The application of statistical methods to monitor and control the quality of a production process.

Control Charts

Plots some statistic of the production process.

• the x-axis is the number of the sample
• the y-axis varies across chart types

Additional lines are provided to monitor the statistic:

• center line (CL): indicates the long-term average (mean or median) value of the statistic.
• lower and upper control limits (LCL, UCL): indicate the threshold at which the process output is considered statistically ‘unlikely’.

Let \overline{u} be the estimate of the mean and \overline{s} be the estimate of the standard deviation (i.e., variance is \overline{s}^2). Then typically,

• center line is drawn at \overline{u}
• control limits are drawn at \overline{u} \pm 3 \overline{s}

p-chart

• y-axis: the proportion of nonconforming units in a sample.
• Underlying distribution: Binomial distribution
  • \overline{u} = \overline{p}
  • \overline{s}^2 = \frac{\overline{p}(1-\overline{p})}{n}

c-chart

• y-axis: some “count”-type data, typically total number of nonconformities per unit.
• Underlying distribution: Poisson distribution
  • \overline{u} = \overline{c}
  • \overline{s}^2 = \overline{c}

References

• https://en.wikipedia.org/wiki/Control_chart
• https://en.wikipedia.org/wiki/P-chart
• https://en.wikipedia.org/wiki/C-chart
• https://en.wikipedia.org/wiki/U-chart