Given the Following Process Control Data for a Normally Distributed

Essay

Given the following process control data for a normally distributed quality variable (three samples of size four each): $$\begin{array} { r} { \text { Measurements } } \\\begin{array} { l l l l l } \text { Machine } &\\\hline \# 1 & 15 & 14 & 15 & 12 \\\# 2 & 18 & 16 & 20 & 16 \\\# 3 & 16 & 17 & 16 & 17\end{array}\end{array}$$ If the process is known to have a mean of 15 and a standard deviation of 3, what are the three-sigma upper and lower control limits for an x-bar chart?