2 1 4 _ 2
сигма = --- x сумма (X - X) .
Б 3 i=1 Б Б
i
2.3. Дисперсию проб всех 10 партий и среднюю дисперсию вычисляют по формулам:
2 2
сигма + сигма
А Б
2 i i
сигма = ------------------
i 2
где i = 1, 2,..., 10.
10 2
сумма сигма
_____2 i=1 i
сигма = --------------- .
10
2.4. Среднее квадратическое отклонение по 10 партиям вычисляют по формуле
_____
_____ 2
сигма = кв. корень сигма .
2.5. Средний коэффициент вариации (V) контролируемого показателя вычисляют по формуле
_____
сигма
V = ----- x 100 .
_
X
2.6. Категории однородности материала классифицируют по п. 3.3.3 настоящего стандарта.
Пример обработки результатов для расчета коэффициента вариации показателя качества приводится в таблице.
Пример обработки результатов для расчета коэффициента вариации показателя качества
Материал - смесь хромомагнезитовая марки СХМ контролируемый показатель - массовая доля Сr2O3, %
+----------+--------------------------------------------------------------------------------------------------------------------------------+
|Номер | Проба A |
|партии +-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
| |X |X |X |X | _ | _ 2 | _ 2 | _ 2 | _ 2 | 2 1 10 2 |
| | 1 | 2 | 3 | 4 | X |(X - X ) |(X - X ) |(X - X ) |(X - X ) |сигма = --- x сумма (X - X ) |
| | | | | | A | A A | A A | A A | A A | A 3 i=1 A A |
| | | | | | | 1 | 2 | 3 | 4 | i |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|1 |17,4 |18,6|14,9|16,8|16,925| 0,226 | 2,806 | 4,101 | 0,016 | 2,383 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|2 |15,0 |19,9|19,6|18,0|18,125| 9,766 | 3,151 | 2,560 | 0,016 | 5,164 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|3 |20,8 |20,3|19,5|18,4|19,750| 1,103 | 0,303 | 0,063 | 1,823 | 1,097 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|4 |31,0 |29,7|31,4|27,1|29,800| 1,440 | 0,010 | 2,560 | 7,29 | 3,767 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|5 |27,2 |24,6|26,0|25,7|25,875| 1,756 | 1,626 | 0,016 | 0,031 | 1,143 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|6 |32,7 |31,0|26,7|32,9|30,825| 3,516 | 0,031 | 17,016 | 4,301 | 8,288 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|7 |32,7 |31,0|32,9|32,3|32,225| 0,226 | 1,501 | 0,456 | 0,075 | 0,756 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|8 |35,4 |33,3|34,6|32,4|33,925| 2,176 | 0,391 | 0,456 | 2,326 | 1,783 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|9 |19,3 |21,1|17,5|18,4|19,075| 0,051 | 4,101 | 2,481 | 0,456 | 2,363 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|10 |20,0 |17,6|17,3|18,3|18,300| 2,890 | 0,490 | 1,000 | 0,000 | 1,460 |
+----------+-----+----+----+----+------+----------------+---------------+---------------+---------------+-----------------------------------+
|Сумма | | |
+----------+--------------------------------------------------------------------------------------------+-----------------------------------+
|Среднее | |
+----------+--------------------------------------------------------------------------------------------------------------------------------+
_____
_____ 2
Сигма = кв. корень Сигма = 1,588
_____
Сигма
V = ------x 100 = 6,427
_
X
+---------+----------------------------------------------------------------------------------------------------------------------------------+---------------------------------+---------------------+
|Номер | Проба Б | 2 2 | _ _ |
|партии +----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+ сигма + сигма | X + X |
| |X |X |X |X |_ | _ 2 | _ 2 | _ 2 | _ 2 | 2 1 10 _ 2 | А Б |_ A Б |
| | 5 | 6 | 7 | 8 |Х |(Х -Х ) |(Х -Х ) |(Х -Х ) |(Х -Х ) |сигма = --- x сумма (X - X) | 2 i i |X = -------- |
| | | | | | Б | Б Б | Б Б | Б Б | Б Б | Б 3 i=1 Б |сигма = ----------------- | i 2 |
| | | | | | | 1 | 2 | 3 | 4 | i | i 2 | |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|1 |17,3| 17,1 | 14,0 |16,4| 16,2 | 1,21 | 0,81 | 4,84 | 0,40 | 2,300 | 2,342 | 16,56 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|2 |22,9| 19,5 | 20,4 |20,0| 20,7 | 4,84 | 1,44 | 0,09 | 0,490 | 2,287 | 3,726 | 19,41 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|3 |20,0| 20,5 | 19,5 |20,5|20,125| 0,016 | 0,141 | 0,391 | 0,141 | 0,412 | 0,755 | 19,94 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|4 |31,8| 30,8 | 31,4 |28,0| 30,5 | 1,690 | 0,090 | 0,810 | 6,250 | 2,947 | 5,241 | 30,15 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|5 |27,0| 28,2 | 25,1 |26,5| 26,7 | 0,090 | 2,250 | 2,560 | 0,040 | 1,647 | 1,395 | 26,2 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|6 |32,5| 28,8 | 32,7 |32,3|31,575| 0,856 | 7,701 | 1,266 | 0,526 | 3,450 | 5,869 | 31,2 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|7 |32,9| 31,1 | 33,3 |31,6|32,225| 0,456 | 1,266 | 1,156 | 0,391 | 1,090 | 0,923 | 32,23 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|8 |35,0| 34,5 | 33,9 |33,0|34,100| 0,810 | 0,160 | 0,040 | 1,210 | 0,740 | 1,262 | 34,01 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|9 |18,5| 19,8 | 17,3 |21,1|19,175| 0,456 | 0,391 | 3,516 | 3,706 | 2,690 | 2,527 | 19,13 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|10 |18,9| 17,0 | 18,4 |19,0|18,325| 0,331 | 1,756 | 0,006 | 0,456 | 0,850 | 1,155 | 18,31 |
+---------+----+-------+------+----+------+---------------+---------------+-------------+--------------+-------------------------------------+---------------------------------+---------------------+
|Сумма | | 25,195 | 247,14 |
+---------+----------------------------------------------------------------------------------------------------------------------------------+---------------------------------+---------------------+
|Среднее | | 2,520 | 24,71 |
+---------+----------------------------------------------------------------------------------------------------------------------------------+---------------------------------+---------------------+