A new machine is in the shop floor, the supplier wants it accepted, and the contract specifies a Cmk of 1.67. What happens next will determine whether the machine is even allowed into series production. The machine capability study is the litmus test, and it follows stricter rules than the subsequent process monitoring. An error in its execution often isn’t noticed until mass production begins, by which time the cost of rectifying the problem is significantly higher.
The most common mistake: equating machine capability studies with process capability studies. However, they measure different things. The machine capability study isolates the machine under ideal conditions, while the process capability study considers the entire process, including workers, materials, tool changes, and the environment. Anyone who confuses the two will determine the wrong sample size, select the wrong control limit, and obtain a metric that does not measure what the customer requires.
This article outlines the complete MFU process in five steps, explains how to calculate Cm and Cmk using a worked example, details the limit values according to VDA Volume 5, and highlights the typical errors that invalidate an analysis. You’ll also learn why the required Cmk is higher than the subsequent Cpk and how to document an MFU in a way that stands up to an audit.
KEY POINTS AT A GLANCE
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IN SHORTThe machine capability study (MFU) evaluates whether a machine is capable under ideal, constant conditions. The assessment is based on a continuous sample of at least 50 parts, evaluated using Cm and Cmk, with a typical requirement of Cmk 1.67 according to VDA Volume 5. It serves as the foundation for, but is not a substitute for, the subsequent process capability study. |
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CONTENTS OF THIS ARTICLE |
What is a machine capability study?
The machine capability study, or MFU for short, is a short-term procedure that evaluates a machine’s capability under idealized conditions. All variable factors are deliberately kept constant: same material, same operator, same settings, no tool changes.
The goal is to evaluate the machine alone. If it exhibits excessive variation under the best conditions, it will do so even more under real-world conditions. The MFU thus serves as a filter: Any machine that fails it should not even enter mass production.
| Variable | In the MFU | For PFU |
|---|---|---|
| Material | One batch | Actual batch diversity |
| Operator | One | Varies |
| Tool | No change | With change |
| Time period | Continuous | Spread across shifts |
The purpose of these idealized conditions becomes clear through error logic. If a machine exhibits excessive variation even under optimal conditions, the cause lies within the machine itself—for example, in bearing play, guide inaccuracy, or drive fluctuation. These causes can be corrected before the process begins, with all its additional disturbances. The MFU thus acts as a filter that prevents costly rework in series production.
MFU and PFU: The Crucial Difference
MFU measures the short-term capability of the machine, while the process capability study (PFU) measures the long-term capability of the entire process. The Cmk value from the MFU is therefore almost always better than the subsequent Cpk value because the MFU filters out all disturbances that the process introduces later on.
| Characteristic | MFU | PFU |
|---|---|---|
| Metric | Cm, Cmk | Cp, Cpk, Pp, Ppk |
| Considered | Only the machine | The entire process |
| Sample | At least 50 parts in a row | At least 25 subassemblies |
| Typical requirement | Cmk 1.67 | Cpk 1.33 |
| Time | Acceptance, Repeat | Ongoing series |
The difference in sample size between the two analyses has a statistical basis. The MFU uses 50 parts at a time because it only needs to estimate the short-term variation under stable conditions. The PFU requires subgroups over time because it must also capture drift. Anyone who confuses the MFU with the PFU sample size—or vice versa—will, in either case, obtain a metric that does not measure what is required.
The interplay of both tests results in a logical sequence for the ramp-up phase. First, the MFU demonstrates that the machine is fundamentally capable; then, the PFU verifies that the entire process performs consistently under real-world conditions. A passed MFU is thus the ticket to series production, while the PFU serves as proof that series production delivers consistently. Both steps build on one another and cannot be interchanged.
The MFU Process in Five Steps
An MFU follows a set procedure. Anyone who skips a step risks receiving a Cmk that will not be recognized in the audit.
| Step | Action | What to Watch For |
|---|---|---|
| 1 Preparation | Let the machine warm up; establish operating conditions | Do not change any settings during the test |
| 2 Production | Produce at least 50 parts continuously | Document the production sequence |
| 3 Measurement | Measure all parts in production sequence | Verify the capability of the measuring equipment beforehand |
| 4 Evaluation | Check the distribution; calculate Cm and Cmk | Confirm normal distribution |
| 5 Evaluation | Check against the limit value, document | Store the results in an audit-traceable manner |
The second step is the most critical. The 50 parts must be produced in a single, uninterrupted production run. As soon as the machine is readjusted during the process, the test is invalid because the machine is no longer being evaluated on its own.
The final step—documentation—is often underestimated. An MFU is only valid evidence if the raw data, boundary conditions, calculations, and evaluation are traceably linked. If the boundary conditions are not specified, an auditor cannot evaluate the test and will reject it. The documentation is not an appendix but an integral part of the evidence.
A word about the order of measurement. The parts must be measured in the exact order in which they were manufactured, as this is the only way to identify trends within the analysis. If the order is reversed, information about a possible drift over the 50 parts is lost, and a systematic effect remains undetected.
Calculate Cm and Cmk
The calculation of Cm and Cmk follows the same logic as that for Cp and Cpk. Cm is the quotient of the tolerance width and six times the standard deviation of the sample. Cmk is the smaller of the two one-sided values and takes the mean into account.
