Table S$6\mathrm{.}1-$ Factors for Computing Control Chart Limits $(3$ sigma$)$

Auto pistons at Wenming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of $10$

pistons produced each day, the mean and the range of this diameter have been as follows:

$$

Day Mean Bold x overbarxAuto pistons at Wenming Chung's plant in Shanghai are produced in a forging process, and the diameter

is a critical factor that must be controlled. From sample sizes of $10$

pistons produced each day, the mean and the range of this diameter have been as follows:

a$)$ What is the value of $\stackrel{}{x}?$

$\stackrel{}{x}=,$ mm $($round your response to two decimal places$).$

b$)$ What is the value of $\frac{?}{\text{b}\text{a}\text{r}}(R)?$

$\frac{?}{\text{b}\text{a}\text{r}}(R)=,mm($round your response to two decimal places$).$

c$)$ What are the $UC{L}_{\stackrel{}{x}}$ and $LC{L}_{\stackrel{}{x}}$ using $3-$sigma?

Upper Control Limit $(UC{L}_{-})=,mm($round your response to two decimal places$).$

Lower Control Limit $(LC{l}_{\stackrel{}{x}})=,mm($round your response to two decimal places$).$

d$)$ What are the $UC{L}_R$ and $LC{L}_R$ using $3-$sigma?

Upper Control Limit $(UC{L}_R)=,mm($round your response to two decimal places$).$

Lower Control Limit $(LC{L}_R)=,mm($round your response to two decimal places$).$

$($mm$)$

Range R

$($mm$)$

$1154\mathrm{.}94\mathrm{.}4$

$2155\mathrm{.}24\mathrm{.}6$

$3153\mathrm{.}64\mathrm{.}3$

$4153\mathrm{.}54\mathrm{.}8$

$5158\mathrm{.}64\mathrm{.}5$