320001000000640015000000fb0240fe0000000000009001
000000000402001054696d6573204e657720526f6d616e0000b4040000002d0101000400
0000f001000008000000320ae002931a010000007c0008000000320ae002391501000000
7c0008000000320ae0022e13010000007c0008000000320ae002b30d010000007c000800
0000320ae002a80b010000007c0008000000320ae0022b06010000007c0015000000fb02
c0fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000b4
040000002d01000004000000f001010008000000320a5003741901000000330008000000
320a62011217010000006f0008000000320a5003061201000000320008000000320a6201
9a0f010000006f0008000000320a5003990a01000000310008000000320a620150080100
00006f0008000000320a62014e00010000006f000a00000026060f000a00ffffffff0100
0000000010000000fb021000070000000000bc02000000cc0102022253797374656d00cc
040000002d01010004000000f0010000030000000000

Таблиця 1.

Функції YП о х и б к иАбсолютна, Відносна,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Проте така оцінка дає завищені результати і її застосування доцільно при
2 або 3 складових похибки. При більшому числі складових випадкової
похибки опосередкованих вимірювань (за числом аргументів m), абсолютну
випадкову похибку результату опосередкованих вимірювань слід обчислювати
за правилами підсумовування незалежних випадкових величин, тобто
геометрично
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.

Величину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 називають середнім квадратичним значенням абсолютної
випадкової похибки опосередкованих вимірювань.

Тоді СКЗ відносної випадкової похибки опосередкованих вимірювань
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.

При роздільній оцінці систематичних і випадкових похибок результату
опосередкованих вимірювань необхідно мати на увазі таке. Очевидно, що
оцінити систематичну похибку результату опосередкованих вимірювань
неможливо, не знаючи оцінок систематичних похибок початкових величин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. Але якщо вони
відомі, то їх необхідно вилучити з результатів прямих вимірювань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, а потім
оцінити результат опосередкованого вимірювання за цими виправленими
значеннями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. Водночас така
оцінка систематичної похибки може бути проведена після закінчення
експерименту. Тоді її у вигляді поправки необхідно врахувати в
остаточному результаті опосередкованого вимірювання. Оцінка
систематичної похибки може використовуватися також під час підготовки до
експерименту, як орієнтовна оцінка. Наприклад, якщо припустити, що
похибка результату опосередкованого вимірювання визначається тільки
похибкою ЗВТ при вимірюванні величин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, причому в цих
ЗВТ переважаючою є систематична похибка (випадковою похибкою можна
знехтувати), то на підставі оцінки систематичної похибки за певною
формулою при (провівши формальну заміну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,
picscalex1000100090000039b0100000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c020003c0091200000026060f001a00ffffffff00001000
0000c0ffffffabffffff80090000ab0200000b00000026060f000c004d61746854797065
0000800015000000fb02c0fe0000000000009001000000000402001054696d6573204e65
7720526f6d616e0000da040000002d01000008000000320a70022709010000006a001500
0000fb02c0fe0000000000009001000000cc0402001054696d6573204e657720526f6d61
6e00ccda040000002d01010004000000f001000008000000320a7002f80601000000f100
15000000fb02c0fe0000000000009001000000000402001054696d6573204e657720526f
6d616e0000da040000002d01000004000000f001010008000000320a7002cd0201000000
6a0015000000fb0240fe0000000000009001000000cc0402001054696d6573204e657720
526f6d616e00ccda040000002d01010004000000f001000008000000320a0002a3070100
0000d50015000000fb0240fe0000000000009001000000000402001054696d6573204e65
7720526f6d616e0000da040000002d01000004000000f001010008000000320a9001fb07
01000000880015000000fb0240fe0000000000009001000000cc0402001054696d657320
4e657720526f6d616e00ccda040000002d01010004000000f001000008000000320a0002
490101000000d50015000000fb0240fe0000000000009001000000000402001054696d65
73204e657720526f6d616e0000da040000002d01000004000000f001010008000000320a
9001a10101000000880010000000fb0240fe000000000000900100000002000200105379
6d626f6c0002040000002d01010004000000f001000008000000320a0002c80501000000
440008000000320a0002ab0301000000ae0008000000320a000239000100000044000a00
000026060f000a00ffffffff01000000000010000000fb021000070000000000bc020000
00cc0102022253797374656d00cc040000002d01000004000000f0010100030000000000
) можна вибрати ЗВТ з такими границями допустимих систематичних похибок,
щоб похибка результату опосередкованих вимірювань величини Y не
перевищувала заданого значення.

