Capability Analysis (Normal)

Summary

Provides a very complete set of performance measures, including standard Six Sigma statistics (short-term Z, long-term Z, and so on), traditional capability measures (Cp, Cpk, Pp, Ppk, and so on), and observed and expected defect rates (the expected rates are based on normal probabilities).

However, the report does not include any means for assessing process stability (for example, control charts), nor does it include any means for determining if an adequate amount of data has been collected.

Answers the questions:
  • What is the capability of the process (both long-term and short-term) at the start of the process improvement project?
  • What is the capability of the process (both long-term and short-term) after improvements have been made?
When to Use Purpose
Start of project Perform a baseline capability analysis on the process to determine its performance at the start of the project and to set improvement goals for the project.
Mid-project Perform a capability analysis after improvements have been implemented to confirm that the process performs as expected.
End of project Perform a capability analysis after implementing controls to obtain a final assessment of process capability and also determine whether the improvement goals of the project were attained.

Data

Continuous Y (output), at least one specification.

How-To

  1. Verify that the measurement system for the Y data is adequate.
  2. Establish a data collection strategy to ensure that you are using rational subgroups whenever possible.
  3. Collect data for the rational subgroups and enter the data into Minitab. In the Minitab worksheet, you can enter all the data in a single column or you can enter each subgroup into a row. You can also enter the data into databases, text files, Microsoft Excel worksheets, and so on. Minitab can directly import data from these sources.
  4. To produce the Capability Analysis (Normal) report, you must provide at least one specification limit.
  5. You can define the specification limits as boundaries. This means that you cannot have data outside of the specification limit (for example, the yield from a chemical process cannot be > 100%). If you do, Minitab will not calculate the expected DPMO for whichever limit has been defined as a boundary. If you define both specification limits as boundaries, Minitab will not calculate an expected DPMO (you have said it is impossible to have a defect).
  6. You may use the Box-Cox transformation if your data are not normal.
  7. Click Options to select which capability statistics to display. You can choose to include benchmark Z's.

Guidelines

  • Data are assumed to come from a normal distribution. While this statement is true, the consequences of having nonnormal data are not serious if the data are reasonably normal. You can transform badly skewed data using a transformation, such as the Box-Cox, which is an option in this report.
  • The short-term Z statistics in the Capability Analysis (Normal) report are different than those reported in the Six Sigma Process Report. The reason is that the Six Sigma Process Report uses an absolute best-case approach (the process is centered on its target and only common-cause variation is present) when calculating the short-term Z, while the Capability Analysis (Normal) report uses a less-than-best-case approach (the process has only common-cause variation, but it is not assumed to be centered on its target). The Six Sigma Process Report, therefore, gives a better estimate of the absolute process potential.
  • Sometimes, you will have trouble collecting data in rational subgroups. In these cases, you should use the long-term standard deviation and resulting long-term Z to establish the short-term Z (by subtracting a "typical" value for process shift) than to estimate the short-term Z from a moving average. The moving average assumes that consecutive items are somewhat alike, which can be an unsafe assumption in many cases. Unlike the Six Sigma Process Report, which includes this option, you must do this manually in Capability Analysis (Normal).
  • The Capability Analysis (Normal) report and the Capability Sixpack (Normal) report are best used together. The Capability Analysis (Normal) report displays more statistics than the Capability Sixpack (Normal) report. However, the Capability Sixpack (Normal) report includes graphs for validating process stability and reasonable normality, which is critical when using the performance measures.
  • If you have discrete numeric data from which you can obtain every equally spaced value, and you have measured at least 10 possible values, your data often are evaluated as though they are continuous.
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