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

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.[1]

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

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