Оцінка результатів і похибок сумісних та сукупних вимірювань

Загальною ознакою сумісних і сукупних вимірювань, відповідно до їх
визначення (див. § 1.5), є те, що значення шуканих величин визначають,
розв’язуючи систему рівнянь, які зв’язують шукані величини з деякими
іншими величинами, вимірюваними прямими або опосередкованими методами,
причому вимірюють декілька комбінацій значень цих величин. Вимірювання,
проведені для кожної комбінації, дозволяють одержати одне рівняння, а
сукупність цих рівнянь для всіх комбінацій являє собою систему рівнянь,
в яку входять також усі значення шуканих величин. Цю систему рівнянь,
відповідно до (1.7), запишемо для стислості записів у вигляді
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, (4.36)

деpicscalex100010009000003ad00000002001500000000000500000009020000000004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 значення
шуканих величин, ;
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 значення величин, вимірюваних прямими або опосередкованими
методами в q-му досліді, ;

n число дослідів;

k число величин, які вимірюються в кожному досліді;

m число шуканих величин.

Рівняння, як і рівняння, за формою однакові для сумісних і сукупних
вимірювань. Їх відмінністю є тільки фізична суть шуканих величин.

Якщо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 є значеннями
тієї самої фізичної величини (наприклад, масами гир певного набору або
довжинами лінійних мір), то вимірювання сукупні. Якщо ж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 значення
різних фізичних величин (наприклад, опору і температури), то вимірювання
сумісні. Ще раз підкреслимо, що такий поділ вимірювань дуже умовний, але
він традиційно існує.

Після проведення n дослідів одержують n комбінацій значень вимірюваних
величин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. Підставляючи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 у початкову
систему і проводячи необхідні перетворення, одержимо систему рівнянь
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Рівняння (4.37) містять у собі шукані величини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 і числові
коефіцієнти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. Для визначення m невідомих значень шуканих величин необхідно мати
m рівнянь. Тоді результати вимірювань величин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 і довірчі
границі їх похибок можна знайти за методиками обробки результатів
опосередкованих вимірювань. Проте, з метою зменшення похибок результатів
вимірювань, дослідів проводять дещо більше, ніж число m невідомих
величинpicscalex100010009000003ad000000020015000000000005000000090200000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, тобто .

Оскільки точність вимірювання величин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 обмежена, то
умовні рівняння одночасно не перетворюються в тотожності при жодних
значеннях шуканих величин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, а отже, не
виникає можливості визначення їх істинних значень. Тому задача зводиться
до знаходження оцінок шуканих величин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, найбільш
наближених до істинних значень. Позначимо такі оцінки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. Якщо
значення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 підставити
в умовні рівняння, то їх ліві частини, в загальному випадку, будуть
відрізнятися від правих частин. Такі рівняння і названі умовними. Для
одержання тотожності введемо в праві частини умовних рівнянь деякі
величини , які називають залишковими похибками умовних рівнянь або
відхилами. Звідси маємо
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. (4.38)

Для розв’язання системи умовних рівнянь застосовується метод найменших
квадратів (МНК), згідно з яким оцінки
picscalex100010009000003d20000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02000320021200000026060f001a00ffffffff00001000
0000c0ffffffa4ffffffe0010000a40200000b00000026060f000c004d61746854797065
0000800015000000fb02c0fe0000000000009001000000000402001054696d6573204e65
7720526f6d616e0000a0040000002d01000008000000320a70028501010000006a001500
0000fb0240fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e0000a0040000002d01010004000000f001000008000000320a97019100010000008800
10000000fb0240fe0000000000009001000000020002001053796d626f6c000204000000
2d01000004000000f001010008000000320a000239000100000055000a00000026060f00
0a00ffffffff01000000000010000000fb021000070000000000bc02000000cc01020222
53797374656d00cc040000002d01010004000000f0010000030000000000 вибирають
так, щоб мінімізувати суму квадратів відхилів
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.

