Machine Capability Study (MFU)

Overview

The Machine Capability Study (MFU) is a central tool of quality assurance used to assess the ability of a machine or manufacturing process to produce parts within specified tolerance limits. In contrast to process capability analysis (SPC/Ppk), the MFU considers exclusively the short-term variation of a machine under controlled conditions.

The MFU is typically conducted in the following cases:

• New acquisition of a machine (acceptance inspection)
• Maintenance or repair
• Relocation of a machine to a new site
• Periodic inspection as part of preventive maintenance

Info: The MFU measures the inherent capability of the machine itself, without influences such as tool wear, material changes, or operator effects. For evaluation of the overall process, use the Process Capability Analysis (Ppk).

Typical Procedure

1. Set up the machine under stable conditions (same operator, same material, same environment)
2. Produce at least 50 consecutive parts (recommended: 50 to 100 parts)
3. Measure all parts and enter the measurement values in my8data
4. Specify tolerance limits (USL/LSL) and optionally the target value
5. Perform the evaluation and assess the capability indices

Overview of Capability Indices

Warning: A high Cm value alone is insufficient. Only when Cmk also reaches the threshold is it ensured that the process both spreads sufficiently narrowly and is centered within the tolerance.

Data Entry and Specifications

Enter Measurement Values

In my8data, you have several ways to record your measurement data for the MFU:

• Manual entry: Enter the measurement values directly in the input table. Use the Tab key to quickly move between fields.
• Import from Excel/CSV: Upload a prepared file with your measurement values. The data is automatically detected and loaded.
• Clipboard (Copy & Paste): Copy measurement values from any source and paste them into the input field.

Set Specification Limits

To calculate machine capability, you must define the specification limits (tolerance limits):

Tip: If you have only a one-sided tolerance (e.g., only a maximum), leave the corresponding field empty. The calculation will then determine only the one-sided index.

Sample Size

For a meaningful MFU, the sample size should be at least n = 50. The following table shows recommended sample sizes:

Info: According to VDA Volume 5 and AIAG SPC Reference Manual, a sample size of at least 50 parts is recommended for machine capability studies.

Capability Indices Cm and Cmk

Machine Capability Index Cm

The Cm value (Machine Capability Index) describes the ratio of tolerance width to the measured variation of the machine. It indicates how much space the process has within the tolerance, regardless of where the mean is located.

Formula:

Cm = (USL - LSL) / (6 * s)

Where:
- USL: Upper Specification Limit
- LSL: Lower Specification Limit
- s: Standard deviation of the sample

A Cm value of 1.00 means that the process variation (6s) exactly equals the tolerance width. In practice, significantly higher values are required.

Critical Machine Capability Index Cmk

The Cmk value (Critical Machine Capability Index) additionally considers the position of the mean relative to the tolerance center, in addition to the variation. It is always less than or equal to the Cm value.

Formula:

Cmk = min((USL - x̄) / (3 * s), (x̄ - LSL) / (3 * s))

Where:
- x̄: Arithmetic mean of the sample
- The smaller of the two values is decisive

Evaluation of Capability Indices

Tip: If Cm differs significantly from Cmk, this indicates that the machine spreads sufficiently narrowly, but the mean is not centered. In this case, a simple adjustment of the machine setting can often help.

Confidence Intervals

The calculated indices are based on a sample and are therefore subject to statistical uncertainty. my8data automatically calculates confidence intervals that indicate the range in which the true index value lies with a certain probability.

Info: With larger sample sizes, the confidence intervals become narrower, which increases the significance of the analysis.

Distribution Analysis

Normality Test

A fundamental prerequisite for calculating Cm and Cmk is that the measurement values are normally distributed. my8data automatically performs a normality test to verify this assumption.

The following test methods are used:

Warning: If the normality test shows a significant deviation from normal distribution (p-value < 0.05), the calculated Cm/Cmk values should be interpreted with caution. In such cases, data transformation or the use of alternative distribution models may be necessary.

Histogram

The histogram displays the distribution of measurement values graphically. It shows how frequently certain measurement value ranges occur and enables a visual assessment of the distribution.

The histogram displays the following elements:

• Bars: Frequency of measurement values per class
• Normal Distribution Curve: Theoretical normal distribution based on mean and standard deviation
• Specification Limits: Red vertical lines at USL and LSL
• Mean: Green vertical line at the arithmetic mean

Probability Plot

In the probability plot (Normal Probability Plot), measurement values are plotted against the expected quantiles of the normal distribution. If the points lie approximately on a straight line, this supports a normal distribution.

Interpretation of Distribution Analysis

Tip: Use the distribution analysis not only to validate the normal distribution assumption, but also as a diagnostic tool to identify potential problems early.