NP chart

A np-chart is a type of control chart used to monitor the number of nonconforming units when measuring subgroups at regular intervals from a process.

Each point on the chart represents the number of nonconforming units in a subgroup.

The center line is the average number of nonconforming units. If unspecified, the process average proportion of nonconforming units is the total nonconforming units divided by the sum of subgroup sizes. Note that the center line varies when the subgroup sizes are unequal.

The control limits are either:
  • A multiple (k) of sigma above and below the center line. Default k=3.
  • Probability limits, defined as the probability (alpha) of a point exceeding the limits. Default alpha=0.27%.

A Binomial distribution is assumed. That is, units are either conforming or nonconforming, and that nonconformities are independent; the occurrence of a nonconforming unit at a particular point in time does not affect the probability of a nonconforming unit in the periods that immediately follow. Violation of this assumption can cause overdispersion; the presence of greater variance that would be expected based on the distribution. When k-sigma limits are used the normal approximation to the binomial distribution is assumed adequate which may require large subgroup sizes when the proportion of nonconforming units is small.

A np-chart is useful when the number of units in each subgroup is constant as interpretation is easier than a p-chart. For data with different subgroup sizes the center line and control limits both vary making interpretation difficult. In this case, you should use a p-chart which has a constant center line but varying control limits.

For small subgroup sizes, the lower control limit is zero in many situations. The lack of a lower limit is troublesome if the charts use is for quality improvement as the lower limit is desirable as points appearing below that value may reflect a significant reduction in the number of nonconforming units. It is necessary to increase the subgroup size to overcome this issue.