Розв’язання задачі в самому загальному випадку, коли умовні рівняння
нелінійні, а результати окремих вимірювань корельовані, дещо утруднено.
Тому розглянемо окремий випадок, коли умовні рівняння лінійні або
приведені до лінійного вигляду, а результати вимірювань величин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 рівноточні і некорельовані. Тоді оцінки, одержані
методом найменших квадратів, будуть обґрунтованими і незміщеними, а при
нормальному розподілі результатів вимірювань ще й ефективними. У цьому
випадку система рівнянь може бути приведена до вигляду
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 (4.39)

деpicscalex1000100090000033201000003001500000000000500000009020000000004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 коефіцієнти, одержані із системи рівнянь після її
лінеаризації (якщо вона нелінійна) і підстановки значень величин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, причому q 
рядок, j стовпчик;
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 постійна величина.

Сума квадратів відхилів визначається із системи рівнянь
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Як відомо, необхідною умовою мінімуму диференціальної функції багатьох
змінних, у даному випадку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, є виконання рівнянь:
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Їх можна розглядати як рівняння відносно величин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у
математичній статистиці вони називаються нормальними рівняннями.

Використовуючи рівність, знайдемо частинні похідні і прирівняємо їх до
нуля:
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Запишемо одержану систему рівнянь у компактному вигляді
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Ця система рівнянь є лінійною відносно шкали величин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. Внаслідок
розв’язання системи нормальних рівнянь одержують m невідомих величин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. Для
спрощення запису цієї моделі використовують позначення Гаусса для сум:
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;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;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.

