Machine Capability Index (Cmk)

What is Machine Capability Index (Cmk)?

Machine Capability Index (Cmk) evaluates whether a specific machine can produce parts within specification limits under controlled, short-term conditions. It is typically assessed during machine acceptance trials (Run-off) using 50 consecutive parts measured from a single setup.

Cmk is calculated identically to Cpk but uses only machine-level variation (single operator, single material batch, short time span). This isolates the machine's inherent capability from process-level noise like operator changes, material lot variation, and environmental drift.

The standard requirement is Cmk ≥ 1.67 for machine acceptance, which is stricter than the Cpk ≥ 1.33 required for ongoing production. The higher threshold provides a safety margin, recognizing that long-term process variation will always be greater than short-term machine-only variation.

Formula: Cm = (USL - LSL) / (6 × σ_machine) Cmk = min((USL - x̄) / (3 × σ), (x̄ - LSL) / (3 × σ)) where σ is from short-term machine-only data

Example Calculation

Grinding machine acceptance test: USL = 25.05 mm, LSL = 24.95 mm. 50 parts: Mean = 25.01 mm, σ = 0.012 mm. Cm = (25.05 − 24.95) / (6 × 0.012) = 1.39. Cmk = min(1.11, 1.67) = 1.11. The machine fails acceptance because its mean is off-center (Cmk < 1.67).

When to Use This Calculator

• During machine acceptance trials (run-off) to verify that a new or rebuilt machine meets Cmk ≥ 1.67 before sign-off and payment
• After machine maintenance or overhaul to confirm that the machine has been restored to its original capability
• When comparing bids from machine tool vendors — require Cmk studies as part of the purchase specification to ensure quoted tolerances are achievable
• Before starting a Cpk study — if Cmk is insufficient, the process will never be capable regardless of operator skill or material quality
• When isolating variation sources — if Cmk is good but Cpk is poor, the problem lies in process-level factors (operators, materials, environment), not the machine itself

Common Mistakes to Avoid

• Mixing data from multiple setups, operators, or material lots — Cmk must isolate machine-only variation; any additional variation sources inflate σ and reduce the index
• Using fewer than 50 consecutive parts — the standard requires 50 parts produced in a single uninterrupted run; smaller samples give unreliable estimates
• Not measuring parts in production order — trend analysis (drift, oscillation) requires sequential data; random measurement order hides systematic machine behavior
• Accepting Cmk ≥ 1.33 for new machines — the standard threshold is Cmk ≥ 1.67, which is intentionally higher than the Cpk ≥ 1.33 production requirement to provide a safety margin for process-level variation
• Performing the study under non-representative conditions — use production speeds, feeds, and materials; a study under ideal lab conditions does not reflect real machine capability

How to Interpret Results

• Cmk < 1.33 means the machine cannot produce within specification — reject the machine or require rework/adjustment from the vendor
• Cmk 1.33-1.67 is marginal — the machine might be acceptable for non-critical dimensions but does not meet the standard machine acceptance threshold
• Cmk ≥ 1.67 meets the standard acceptance criterion — the machine has sufficient capability with margin for additional process variation
• Cmk > 2.0 indicates excellent machine precision — provides a comfortable buffer for process-level variation sources
• If Cm >> Cmk, the machine is precise but the mean is off-center — adjust the machine offset to center the distribution and improve Cmk

Related Standards & References

• VDA Volume 5 — German automotive standard for capability of measurement processes, including Cmk requirements and methodology
• AIAG SPC Reference Manual — Includes machine capability study procedures for automotive supplier qualification
• ISO 22514-3 — Machine performance studies methodology including sample size requirements and test procedures
• DIN 8602 — German standard for machine acceptance testing methodology used by machine tool manufacturers

Frequently Asked Questions

What is the difference between Cmk and Cpk?

Cmk measures machine capability under short-term, controlled conditions (single operator, material, setup). Cpk measures process capability including all sources of variation (multiple operators, material lots, environmental changes). Cmk is always ≥ Cpk. A machine with Cmk = 2.0 might show Cpk = 1.4 in production due to additional variation sources.

How many parts should I measure for Cmk?

The standard practice is 50 consecutive parts from a single uninterrupted production run. Some automotive OEMs (VDA 5) require 50 parts; others accept 25 for initial studies. The parts should be measured in production order to detect any trends or patterns. Never cherry-pick parts or mix parts from different setups.