Capability Analysis (Poisson)

Summary

The Capability Analysis (Poisson) report measures the stability of a single process step (or data-collection point) over time and reports on the long-term capability (using DPU, there is no DPMO or Z) of that step based on the observed average defective rate. You can use this report for projects in which the measurement system is only capable of counting the number of defects observed in a unit as a means of measuring performance.

Answers the questions:
  • What is the capability of a single process step, or data collection point, at the start of the process improvement project?
  • What is the capability of the process step, or data collection point, after improvements have been made?
  • Was the process stable during these assessments?
When to Use Purpose
Start of project Perform a baseline capability analysis on the process to determine the capability of a single process step, or data-collection point, at the start of the project. A baseline analysis helps you set improvement goals for the project.
Mid-project Perform a confirmation capability analysis after improvements have been implemented to confirm that the process performs as predicted.
End of project Perform a capability analysis after implementing controls to obtain a final assessment of process capability, and also to determine whether the improvement goals of the project were attained.

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 a defect (what it is and is not).
  2. Verify you can accurately assess each unit (that is, 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 into one column. In another column, enter the size of each sampled unit. 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 of the analysis.

Guidelines

  • The Capability Analysis (Poisson) report requires that you have a clear definition as to what constitutes a defect and what does not. Use this report for processes in which the measurement system is capable of recording the number of observed defects in each unit sampled.
  • This analysis measures the capability and evaluates the stability of the process, using a U chart. You can optionally run tests for special causes on the U chart.
  • This analysis provides a value of defects per unit (DPU), which can be used to obtain an estimate of the throughput yield (a metric commonly associated with Six Sigma) by using the approximation YTP = exp(-DPU). However, note that this approximation is only accurate when the ratio of observed defects to total opportunities approaches 0 (implies either a high opportunity count or a low defect count). The exp(-DPU) approximation always overestimates the true throughput yield, and the severity of the overestimation is dramatic for low opportunity counts.
  • For this reason, if you know the opportunity count per unit, and you observe the number of defects, you should use the Capability Analysis (Binomial) report rather than the Capability Analysis (Poisson) report. You should only use the Capability Analysis (Poisson) report when you have an unknown (but high) opportunity count. For example, how many defects in a square yard of cloth? There are infinite opportunities. On the other hand, if you must fill in 20 pieces of information on a form and you are counting the defects (incorrect information) on the form, there are 20 opportunities per form. The first example is a valid use of the Capability Analysis (Poisson) report; however, the second example is one in which the Capability Analysis (Binomial) report would be better. In both cases, Minitab's Six Sigma Product Report may be a better choice.
  • While Capability Analysis (Poisson) report does not integrate the performance of multiple process steps into a single measure, both the Capability Rollup Report and Minitab's Six Sigma Product Report integrate multiple steps (either attribute or continuous) into a single capability measure (including adjusting for process irregularities).
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