Cpk 1.67. This figure appears in many OEM specifications as a minimum requirement for quality-critical features. But what does it actually mean? How many defective parts correspond to a Cpk of 1.67? And what is the difference to Ppk 1.67 - two numbers that look identical but say fundamentally different things?
Process performance indicators are the foundation of statistical process control (SPC). They answer a key question: Is my process capable of reliably meeting the required tolerances - and if so, with what safety margin? Without these key figures, quality assurance is guesswork. With them, it is measurable.
This article explains all the relevant process KPIs (Cp, Cpk, Pp, Ppk, Cpm) with formulas, calculation examples and the key question: When to use which KPI - and how high should it be?
THE MOST IMPORTANT FACTS IN BRIEF
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BRIEFLY SUMMARIZED
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Process KPIs answer a statistical question: How well does the distribution of my measured values fit into the specified tolerance? This requires two pieces of information: the tolerance limits (USG = lower specification limit, OSG = upper specification limit) and the process distribution (mean value µ and dispersion σ).
The four basic terms
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THE BASIC IDEA BEHIND ALL PROCESS KPIS All process KPIs compare the ratio of tolerance width to process variation. Simplified: Key figure = tolerance width / (6 × σ). The greater this ratio, the more leeway the process has in relation to the tolerance limits. With Cpk = 1.0, the ±3σ limits of the process are exactly within the tolerance limits. This corresponds to 2,700 ppm scrap with a centered process. At Cpk = 1.33, the ±4σ limits are within the tolerance limits. This corresponds to 64 ppm scrap. At Cpk = 1.67, the ±5σ limits are within the tolerance limits. This corresponds to 0.6 ppm scrap. |
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Cpk 1.0 = 2,700 ppm scrap (0.27 %) with centered, stable process |
Cpk 1.33 = 64 ppm scrap (0.0064 %) IATF series production minimum Cpk |
Cpk 1.67 = 0.6 ppm scrap (6 × 10-⁵ %) IATF safety features Minimum Cpk |
Cpk 2.0 = 0.002 ppm - Six Sigma level Motorola / Six Sigma standard |
Five key figures cover all relevant aspects of process capability analysis. Each one answers a slightly different question - and each one is used in a different context.
| Cp Potential key figure | |
|---|---|
| Formula | Cp = (OSG - USG) / (6 × σ̂) |
| What it measures | Ratio between tolerance range and short-term process variation.Does not take into account whether the process is centered. |
| Use if | As a first overview of the process potential. Always consider together with Cpk . |
| Do not use if | Process is not centered: Cp can be good even though many parts are out of tolerance. |
| Practical example | T = 0.5 mm, σ̂ = 0.05 mm → Cp = 1.67. Good potential. |
| Cpk Key performance indicator | |
|---|---|
| Formula | Cpk = min[(OSG - µ) / (3σ̂), (µ - USG) / (3σ̂)] |
| What it measures | Smallest distance between process center point and nearest tolerance limit, standardized to 3σ̂. Takes centering into account. |
| Use if | As main key figure for the current process performance. Required by IATF, VDA and OEMs. |
| Do not use if | Process is unstable - Cpk is only meaningful for stable, normally distributed processes. |
| Practical example | µ = 10.15 mm, USG = 9.8, OSG = 10.5, σ̂ = 0.05 → Cpk = 2.33. Excellent. |
| Pp Long-term key figure | |
|---|---|
| Formula | Pp = (OSG - USG) / (6 × s) |
| What it measures | Like Cp, but with long-term total dispersion s (from all individual measured values). Shows the actual long-term performance. |
| Use when | According to PPAP/EMPB, to evaluate the overall performance across all influencing factors. |
| Do not use if | As a short-term indicator during ongoing production - Cpk is better suited for this. |
| Practical example | T = 0.5 mm, s = 0.07 mm → Pp = 1.19. Worse than Cp due to long-term effects. |
| Ppk Long-term performance | |
|---|---|
| Formula | Ppk = min[(OSG - µ) / (3s), (µ - USG) / (3s)] |
| What it measures | Like Cpk, but with long-term total scatter s. Shows long-term performance under all influencing factors (batches, shifts, tool changes). |
| Use when | According to PPAP/EMPB. Comparison with Cpk: if Ppk ≪ Cpk, there are systematic long-term effects. |
| Do not use if | As a real-time indicator - Ppk is calculated retrospectively from a longer data set. |
| Practical example | Ppk = 0.98 with Cpk = 1.52 → shift/tool change effects dominate. |
| Cpm Robustness index | |
|---|---|
| Formula | Cpm = (OSG - USG) / (6 × √(σ² + (µ - target value)²)) |
| What it measures | Expands Cpk by deviation of the process center point from the nominal value. Penalizes decentration more than Cpk. |
| Use if | Nominal value is in the center of the tolerance and decentration is particularly undesirable (e.g. for fits). |
| Do not use if | No clear nominal value is defined or the tolerance is asymmetrical. |
| Practical example | µ = 10.05 mm, nominal = 10.0, USG = 9.8, OSG = 10.5, σ = 0.05 → Cpm takes into account the 0.05 mm deviation from the nominal. |
Abstract formulas only become understandable with concrete figures. The following examples show complete calculations for typical production scenarios.
