Question

The standard deviation of linear dimensions P and Q are 3 $\mu m$ and 4 $\mu m,$ respectively. When assembled, the standard deviation (in $\mu m$) of the resulting linear dimension (P + Q) is

• A. 5

Answer 1

The correct option is A 5
$\text{According to Root Sum Square or RSS model}$

${\sigma }_a=\sqrt{{\sum }_{i=1}^n{\sigma }_i^2}$

$\text{Where,}{\sigma }_a\text{assembly tolerance standard deviation}$

${\sigma }_i=i^{th}\text{component tolerance standard deviation}$

$\text{Here,}{\sigma }_P=3\mu m\text{and}{\sigma }_Q=4\mu m$

${\sigma }_a=\sqrt{{\sigma }_P^2+{\sigma }_Q^2}=\sqrt{3^2+4^2}=5\mu m$