З урахуванням цих позначень система нормальних рівнянь набуває вигляду

picscalex100010009000003a70800000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600c60251200000026060f001a00ffffffff00001000
0000c0ffffffa4ffffff20250000040c00000b00000026060f000c004d61746854797065
0000e00210000000fb0215fd0901000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a1a020b01010000005b0010000000fb0215fd09010000
00009001000000020002001053796d626f6c0002040000002d01010004000000f0010000
08000000320a1a02ab05010000005d0010000000fb0215fd090100000000900100000002
0002001053796d626f6c0002040000002d01000004000000f001010008000000320a1a02
b909010000005b0010000000fb0215fd0901000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320a1a02950e010000005d00
10000000fb0215fd0901000000009001000000020002001053796d626f6c000204000000
2d01000004000000f001010008000000320a1a028f15010000005b0010000000fb0215fd
0901000000009001000000020002001053796d626f6c0002040000002d01010004000000
f001000008000000320a1a02b11a010000005d0010000000fb0215fd0901000000009001
000000020002001053796d626f6c0002040000002d01000004000000f001010008000000
320a1a02301f010000005b0010000000fb0215fd09010000000090010000000200020010
53796d626f6c0002040000002d01010004000000f001000008000000320a1a02e8220100
00005d0010000000fb0215fd0901000000009001000000020002001053796d626f6c0002
040000002d01000004000000f001010008000000320a52050b01010000005b0010000000
fb0215fd0901000000009001000000020002001053796d626f6c0002040000002d010100
04000000f001000008000000320a5205e705010000005d0010000000fb0215fd09010000
00009001000000020002001053796d626f6c0002040000002d01000004000000f0010100
08000000320a5205f509010000005b0010000000fb0215fd090100000000900100000002
0002001053796d626f6c0002040000002d01010004000000f001000008000000320a5205
0d0f010000005d0010000000fb0215fd0901000000009001000000020002001053796d62
6f6c0002040000002d01000004000000f001010008000000320a52050716010000005b00
10000000fb0215fd0901000000009001000000020002001053796d626f6c000204000000
2d01010004000000f001000008000000320a5205651b010000005d0010000000fb0215fd
0901000000009001000000020002001053796d626f6c0002040000002d01000004000000
f001010008000000320a5205e41f010000005b0010000000fb0215fd0901000000009001
000000020002001053796d626f6c0002040000002d01010004000000f001000008000000
320a5205d823010000005d0010000000fb0215fd09010000000090010000000200020010
53796d626f6c0002040000002d01000004000000f001010008000000320a2a0b0b010100
00005b0010000000fb0215fd0901000000009001000000020002001053796d626f6c0002
040000002d01010004000000f001000008000000320a2a0b2d06010000005d0010000000
fb0215fd0901000000009001000000020002001053796d626f6c0002040000002d010000
04000000f001010008000000320a2a0bcf09010000005b0010000000fb0215fd09010000
00009001000000020002001053796d626f6c0002040000002d01010004000000f0010000
08000000320a2a0b2d0f010000005d0010000000fb0215fd090100000000900100000002
0002001053796d626f6c0002040000002d01000004000000f001010008000000320a2a0b
2716010000005b0010000000fb0215fd0901000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320a2a0bcb1b010000005d00
10000000fb0215fd0901000000009001000000020002001053796d626f6c000204000000
2d01000004000000f001010008000000320a2a0b2520010000005b0010000000fb0215fd
0901000000009001000000020002001053796d626f6c0002040000002d01010004000000
f001000008000000320a2a0b5f24010000005d0010000000fb0240fe0000000000009001
000000020002001053796d626f6c0002040000002d01000004000000f001010008000000
320a4d0a390001000000ef0008000000320a9d08390001000000ef0008000000320ae10b
390001000000ee0008000000320a5905390001000000ef0008000000320aa90339000100
0000ef0008000000320aed06390001000000ed0008000000320af901390001000000ec00
08000000320a2e0bd61e010000003d0008000000320a2e0b2a1c01000000550008000000
320a2e0be314010000002b0008000000320a2e0bc711010000002b0008000000320a2e0b
8c0f01000000550008000000320a2e0b8b08010000002b0008000000320a2e0b8c060100
0000550008000000320a5605951e010000003d0008000000320a5605e91b010000005500
08000000320a5605c314010000002b0008000000320a5605a711010000002b0008000000
320a56056c0f01000000550008000000320a56055708010000002b0008000000320a5605
460601000000550008000000320a1e02e11d010000003d0008000000320a1e02351b0100
0000550008000000320a1e026f14010000002b0008000000320a1e022f11010000002b00
08000000320a1e02f40e01000000550008000000320a1e021b08010000002b0008000000
320a1e020a0601000000550015000000fb0240fe00000000000090010000000004020010
54696d6573204e657720526f6d616e0000be040000002d01010004000000f00100000800