An example: A hole has a diameter of 10.00 millimeters with a tolerance of plus or minus 0.05. From 50 parts, the mean is 10.01 with a standard deviation of 0.008. Cm is approximately 2.08, and Cmk is approximately 1.67. The machine barely passes inspection.
A high Cm with a low Cmk means: The machine can manufacture to tight tolerances but is incorrectly adjusted. This is an adjustment issue, not a machine problem, and can be quickly resolved.
Amadeus Lederle, Chief Technology Executive, CSP Intelligence GmbH
Comparing Cm and Cmk is highly diagnostic. A high Cm with a low Cmk indicates a simple misalignment that can be corrected by readjustment. A low Cm, on the other hand, indicates a genuine machine variation problem that cannot be resolved through adjustment but only through mechanical repair. These two metrics thus distinguish between adjustment issues and machine problems.
A simple rule of thumb applies for day-to-day interpretation. If the Cmk is significantly lower than the Cm, you should first check the alignment before working on the machine. Only if proper centering does not sufficiently raise the Cmk is there actually a machine variation problem that must be resolved mechanically.
Limit Values According to VDA Volume 5
The limits for machine capability are higher than those for process capability. The reason is simple: Since the MFU operates under ideal conditions, the buffer must be larger so that the process remains capable later on under real-world conditions.
| Cmk | Evaluation | Consequence | Source |
|---|---|---|---|
| less than 1.67 | Unable | Rework the machine | VDA Volume 5 |
| 1.67 | Capable | Acceptance possible | VDA Volume 5 |
| Starting at 2.00 | Definitely capable | Large buffer for series production | VDA Volume 5 |
The logic behind the higher limit is a buffer principle. There is a loss of capability between the ideal MFU and the actual production run because the process introduces additional variation. The required Cmk of 1.67 creates precisely this buffer so that the subsequent Cpk still reaches the required 1.33. Anyone who barely passes the MFU with a Cpk of 1.33 risks an uncapable production process.
In practice, some customers require not only a minimum Cmk but also a minimum Cm value to ensure that the pure machine variation is small enough, regardless of the settings. A high Cmk alone can mask significant variation if the tolerance is very wide. The additional Cm verification closes this gap.
Common Errors in MFU
PRACTICAL NOTEThe most common error is an interrupted sample. If the machine is readjusted between parts 30 and 31, the 50 parts are no longer a valid MFU. Equally critical: an unproven measurement capability. If the measuring instrument itself has excessive variation, any Cmk value is meaningless. |
| Error | Effect | Correct |
|---|---|---|
| Sample interrupted | MFU invalid | 50 parts at a time |
| Measuring equipment not capable | Cmk distorted | MSA prior to MFU |
| Distribution not verified | Incorrect Cmk | Confirm normal distribution |
| Warm-up phase missing | Initial drift distorted | Let the machine warm up first |
The same applies to MFU: Most invalid results are not caused by calculation errors, but by violated boundary conditions. An interrupted sample, an uncalibrated measuring instrument, or a missing warm-up phase render the Cmk value meaningless, no matter how accurately the calculations are performed afterward. Discipline during execution is more important than the accuracy of the evaluation.
Documenting MFU Digitally
An MFU is only audit-ready when the raw data, calculations, and evaluations are traceably linked. The CSP Manufacturing OS records measurement values directly at the machine, automatically calculates Cm and Cmk, and archives the complete analysis in an audit-proof manner. During an audit, every machine acceptance can be verified at the push of a button. Our article on process data management in manufacturing explains how to set up a comprehensive database for this purpose.
In addition to the calculations themselves, the repeatability of the MFU is a key argument in favor of a system-supported solution. Since the analysis must be repeated after every significant change and at fixed intervals, the manual effort quickly adds up. Automated data collection and evaluation turn this repetition into a routine task rather than a project.
Frequently Asked Questions
What is a machine capability study?
A machine capability study (MFU) evaluates a machine’s capability under constant, idealized conditions. It uses a continuous sample of at least 50 parts and is evaluated using Cm and Cmk.
How many parts are needed for an MFU?
For a valid MFU, at least 50 parts produced in an uninterrupted production run are measured. This minimum number ensures a reliable estimate of the standard deviation.
What is the difference between an MFU and a PFU?
The MFU evaluates the machine alone under ideal conditions and uses Cm and Cmk. The process capability study (PFU) evaluates the entire process over time and uses Cp, Cpk, Pp, and Ppk.
What Cmk value is required?
In the automotive industry, VDA Volume 5 typically requires a Cmk of at least 1.67. This higher value provides the necessary buffer for later mass production conditions.
How is Cmk calculated?
Cmk is the smaller of the two one-sided values: the distance from the mean to the upper limit divided by three times the standard deviation, and the same expression for the lower limit. The smaller value is the Cmk.
Why is a higher Cmk required than a higher Cpk?
The MFU operates under ideal conditions without disturbances. The process will later introduce additional variation. The higher Cmk of 1.67 provides the buffer so that the process can still achieve a Cpk of at least 1.33.
Does the MFU need to be repeated?
Yes, in the event of significant changes to the machine, after major maintenance, and at specified intervals. The exact frequency of repetition is determined by the customer or internal guidelines.