Capability Analysis (Nonnormal)

Summary

Provides a complete set of performance measures including standard Six Sigma statistics (for example, long-term Z and DPMO), "traditional" capability measures (for example, Pp and Ppk), and observed and expected defect rates.

The Capability Analysis: Nonnormal 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.

You have the option of choosing from 13 different distributions or using a Johnson Transformation for cases where none of the distributions provide an adequate fit to the data.

Answers the questions:
  • What is the capability of the process (long-term only) at the start of the process improvement project?
  • What is the capability of the process (long-term only) 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. 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

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 define how you will sample subgroups over time. Ensure you are using rational subgroups whenever possible.
  3. Collect data for the rational subgroups and enter the data into Minitab. You can enter all the data in a single column in the Minitab worksheet, or you can enter each subgroup into a row of the worksheet. Minitab can also directly import from databases, text files, Microsoft Excel, and so on.
  4. Determine which distribution best fits your data. You can use the Individual Distribution Identification tool in Minitab for this task.
  5. You must provide at lease one specification limit to produce the Capability Analysis: Nonnormal report.
  6. Specification limits can be defined as a boundary. By using a boundary, you are saying that it is impossible to have data outside of the specification limit (for example, the yield from a chemical process cannot be greater than 100%). In that case, Minitab will not calculate the expected DPMO for whichever limit has been defined as a boundary. Note, if you define both specification limits as boundaries, Minitab will not calculate any expected DPMO because you have said it is impossible to have a defect.
  7. The Options button lets you select which capability statistics to display. You may choose to include or not include benchmark Z's.

Guidelines

  • Because this report does not use the normal distribution as its basis, you do not need to verify normality.
  • You must select an alternative distribution to model your data and, more importantly, an appropriate distribution because the performance measures are based on probabilities from the assumed distribution. If you select a poor-fitting distribution, you cannot expect to have very accurate results. Minitab's Individual Distribution Identification tool can help you select a distribution. This tool runs goodness-of-fit tests for all 13 distributions. A low p-value in these tests indicates a poor fit, so select a test with a higher p-value.
  • If none of the distributions fit very well, look at a histogram of your data. You probably do not have badly skewed data, as one of the distributions would have provided a reasonable fit for almost any skewed data. You may have bi-modal data, which no distribution will fit well. This is important information about your process and may help you find a possible solution for your project. If you can find the cause of the bimodality and eliminate it, you will almost always reduce the process variation at the same time. If you have bi-modal data, a suggestion is to use the Process Capability: Normal report for your baseline, and use the Observed PPM as the measure of long-term performance instead of the Expected PPM. After you have eliminated the cause of your bi-modal data, you can try the normal report for your final performance analysis, if your data are reasonably normal.
  • The Capability Analysis: Nonnormal report does not report any short-term performance measures (for example, short-term Z and Cp). If you want to report short-term Z statistics, you can add 1.5 (a typical shift factor) to the reported long-term Z.
  • Capability Analysis: Nonnormal and Capability Sixpack: Nonnormal reports are best used together. While the Capability Analysis: Nonnormal report displays more statistics, the Capability Sixpack: Nonnormal report includes graphs for validating process stability and the goodness of fit for the selected distribution, which are 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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