0000320a2e0bc724010000002e0008000000320a2e0b8a2001000000610008000000320a
c60a811c01000000880008000000320a2e0b171901000000610008000000320a2e0b8c16
01000000610008000000320ac60ae30f01000000880008000000320a2e0bbf0c01000000
610008000000320a2e0b340a01000000610008000000320ac60ae3060100000088000800
0000320a2e0bfb0301000000610008000000320a2e0b700101000000610008000000320a
56054724010000003b0008000000320a5605492001000000610008000000320aee04401c
01000000880008000000320a5605b11801000000610008000000320a56056c1601000000
610008000000320aee04c30f01000000880008000000320a56059f0c0100000061000800
0000320a56055a0a01000000610008000000320aee049d0601000000880008000000320a
5605b50301000000610008000000320a5605700101000000610008000000320a1e025723
010000003b0008000000320a1e02951f01000000610008000000320ab6018c1b01000000
880008000000320a1e02fd1701000000610008000000320a1e02f4150100000061000800
0000320ab6014b0f01000000880008000000320a1e02270c01000000610008000000320a
1e021e0a01000000610008000000320ab601610601000000880008000000320a1e027903
01000000610008000000320a1e02700101000000610015000000fb02c0fe000000000000
9001000000000402001054696d6573204e657720526f6d616e0000be040000002d010000
04000000f001010008000000320a9e0b852301000000710008000000320a9e0b6f210200
0000716d08000000320a9e0b4b1d010000006d0008000000320a9e0bfc1902000000716d
08000000320a9e0b711702000000716d08000000320a9e0bad1001000000320008000000
320a9e0b5d0e01000000320008000000320a9e0ba40d01000000710008000000320a9e0b
190b02000000716d08000000320a9e0b8a0701000000310008000000320a9e0b76050100
0000310008000000320a9e0be00401000000710008000000320a9e0b550202000000716d
08000000320ac605fe2201000000710008000000320ac605e72101000000320008000000
320ac6052e2101000000710008000000320ac6050a1d010000006d0008000000320ac605
961902000000716d08000000320ac6050a1801000000320008000000320ac60551170100
0000710008000000320ac6058d1001000000320008000000320ac6053d0e010000003200
08000000320ac605840d01000000710008000000320ac605f80b01000000320008000000
320ac6053f0b01000000710008000000320ac605440701000000310008000000320ac605
300501000000310008000000320ac6059a0401000000710008000000320ac6050e030100
0000320008000000320ac605550201000000710008000000320a8e020e22010000007100
08000000320a8e02102101000000310008000000320a8e027a2001000000710008000000
320a8e02561c010000006d0008000000320a8e02e21802000000716d08000000320a8e02
6f1701000000310008000000320a8e02d91601000000710008000000320a8e0215100100
0000320008000000320a8e02c50d01000000320008000000320a8e020c0d010000007100
08000000320a8e02990b01000000310008000000320a8e02030b01000000710008000000
320a8e02080701000000310008000000320a8e02f40401000000310008000000320a8e02
5e0401000000710008000000320a8e02eb0201000000310008000000320a8e0255020100
0000710015000000fb0240fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e0000be040000002d01010004000000f001000008000000320a2e0b0e23
010000006c0008000000320a4308de22010000002e0008000000320a43087c2201000000
200008000000320a43084422010000002e0008000000320a4308e2210100000020000800
0000320a4308aa21010000002e0008000000320a4308d8200200000020200c000000320a
4308781c0a0000002020202020202020202008000000320a4308401c010000002e000800
0000320a4308de1b01000000200008000000320a4308a61b010000002e0008000000320a
4308441b01000000200008000000320a43080c1b010000002e000a000000320a4308ea18
050000002020202020000c000000320a43088a140a000000202020202020202020200800
0000320a43085214010000002e0008000000320a4308f01301000000200008000000320a
4308b813010000002e0008000000320a4308561301000000200008000000320a43081e13
010000002e000b000000320a4308ac0f0800000020202020202020200c000000320a4308
4c0b0a0000002020202020202020202008000000320a4308140b010000002e0008000000
320a4308b20a01000000200008000000320a43087a0a010000002e0008000000320a4308
180a01000000200008000000320a4308e009010000002e0009000000320a43082e080400
0000202020200c000000320a4308ce030a0000002020202020202020202008000000320a
43089603010000002e0008000000320a4308340301000000200008000000320a4308fc02
010000002e0008000000320a43089a0201000000200008000000320a4308620201000000
2e0009000000320a43082001030000002020200008000000320a56058722010000006c00
08000000320a1e029721010000006c0011000000fb0240fe000000000000900100000002
040200104d542045787472610002040000002d01000004000000f001010008000000320a
2e0bef12010000004c0008000000320a5605cf12010000004c0008000000320a1e025712
010000004c000a00000026060f000a00ffffffff01000000000010000000fb0210000700
00000000bc02000000cc0102022253797374656d00cc040000002d01010004000000f001
0000030000000000