| Calculation example: Cpk - screw torque | ||
|---|---|---|
| Assembly station, torque specification 25 Nm ± 3 Nm. Measurement of 50 screw connections in 5 subgroups of 10. | ||
| # | Calculation | Calculation result |
| 1 | Record data OSG = 28 Nm, USG = 22 Nm, µ = 25.4 Nm |
Tolerance width T = 6 Nm |
| 2 | Calculate short-term σ̂ R̄ = 1.2 Nm → σ̂ = R̄/d₂ = 1.2/3.078 |
σ̂ = 0.390 Nm |
| 3 | Calculate Cp (28 - 22) / (6 × 0,390) = 6 / 2,340 |
Cp = 2.56 |
| 4 | Calculate Cpk min[(28-25.4)/(3×0.390), (25.4-22)/(3×0.390)] = min[2.22; 2.91] |
Cpk = 2.22 |
| Result: Cpk = 2.22 | ✓ Excellent | |
| Interpretation: Excellent process. Slight decentration towards OSG (Cp > Cpk). Readjustment may be useful to achieve Cp = Cpk . | ||
| Calculation example: Ppk - bore diameter according to PPAP | ||
|---|---|---|
| Pilot production, 125 measured values over 5 shifts. Bore Ø 12H7 (12.000-12.018 mm). | ||
| # | Calculation | Result |
| 1 | Enter data OSG = 12.018 mm, USG = 12.000 mm, µ = 12.009 mm |
125 measured values, 5 layers |
| 2 | Calculate total s Standard deviation from all 125 individual values (incl. layer effects) |
s = 0.0035 mm |
| 3 | Pp calculate 0.018 / (6 × 0.0035) = 0.018 / 0.021 |
Pp = 0.857 |
| 4 | Calculate Ppk min[(12.018-12.009)/(3×0.0035), (12.009-12.000)/(3×0.0035)] = min[0.857; 0.857] |
Ppk = 0.857 |
| Result: Ppk = 0.857 | ✗ Not capable (< 1.0) | |
| Interpretation: Not capable (< 1.0). Too much scatter despite good centering - probably layer or tool effects. Cause analysis required. | ||
Process KPIs only gain their meaning through reference values. The following traffic light classification shows how Cpk and Ppk values are evaluated in manufacturing practice - in accordance with IATF 16949 and VDA requirements.
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Class |
Value from |
Value to |
Rating |
PPM share |
Measure |
|---|---|---|---|---|---|
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Class A |
≥ 2,0 |
∞ |
Excellent - Six Sigma level |
< 0,002 |
No measure necessary. Process control can be reduced. |
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Class B |
1,67 |
< 2,0 |
Very good - safety features fulfilled |
< 0,6 |
Maintain. Regular Cpk inspection. IATF safety requirement fulfilled. |
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Class C |
1,33 |
< 1,67 |
Good - series production fulfilled |
< 64 |
Accepted. Strive for continuous improvement. IATF series production minimum fulfilled. |
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Class D |
1,0 |
< 1,33 |
Conditionally capable - monitoring required |
< 2.700 |
100% inspection or increased inspection frequency. Initiate improvement measures. |
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Class E |
< 1,0 |
- |
Not capable - immediate action required |
> 2.700 |
Stop production or 100% inspection. Root cause analysis (8D). Process improvement. |
The comparison of Cp and Cpk provides more information than any key figure alone. The following matrix shows the most important combinations and what they reveal about the process status.
