u Chart

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Control Chart - u Chart


Purpose

The u Chart is used to observe and evaluate a process behavior over time and take corrective action if necessary. They plot defects per unit data collected from subgroups of equal or unequal size. It differ from c Charts in that they plot the proportion of defects, rather than the number of defects



u Charts measure discrete data. It is similar to c Charts in that they are used in cases where a single unit is likely to have many defects. The differences are in the calculation of control limits and that the plotted points represent the average number of nonconformities per unit. A u Chart is used when the unit size of a subgroup varies from subgroup to subgroup.

Anatomy

Control Chart - U Chart

Reference: Statistical Process Control – Ford/GM/Chrysler

Terminology

A. Sample Count – Numbers of defects per unit observed

B. Sample Number – The chronological index number for the sample, or subgroup, whose numbers of defects per unit 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 times the square root of the process Standard Deviation

D. Process Average Number of Defects per Unit – Average value of the number of defects per unit, 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 timesthe square root of the process Standard Deviation

F. Plot of number of defects per unit vs sample number. Any excursion in this plot above the UCL or below the LCL represents an out-of-control condition and should be investigated

G. u Chart – The title "u" Chart refers to the number of defects per unit in a subgroup

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

The chart may be used in situation where the sample includes more than one unit, and must always be used when the sample size varies from one period to the next

When To Use u Charts

  • Primarily used to follow trends and cycles over time
  • When the subgroup size varies from subgroup to subgroup
  • When the probability of an occurrence is less than 10 percent
  • When occurrences are independent from one another

U charts are used when counting the number of occurrences of many defects across many items.


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.

7. Count each "ci", the number of nonconformities for each of the i subgroups

8. Compute the Process Average Number of Nonconformities per Unit u

9. Compute Upper Control Limit UCLu

10. Compute Lower Control Limit LCLu

11. Plot the 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 U Chart to Statistical Quality Control.

From U Chart to Free Six Sigma Tools.

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