Summary

A statistical process control (SPC) tool that plots the number of defects in each sampled unit over time. You can use the U chart for processes where the measurement system is only capable of counting the number of defects in a sampled unit. The U chart is an industry standard for monitoring/ controlling process outputs over time and can be used for samples that are different sizes (e.g. different sized units or different sized lots of like sized units).

Answers the questions:
  • How much common-cause variation does the process exhibit?
  • Is the process stable over time?
  • Did special causes exist during the timeframe of the plotted data?
  • Does evidence suggest something has changed or the process is performing differently than expected?
  • Does the defect rate of the process change at different levels of a process input?
  • Do the dynamic patterns of the process output change at different levels of a process input?
When to Use Purpose
Pre-project Assist in project selection by identifying the process steps that exhibit high defect rates, unstable variation, or other symptoms pointing to the need for improvement.
Start of project Verify process stability when performing a baseline capability analysis.
Mid-project Investigate effects of input variables on process output over time.
Mid-project Verify process stability when performing confirmation runs after implementing improvements.
End of project Verify process stability after implementing controls to obtain a final assessment of process capability.
End of project Graphically compare the pre-project process dynamic behavior to the post-improvement dynamic behavior.
Post-project Control inputs to the improved process after the project is complete.
Post-project Monitor output of the improved process after the project is complete.

Data

Discrete numeric Y (number of defects), size of inspected unit (for example, square inches of surface or words of text).

How-To

  1. Define what is and what is not a defect.
  2. Verify you can accurately assess each unit (verify the measurement system).
  3. Establish a data collection strategy to define how you will sample units over time.
  4. In Minitab, enter the number of observed defects from each sampled unit in one column and the size of each sampled unit in another column. If the units are all the same size, you can specify a constant instead of using a separate column.
  5. You can also use a historical process defects-per-unit as the basis for establishing control limits.
  6. Optionally, Minitab can evaluate four rules to determine if special causes are present.
  7. Optionally, you can identify meaningful process stages and input conditions in the chart by entering a categorical variable into an additional column. Stages have different center lines and control limits that help you make comparisons across stages. For example, you can examine changes in the process defect rate before, during, and after the implementation of a new procedure on one U chart.

Guidelines

  • If your sample sizes are different, your calculated control limits will also be different. However, if the largest or smallest sample size differs from the average sample size by more than 25%, you should use a constant sample size because it will result in constant control limits and makes the chart more easily understood.
  • A defect is any nonconformance of a product or service. To count defects or defectives, you must have a clear definition as to what does and does not constitute a defect.
  • The defect rate is the average number of defects per unit. A process output (product or service) can have a defect rate less than or greater than one.
  • You can use a categorical variable with the U chart to show the effects of different input conditions. Minitab refers to this as stages. For example, if you want to examine the defect rate of a forms processing operation (Y) to see whether differences exist between three shifts, you can use the shift as the stage variable and see whether the mean, variation, or within-shift patterns change between the three shifts.
  • When using a categorical variable to set up stages for the U chart, you should have at least 30 observations in each stage. The U chart requires enough data within each stage to reliably estimate the within-stage process defect rate.
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