Capability analysis

When measuring continuous data, use capability analysis to determine whether the process is capable of producing output that meets customer requirements.

Normal capability analysis

Use normal capability analysis to provide 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

Your data must be continuous Y (output), with at least one specification.

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 normal capability analysis 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 normal capability analysis 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 normal capability analysis.
  • The normal capability analysis and the Normal Capability Sixpack are best used together. The normal capability analysis displays more statistics than the Normal Capability Sixpack. However, the Normal Capability Sixpack 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.

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 a normal capability analysis, 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.

For more information, go to Insert an analysis capture tool.

Nonnormal capability analysis

Use a nonnormal capability analysis to provide 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.

A nonnormal capability analysis does not include any way to assess process stability, for example, control charts, and it does not include any way to determine 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

Your data must be a continuous Y (output), with at least one specification.

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 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, 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 eliminate the cause of your bi-modal data, you can try the normal report for your final performance analysis, if your data are reasonably normal.
  • A nonnormal capability analysis 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.
  • A nonnormal capability analysis and the Nonnormal Capability Sixpack are best used together. While a nonnormal capability analysis displays more statistics, the Nonnormal Capability Sixpack includes graphs to validate 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.

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 a nonnormal capability analysis.
  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. Click Options to select which capability statistics to display. You can choose to include benchmark Z's.

For more information, go to Insert an analysis capture tool.

Normal Capability Sixpack

Use a Normal Capability Sixpack to provide a complete analysis of process stability using six charts including control charts, subgroup charts, process capability charts (both long-term and short-term), and a normal probability plot (for verifying reasonable normality). The analysis also includes only the traditional capability measures of Cp, Cpk, Pp, Ppk - it does not provide any of the standard Six Sigma performance measures (long-term Z, short-term Z, DPMO).

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?
  • Was the process stable during these assessments?
When to Use Purpose
Start of project Perform a baseline capability analysis to determine process 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

Your data must be continuous Y (output), with at least one specification.

Guidelines

  • Data are assumed to come from a normal distribution; however, the consequences of having non-normal data are not serious if the data are reasonably normal. Badly skewed data can be easily fixed using a transformation, such as the Box-Cox, which is an option in this report.
  • A normal capability analysis and the Normal Capability Sixpack are best used together. While a normal capability analysis displays more statistics, the Normal Capability Sixpack includes graphs to validate process stability and reasonable normality, 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 are evaluated as though they are continuous.

How-to

  1. Verify 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. In the Minitab worksheet, you can enter all the data in a single column or you can enter each subgroup into a row. Minitab can also directly import from databases, text files, Microsoft Excel, and so on.
  4. You must provide at lease one specification limit to produce the Normal Capability Sixpack.
  5. You can use the Box-Cox transformation if your data are not reasonably normal.

For more information, go to Insert an analysis capture tool.

Nonnormal Capability Sixpack

Use the Nonnormal Capability Sixpack to provide a complete analysis of process stability using six charts including control charts, subgroup charts, and process capability charts (long-term only), and a probability plot for the selected distribution (for verifying a reasonable fit to the data). The analysis also includes only the traditional capability measures of Pp, Ppk; it does not provide any of the standard Six Sigma performance measures (long-term Z, short-term Z, DPMO).

The Nonnormal Capability Sixpack gives you 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?
  • Was the process stable during these assessments?
When to Use Purpose
Start of project Perform a baseline capability analysis to determine process performance at the start of the project. The 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

Your data must be continuous Y (output), with at least one specification.

Guidelines

  • Because the Nonnormal Capability Sixpack 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. It is important that you select an appropriate distribution, as 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.
  • The Individual Distribution Identification tool in Minitab can help you select a distribution. This tool runs goodness-of-fit tests for all 13 distributions. Low p-values in these tests indicate poor fits, so select one 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 because 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 fact 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 bi-modality 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 a normal capability analysis for your baseline, and use the observed PPM as the measure of long-term performance instead of the expected PPM. Once 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.
  • A nonnormal capability analysis and the Nonnormal Capability Sixpack are best used together. While a nonnormal capability analysis displays more statistics, the Nonnormal Capability Sixpack includes graphs to validate 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, you data are often evaluated as though they are continuous.

How-to

  1. Verify 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 them 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. 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 step.
  5. You must provide at least one specification limit to produce the Nonnormal Capability Sixpack.

For more information, go to Insert an analysis capture tool.

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