Np-chart (original) (raw)

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 p ¯ = ∑ i = 1 m ∑ j = 1 n { 1 if x i j defective 0 otherwise m {\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}}} {\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 n p ¯ ± 3 n p ¯ ( 1 − p ¯ ) {\displaystyle n{\bar {p}}\pm 3{\sqrt {n{\bar {p}}(1-{\bar {p}})}}} {\displaystyle n{\bar {p}}\pm 3{\sqrt {n{\bar {p}}(1-{\bar {p}})}}}
Plotted statistic n p ¯ i = ∑ j = 1 n { 1 if x i j defective 0 otherwise {\displaystyle n{\bar {p}}_{i}=\sum _{j=1}^{n}{\begin{cases}1&{\mbox{if }}x_{ij}{\mbox{ defective}}\\0&{\mbox{otherwise}}\end{cases}}} {\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 n p ¯ ± 3 n p ¯ ( 1 − p ¯ ) {\displaystyle n{\bar {p}}\pm 3{\sqrt {n{\bar {p}}(1-{\bar {p}})}}} {\displaystyle n{\bar {p}}\pm 3{\sqrt {n{\bar {p}}(1-{\bar {p}})}}}, where n is the sample size and p ¯ {\displaystyle {\bar {p}}} {\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, n {\displaystyle n} {\displaystyle n}, is constant.

See also

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References

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  1. ^ Montgomery, Douglas (2005). Introduction to Statistical Quality Control. Hoboken, New Jersey: John Wiley & Sons, Inc. p. 279. ISBN 978-0-471-65631-9. OCLC 56729567. Archived from the original on 2008-06-20.