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Cp |
Cpk |
Meaning |
Typical cause |
Measure |
|---|---|---|---|---|
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2,0 |
2,0 |
Perfect, centered process with excellent capability |
No problem - ideal condition |
Maintain. Extend inspection interval if necessary. |
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1,67 |
1,67 |
Very good, centered process - safety requirement fulfilled |
Process well adjusted and stable |
IATF safety feature: no measure necessary. |
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2,0 |
0,8 |
Process would have enough potential, but is strongly decentered |
Tool wear, setting errors, thermal drift |
Readjust process (shift mean value). Analyze reason for decentration. |
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0,8 |
0,8 |
Process has too much scatter - not capable even when centered |
Machine too imprecise, material variance too high, measuring system error |
Scatter reduction: Perform MSA, machine overhaul, activate SPC. |
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1,5 |
0,5 |
High scatter AND strong decentration at the same time |
Complex: unstable process with several disturbance variables |
100% check immediately. Control chart for process stabilization. Systematically separate causes. |
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1,33 |
1,25 |
Slight decentration with otherwise good process |
Small setting deviation or slight tool wear |
Readjust the process. Check setting value. Cp is approaching Cpk. |
Cpk without a control chart is like body temperature without a clinical thermometer - you know the value, but not the trend. Process performance indicators and SPC belong together.
-Amadeus Lederle CTE, CSP Intelligence GmbH
Process KPIs are not an academic exercise in the automotive industry - they are contractual requirements that must be verified for PPAP, EMPB and series monitoring. The following matrix shows the most important requirements.
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Standard / OEM |
Minimum Cpk start-up |
Minimum Cpk series |
Minimum Cpk Safety |
Remark |
|---|---|---|---|---|
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IATF 16949 / VDA general |
1,67 |
1,33 |
1,67 |
Basic requirement. Cpk from subgroups (short-term). At least 30 measured values for initial samples. |
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BMW Group |
1,67 |
1,33 |
1,67 |
BMW SQA: additionally Ppk ≥ 1.33 for long-term stability verification according to PPAP. |
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Volkswagen / VDA |
1,67 |
1,33 |
1,67 |
VDA Volume 4 / Formula-Q: Ppk ≥ 1.33 according to EMPB. Special features: Cpk ≥ 1.67. |
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Mercedes-Benz |
1,67 |
1,33 |
1,67 |
MBDC: Evidence for each characteristic in the control plan. Monthly reports for each special feature. |
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Ford (AIAG PPAP) |
1,67 |
1,67 |
1,67 |
Ford requires Cpk ≥ 1.67 from start of production for all KPCs. No exceptions without approval. |
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Stellantis (ANPQP) |
1,67 |
1,33 |
1,67 |
ANPQP Level C: complete proof of capability. Response plan prescribed for Cpk < 1.33. |
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Bosch internal |
2,0 |
1,67 |
2,0 |
Bosch as Tier 1: own requirements often stricter than OEM specifications. Cpk ≥ 2.0 for new lines. |
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ISO 9001 (general) |
- |
1,33 |
- |
No direct Cpk specification, but process control required. Cpk 1.33 as industry standard. |
Process indicators are frequently calculated - but even more frequently misinterpreted or applied under the wrong conditions.
The following list shows the most critical errors made in practice.
Error 1: Cpk without stability check
A Cpk value is only meaningful if the process is stable. Stability means: The process only shows random variation, no systematic patterns, trends or jumps.
Without a stability check (e.g. Shewhart control chart), a good Cpk can conceal an unstable situation - and a poor Cpk can overweight a temporary problem.
Error 2: Non-normally distributed data
All the key figures described assume normal distribution. With clearly non-normally distributed data (e.g. bimodal distributions, right-skewed measurements), Cpk provides incorrect reject probabilities. Check: Histogram, Anderson-Darling test or Shapiro-Wilk test before calculating the key figure.
