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The contribution of the random errors is given by:
𝑳−𝟏
𝑲−𝟏
+∑(𝒆 𝒊,𝒍,𝒌 ). (𝒆 𝒊,𝒍,𝒌 ) 𝑻
𝑻
𝒊,𝒍 𝒓𝒂𝒏𝒅
𝒓𝒂𝒏𝒅 =∑[𝑪]
+(𝒆 𝒊,𝑳,𝑲 ∗
𝒊,𝑳,𝑲 ∗
[𝑪] 𝒊,𝑲
). (𝒆
)
𝒍=𝟏
𝒌=𝟏
and
𝑲 𝒍
𝒊,𝒍,𝒌 ). (𝒆 𝒊,𝒍,𝒌 ) 𝑻
𝒓𝒂𝒏𝒅 =∑(𝒆
[𝑪] 𝒊,𝒍
𝒌=𝟏
The systematic errors are:
).(∑𝒆 𝒊,𝑳,𝒌 +𝒆 𝒊,𝑳,𝑲 ∗ 𝑲 𝒍 𝒌=𝟏 ) 𝑻
+(∑𝒆 𝒊,𝑳,𝒌 +𝒆 𝒊,𝑳,𝑲 ∗ 𝑲 𝒍 𝒌=𝟏
𝑳−𝟏
𝒊,𝑲 𝒔𝒚𝒔𝒕
𝒔𝒚𝒔𝒕
[𝑪]
=∑[𝑪] 𝒊,𝒍
𝒍=𝟏
𝑻
=(∑𝒆 𝒊,𝒍,𝒌 𝑲 𝒍 𝒌=𝟏
)(∑𝒆 𝒊,𝒍,𝒌 𝑲 𝒍 𝒌=𝟏
𝒊,𝒍 𝒔𝒚𝒔𝒕
[𝑪]
)
And finally the well by well and global errors:
𝒘𝒆𝒍𝒍 = 𝑬
𝒊,𝑲 . 𝑬 𝒊,𝑲 𝑻
[𝑪] 𝒊,𝑲
𝑲 𝒍
𝑳−𝟏
+∑𝒆 𝒊,𝑳,𝒌 +𝒆 𝒊,𝑳,𝑲 ∗ 𝑲−𝟏 𝒌=𝟏
𝑬 𝒊,𝑲 𝒘𝒆𝒍𝒍 =∑(∑𝒆
)
𝒊,𝒍,𝒌
𝒍=𝟏
𝒌=𝟏
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