Як відомо, розв’язання такої лінійної системи є лінійними комбінаціями
величин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:
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де коефіцієнти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 знаходять,
розв’язуючи систему рівнянь (4.44) за допомогою визначника для кожної з
шуканих величин:
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,

де
picscalex100010009000003ac0400000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c026009a01b1200000026060f001a00ffffffff00001000
0000c0ffffffbcffffff601b00001c0900000b00000026060f000c004d61746854797065
0000200210000000fb0218fd0901000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a3002ea03010000005b0010000000fb0218fd09010000
00009001000000020002001053796d626f6c0002040000002d01010004000000f0010000
08000000320a3002c208010000005d0010000000fb0218fd090100000000900100000002
0002001053796d626f6c0002040000002d01000004000000f001010008000000320a3002
b50b010000005b0010000000fb0218fd0901000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320a30025c10010000005d00
10000000fb0218fd0901000000009001000000020002001053796d626f6c000204000000
2d01000004000000f001010008000000320a30024f13010000005b0010000000fb0218fd
0901000000009001000000020002001053796d626f6c0002040000002d01010004000000
f001000008000000320a3002a918010000005d0010000000fb0218fd0901000000009001
000000020002001053796d626f6c0002040000002d01000004000000f001010008000000
320abc07ea03010000005b0010000000fb0218fd09010000000090010000000200020010
53796d626f6c0002040000002d01010004000000f001000008000000320abc0744090100
00005d0010000000fb0218fd0901000000009001000000020002001053796d626f6c0002
040000002d01000004000000f001010008000000320abc07af0b010000005b0010000000
fb0218fd0901000000009001000000020002001053796d626f6c0002040000002d010100
04000000f001000008000000320abc07d810010000005d0010000000fb0218fd09010000
00009001000000020002001053796d626f6c0002040000002d01000004000000f0010100
08000000320abc074313010000005b0010000000fb0218fd090100000000900100000002
0002001053796d626f6c0002040000002d01010004000000f001000008000000320abc07
1f19010000005d0009000000fa02000010000000000000002200040000002d0100000500
00001402440063030500000013021c0963030500000014024400471b0500000013021c09
471b15000000fb02c0fe0000000000009001000000000402001054696d6573204e657720
526f6d616e0000e8040000002d01020004000000f001010008000000320a300842170200
0000716d08000000320a30089b1402000000716d08000000320a3008ae0f02000000716a
08000000320a3008070d02000000716d08000000320a30087f0801000000310008000000
320a3008e90701000000710008000000320a3008420502000000716d08000000320aa402
cc1602000000716d08000000320aa4023d1501000000310008000000320aa402a7140100
0000710008000000320aa402320f02000000716a08000000320aa402a30d010000003100
08000000320aa4020d0d01000000710008000000320aa402fd0701000000310008000000
320aa402670701000000710008000000320aa402d80501000000310008000000320aa402
420501000000710015000000fb0240fe0000000000009001000000000402001054696d65
73204e657720526f6d616e0000e8040000002d01010004000000f001020008000000320a
c0074f1601000000610008000000320ac007a81301000000610008000000320ac007bb0e
01000000610008000000320ac007140c01000000610008000000320ac007f60601000000
610008000000320ac0074f0401000000610008000000320a3402d9150100000061000800
0000320a3402b41301000000610008000000320a34023f0e01000000610008000000320a
34021a0c01000000610008000000320a3402740601000000610008000000320a34024f04
01000000610008000000320a2005390001000000440015000000fb0240fe000000000000
9001010000000402001054696d6573204e657720526f6d616e0000e8040000002d010200
04000000f001010008000000320ac007e81201000000200008000000320ac0071b110100
0000200008000000320ac007540b01000000200008000000320ac0078709010000002000
08000000320ac0078f0301000000200008000000320a20052114010000002e0008000000
320a2005bf1301000000200008000000320a20058713010000002e0008000000320a2005
251301000000200008000000320a2005ed12010000002e0008000000320a20051b120200
000020200c000000320a2005bb0d0a0000002020202020202020202008000000320a2005
830d010000002e0008000000320a2005210d01000000200008000000320a2005e90c0100
00002e0008000000320a2005870c01000000200008000000320a20054f0c010000002e00
09000000320a20050d0b03000000202020000c000000320a2005ad060a00000020202020
20202020202008000000320a20057506010000002e0008000000320a2005130601000000
200008000000320a2005db05010000002e0008000000320a200579050100000020000800
0000320a20054105010000002e0009000000320a20058f03040000002020202009000000
320a3402cc19030000002020200008000000320a3402f41201000000200008000000320a
34029f1001000000200008000000320a34025a0b01000000200008000000320a34020509
01000000200008000000320a34028f0301000000200011000000fb0240fe000000000000
900100000002040200104d542045787472610002040000002d01010004000000f0010200
08000000320ac0075a11010000004b0008000000320ac007c609010000004b0008000000
320a34026611010000004b0008000000320a3402cc09010000004b0010000000fb0240fe
0000000000009001000000020002001053796d626f6c0002040000002d01020004000000
f001010008000000320a2005ed01010000003d000a00000026060f000a00ffffffff0100
0000000010000000fb021000070000000000bc02000000cc0102022253797374656d00cc
040000002d01010004000000f0010200030000000000;
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.

Визначник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 одержаний заміною у визначнику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-го стовпця стовпцем вільних членів у (4.44).

Отже,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.

