np-chart

np-chart
Originally proposed by	Walter A. Shewhart
Process observations
Rational subgroup size	n > 1
Measurement type	Number nonconforming per unit
Quality characteristic type	Attributes data
Underlying distribution	Binomial distribution
Performance
Size of shift to detect	≥ 1.5σ
Process variation chart
Not applicable
Process mean chart
Center line	$n\overline{p}=\frac{\sum _{i=1}^m\sum _{j=1}^n\{\begin{array}{ll}1& \text{if }{x}_{ij}\text{ defective}\\ 0& \text{otherwise}\end{array}}{m}$
Control limits	$n\overline{p}\pm 3\sqrt{n\overline{p}(1-\overline{p})}$
Plotted statistic	$n{\overline{p}}_i=\sum _{j=1}^n\{\begin{array}{ll}1& \text{if }{x}_{ij}\text{ defective}\\ 0& \text{otherwise}\end{array}$

In statistical quality control, the np-chart is a type of control chart used to monitor the number of nonconforming units in a sample. It is an adaptation of the p-chart and used in situations where personnel find it easier to interpret process performance in terms of concrete numbers of units rather than the somewhat more abstract proportion.

The np-chart differs from the p-chart in only the three following aspects:

1. The control limits are $n\overline{p}\pm 3\sqrt{n\overline{p}(1-\overline{p})}$, where n is the sample size and $\overline{p}$ is the estimate of the long-term process mean established during control-chart setup.
2. The number nonconforming (np), rather than the fraction nonconforming (p), is plotted against the control limits.
3. The sample size, $n$, is constant.

See also

• p-chart