X-Chart

369. X-Chart

369.1. $\bar{𝑋}$ -chart

Used to monitor the average of a continuous quality characteristic (e.g., weight, length, temperature), assuming constant sample size per subgroup.

\begin{matrix} {UCL}_{\bar{𝑥}} = \bar{𝑥} + 𝐴_{2} \cdot \bar{𝑅} \\ {UCL}_{\bar{𝑥}} = \bar{𝑥} - 𝐴_{2} \cdot \bar{𝑅} \end{matrix}

Where:

${\bar{𝑥}}_{𝑖}$ : average of subgroup $𝑖$
$\bar{𝑥}$ : grand mean of all subgroup means
$\bar{𝑅}$ : average range of all subgroups
$𝐴_{2}$ : constant dependent on sample size $𝑛$ (e.g., $𝐴_{2} = 0.577$ for $𝑛 = 5$ )

Example