Визначивши з відхили
picscalex100010009000003ad0000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00220021200000026060f001a00ffffffff00001000
0000c0ffffffb7ffffffe0010000570200000b00000026060f000c004d61746854797065
0000800015000000fb02c0fe0000000000009001000000000402001054696d6573204e65
7720526f6d616e000080040000002d01000008000000320a100243010100000071001000
0000fb0240fe0000000000009001000000020002001053796d626f6c0002040000002d01
010004000000f001000008000000320aa00139000100000075000a00000026060f000a00
ffffffff01000000000010000000fb021000070000000000bc02000000cc010202225379
7374656d00cc040000002d01000004000000f0010100030000000000 і підставивши
їх у рівняння (4.42), одержимо такі рівності:
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,

що виражають властивості відхилів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. Ці рівності
застосовуються для перевірки правильності визначення оцінок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 шуканих
величин після розв’язання системи рівнянь.

Визначення оцінок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 шуканих
величин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 пов’язано з
великим обсягом обчислень, який швидко збільшується із збільшенням числа
умовних рівнянь. Останнє необхідно для підвищення точності одержаних
оцінок. У сучасні дні обробка результатів сумісних і сукупних вимірювань
виконується за допомогою ЕОМ за стандартними програмами. Тому точність
оцінок істинних значень вимірюваних величин може бути значно підвищена
при збільшенні числа умовних рівнянь до кількох десятків і навіть
сотень, а в деяких випадках і більше.

Для оцінки точності одержаного розв’язання системи рівнянь звичайно
припускають, що точність визначення коефіцієнтів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 значно вища від
точності визначення коефіцієнтів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. Це припущення, як правило, виправдане в багатьох практичних
випадках. При його виконанні похибки оцінок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 шуканих
величин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 визначаються
тільки дисперсіями результатів вимірювання останніх. А враховуючи, що
згідно з рівняннями оцінки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 є лінійними
комбінаціями величин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, маємо
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,

деpicscalex1000100090000031f01000002001500000000000500000009020000000004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 оцінка дисперсії шуканих величин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picscalex1000100090000031c0100000200150000000000050000000902000000000400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оцінка дисперсії коефіцієнтів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.

Якщо припустити, що всі результати спостережень є рівноточними, а отже,
всі дисперсії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 у
виразі однакові
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,

то оцінка СКВ
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Для обчислення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 рекомендується досить простий вираз
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,

в якому залишкові похибки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 визначають із
рівнянь після визначення оцінок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 згідно з
системою рівнянь.

Якщо точність визначення усіх коефіцієнтів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системи рівнянь
(4.45) приблизно однакова, то оцінку СКВ результату вимірювань величин
визначають за формулою
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деpicscalex100010009000003b200000002001500000000000500000009020000000004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 алгебраїчні доповнення головного визначника D, які одержують
виключенням з нього j-го рядка та j-го стовпця.

З рівнянь випливає, що точність сукупних і сумісних вимірювань залежить
від співвідношення числа шуканих величин m і числа умовних рівнянь n.
Чим значніша умова , тим точніше результати обробки. Якщо m і n близькі,
то результати обробки визначаються з грубими похибками.

Довірчі інтервали для істинних значень усіх вимірюваних величин
одержують за розподілом Стьюдента при числі степенів вільності .

Якщо при сукупних і сумісних вимірюваннях умовні рівняння нелінійні, то
застосовують їх лінеаризацію.

Таким чином, методика обробки результатів сукупних і сумісних вимірювань
така:

1. Записують систему умовних рівнянь при
picscalex100010009000003da0000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00200051200000026060f001a00ffffffff00001000
0000c0ffffffb7ffffffc0040000570200000b00000026060f000c004d61746854797065
0000800015000000fb0240fe0000000000009001000000000402001054696d6573204e65
7720526f6d616e0000b4040000002d01000008000000320aa001e3030100000030001500
0000fb02c0fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e0000b4040000002d01010004000000f001000008000000320a10024601010000007100
10000000fb0240fe0000000000009001000000020002001053796d626f6c000204000000
2d01000004000000f001010008000000320aa0018a02010000003d0008000000320aa001
39000100000075000a00000026060f000a00ffffffff01000000000010000000fb021000
070000000000bc02000000cc0102022253797374656d00cc040000002d01010004000000
f0010000030000000000 підстановкою експериментальних даних у рівняння
початкової залежності.

2. Систему умовних рівнянь приводять до нормального вигляду. Для
обчислення коефіцієнтів нормальних рівнянь складають допоміжну табл. 2,
яка дозволяє також перевірити правильність визначення шуканих величин.

