P-Chart

366. P-Chart

The p-chart monitors the proportion of defectives in each sample, accounting for variable sample sizes.

\begin{matrix} {UCL}_{𝑝_{𝑖}} = \bar{𝑝} + 3 \sqrt{\frac{\bar{𝑝} (1 - \bar{𝑝})}{𝑛_{𝑖}}} \\ {LCL}_{𝑝_{𝑖}} = \bar{𝑝} - 3 \sqrt{\frac{\bar{𝑝} (1 - \bar{𝑝})}{𝑛_{𝑖}}} \end{matrix}

Where:

$𝑑_{𝑖}$ : The number of defective items observed in sample $𝑖$
$𝑝_{𝑖}$ : sample proportion defective

𝑝_{𝑖} = \frac{𝑑_{𝑖}}{𝑛_{𝑖}}

$\bar{𝑝}$ : overall proportion defective

\bar{𝑝} = \frac{\sum 𝑑_{𝑖}}{\sum 𝑛_{𝑖}}

$𝑛_{𝑖}$ : sample size for sample $𝑖$