np-chart

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.

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	$n{\bar {p}}={\frac {\sum _{i=1}^{m}\sum _{j=1}^{n}{\begin{cases}1&{\mbox{if }}x_{ij}{\mbox{ defective}}\\0&{\mbox{otherwise}}\end{cases}}}{m}}$
Control limits	$n{\bar {p}}\pm 3{\sqrt {n{\bar {p}}(1-{\bar {p}})}}$
Plotted statistic	$n{\bar {p}}_{i}=\sum _{j=1}^{n}{\begin{cases}1&{\mbox{if }}x_{ij}{\mbox{ defective}}\\0&{\mbox{otherwise}}\end{cases}}$

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

1. The control limits are $n{\bar {p}}\pm 3{\sqrt {n{\bar {p}}(1-{\bar {p}})}}$, where n is the sample size and ${\bar {p}}$ 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