Таблиця 2.
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…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…
picscalex100010009000003ca0000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
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720526f6d616e0000bd040000002d01000008000000320a1002fa0201000000320008000
000320a1002ae01010000006d0008000000320a10021c0101000000320015000000fb024
0fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000bd0
40000002d01010004000000f001000008000000320aa001320001000000610015000000f
b0240fe0000000000009001010000000402001054696d6573204e657720526f6d616e000
0bd040000002d01000004000000f001010008000000320aa0017d02010000006c000a000
00026060f000a00ffffffff01000000000010000000fb021000070000000000bc0200000
0cc0102022253797374656d00cc040000002d01010004000000f0010000030000000000.
.. … … … … … … … … … … … … … … … … …
… … … … … … … … … … … … … …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…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…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…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…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…
picscalex92010009000003df00000002001500000000000500000009020000000004000
00002010100050000000102ffffff00040000002e0118000500000031020100000005000
0000b0200000000050000000c026002c0031200000026060f001a00ffffffff000010000
000c0ffffffb7ffffff80030000170200000b00000026060f000c004d617468547970650
000600015000000fb0200ff0000000000009001000000000402001054696d6573204e657
720526f6d616e0000cc040000002d01000008000000320a1002ef02010000006e0008000
000320a10021f01020000006e6d15000000fb0240fe00000000000090010000000004020
01054696d6573204e657720526f6d616e0000cc040000002d01010004000000f00100000
8000000320aa001320001000000610015000000fb0240fe0000000000009001010000000
402001054696d6573204e657720526f6d616e0000cc040000002d01000004000000f0010
10008000000320aa0017002010000006c000a00000026060f000a00ffffffff010000000
00010000000fb021000070000000000bc02000000cc0102022253797374656d00cc04000
0002d01010004000000f0010000030000000000picscalex82010009000003d200000002
00150000000000050000000902000000000400000002010100050000000102ffffff0004
0000002e01180005000000310201000000050000000b0200000000050000000c020003a0
031200000026060f001a00ffffffff000010000000c0ffffffa8ffffff60030000a80200
000b00000026060f000c004d617468547970650000800015000000fb0240fe0000000000
009001000000000402001054696d6573204e657720526f6d616e000022040000002d0100
0008000000320a0002e802010000005d0008000000320a0002b000010000006100080000
00320a00021600010000005b0015000000fb02c0fe000000000000900100000000040200
1054696d6573204e657720526f6d616e000022040000002d01010004000000f001000008
000000320a4d01a00101000000320008000000320a700231020100000031000800000032
0a70029b010100000071000a00000026060f000a00ffffffff01000000000010000000fb
021000070000000000bc02000000cc0102022253797374656d00cc040000002d01000004
000000f0010100030000000000…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…
picscalex82010009000003da00000002001500000000000500000009020000000004000
00002010100050000000102ffffff00040000002e0118000500000031020100000005000
0000b0200000000050000000c02a002e0051200000026060f001a00ffffffff000010000
000c0ffffffb7ffffffa0050000570200000b00000026060f000c004d617468547970650
000800015000000fb0240fe0000000000009001000000000402001054696d6573204e657
720526f6d616e000080040000002d01000008000000320aa0012f05010000005d0008000
000320aa001c50201000000610008000000320aa001b00001000000610008000000320aa
0011600010000005b0015000000fb02c0fe0000000000009001000000000402001054696
d6573204e657720526f6d616e000080040000002d01010004000000f0010000080000003
20a1002b00302000000716e08000000320a1002310201000000310008000000320a10029
b010100000071000a00000026060f000a00ffffffff01000000000010000000fb0210000
70000000000bc02000000cc0102022253797374656d00cc040000002d01000004000000f
0010100030000000000…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…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…picscalex82010009000003f70000000200150000000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…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Визначають оцінки шуканих величин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,
розв’язуючи систему нормальних рівнянь, для чого використовують один із
методів:

а) метод, який ґрунтується на послідовному виключенні невідомих (метод
Гаусса);

б) метод із застосуванням визначника.

4. Перевіряють правильність визначення оцінок шуканих величин за
рівняннями.

5. Знаходять оцінку СКВ результатів вимірювань шуканих величин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 за певними формулами.

6. Визначають довірчі інтервали для всіх вимірюваних величин на підставі
розподілу Стьюдента при числі степенів вільності їх вимірювань.

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