np Chart

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Control Chart - np Chart


The np Chart is to observe and evaluate the behavior of a process over time, and take corrective action if necessary. It plots the number of defective units and is applicable to binomially distributed discrete defect data collected from subgroups of equal size.

The chart differs from p Charts in that they plot the actual number of defective units, rather than the proportion of defective units.

np Charts, or number of defectives chart, are similar to p Charts with just a few exceptions. np Charts are used in cases where the subgroup size remains constant. These charts are generally easier to understand because they deal with the actual number of defects rather than percentages.


control chart

np Chart plots the number of defective units.


A. Sample Count – Numbers of defective units observed

B. Sample Number – The chronological index number for the sample, or subgroup, whose numbers of defective units is being referenced

C. Lower Control Limit (LCL) – Represents the lower limit of the variation that could be expected if the process were in a state of statistical control, by convention equal to the Mean minus three Standard Deviations

D. Process Average Number of Units Nonconforming – (np) Average value of the number of defective units, over the period of inspection being referenced

E. Upper Control Limit (UCL) – Represents the upper limit of the variation that could be expected if the process were in a state of statistical control, by convention equal to the Mean plus three Standard Deviations

F. Plot of number of units nonconforming vs sample number. Any point in this plot above the UCL or below the LCL represents an out-of-control condition to be investigated

G. np Chart – Refers to the number of units nonconforming in a subgroup, where n is the subgroup size and p is the probability of a defective unit

H. Out of Control Point – By definition, any point that exceeds either the UCL or the LCL is out of control. Minitab has a number of tests available for out of control conditions, and labels each point with a number corresponding to the test which the point fails

Major Considerations

This chart plots the number of units defective, and not the number of defects

The use of an np Chart is preferred over the p Charts if using the actual number defective is more meaningful than the defectives rate, and the subgroup, or sample, size remains constant from period to period

Large subgroup sizes should always be selected (n>50 is considered normal), and the np value should always be greater than 5

When To Use np Charts

  • Primarily used to follow trends and cycles over time
  • Used when the subgroup size is constant from sample to sample
  • Used to evaluate progress after process changes and/or improvements
  • Used in cases to quickly and inexpensively gather data
  • When there are no specialized skills required to collect the data

The major assumptions in using np charts are identical to p charts. Except for plotting the actual number of defectives instead of the percentage of defects, the np chart is closely related to the p chart.

Application Cookbook

1. Determine purpose of the chart

2. Select data collection point

3. Establish basis for subgrouping

4. Establish sampling interval and determine sample size

5. Set up forms for recording and charting data and write specific instructions on use of the chart

6. Collect and record data. It is recommended that at least 20 samples be used to calculate the Control Limits

7. Count each "npi", the number of nonconforming units for each of the i subgroups

8. Compute the Process Average Number of Units Nonconforming np

9. Compute Upper Control Limit UCLnp

10. Compute Lower Control Limit LCLnp

11. Plot data points

12. Interpret chart together with other pertinent sources of information on the process and take corrective action if necessary

Statistical Process Control Basics

Statistical Process Control

Control Charts

Control Chart Selection

Control Limits

Capability Indices - Cpk, Etc.

Process Capability Study

Statistical Process Control Control Charts

Xbar & R (Range) Chart

Xbar & s (Standard Deviation) Chart

I (Individuals) & MR (Moving Range) Chart

p Chart

np Chart

u Chart

From np Chart to Statistical Quality Control.

From np Chart to Free Six Sigma Tools.

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