In the case of non-normal distribution: use transformed key figures or non-parametric methods.
Error 3: Too few measured values
Cpk from 10 measured values is hardly statistically reliable. The measurement uncertainty of the Cpk estimator is so large with n=10 that even a Cpk of 1.8 can still be below 1.33 in the confidence interval.
VDA recommendation: at least 25-30 measured values for initial assessment, at least 100-125 for PPAP verification.
Error 4: Cpk instead of Ppk according to PPAP
For the production start-up capability verification according to PPAP / EMPB, Ppk is required - not Cpk. The reason: Ppk shows the long-term performance under all production conditions.
A company that supplies Cpk for PPAP supplies the wrong key figure - and may have declared short-term scatter as 'capability', which is not sustainable in long-term production.
Error 5: Missing measurement system analysis (MSA
) A Cpk value always includes the scatter of the measurement system. If the measuring system is poor (high Gage R&R), an apparently poor Cpk is actually a measuring device problem - and not a process problem. As a rule of thumb, measurement system variation should account for less than 10-30% of the total variation. Without MSA verification, no Cpk is trustworthy.
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What is the difference between Cpk and Ppk in simple terms?
Cpk measures the short-term capability of a process - in a sense: 'How good is the process right now, when it is optimally adjusted? Ppk measures long-term performance - 'How good is the process really, over shifts, batches and weeks?' Cpk is almost always higher than Ppk because long-term effects (tool wear, batch changes, temperature fluctuations) increase the real variance. A large difference between Cpk and Ppk is an indication that there are systematic long-term influences that should be reduced.
How many measured values do I need for a valid Cpk calculation?
As a minimum for an initial assessment: 25-30 individual measured values. For a PPAP/EMPB verification: at least 100-125 measured values across all relevant production conditions (different shifts, batches, time periods). With fewer measured values, the statistical estimation error is so large that the Cpk value does not provide a reliable statement - a Cpk of 1.5 from 15 measured values can lie within the confidence interval of 0.9 to 2.1.
What does a negative Cpk value mean?
A negative Cpk value means that the process center point is outside the tolerance limits - in other words, the majority of measurements are out of specification. In practice, this typically happens after an incorrect setting or with a machine that has not been correctly referenced after a crash. A negative Cpk is not a statistical curiosity, but an acute quality emergency.
Can I also calculate Cpk for one-sided tolerances?
Yes - but only the relevant side. For a minimum requirement (only USG, no OSG), Cpk is calculated as (µ - USG) / (3σ̂). For a maximum requirement (only OSG, no USG) as (OSG - µ) / (3σ̂). With one-sided tolerances, the 'minimum' criterion does not apply because there is only one tolerance limit. Cp and Pp cannot be meaningfully calculated for one-sided tolerances without an upper specification.
What is the difference between Cpk and sigma level?
Sigma level (often used in the Six Sigma context) and Cpk both measure process capability, but with different reference models. Cpk = 1.0 corresponds to a 3-sigma process (±3σ to the tolerance limit). However, Six Sigma counts sigma level as the distance from the process mean to the nearest tolerance limit in sigma units and typically adds 1.5 sigma for long-term drift. Therefore, 'Six Sigma' (= 6σ distance) does not correspond to Cpk = 2.0, but Cpk ≈ 1.5 with drift assumption. The sigma level is rarely used in the IATF/VDA context - Cpk applies directly there.
What is the measurement system analysis (MSA / Gage R&R) and why is it relevant for Cpk?
MSA (Measurement System Analysis) or Gage R&R (Repeatability and Reproducibility) analyzes what proportion of the observed measured value fluctuation is attributable to the measurement system - and not to the process. If Gage R&R is > 30 % of the total tolerance, the measuring system is unsuitable for measuring this characteristic. In this case, the measured Cpk is not the true process Cpk, but a mixture of process and measurement error scatter. IATF 16949 section 7.1.5.1 requires verification of the suitability of the measuring system before the Cpk calculation.
Which control chart is suitable for which application?
The most common control charts: x̄/R chart (mean/span) for subgroups of size 2-10 - standard in production. x̄/s chart (mean value/standard deviation) for subgroups > 10 - statistically more efficient. I/MR card (individual values/moving range) for individual measured values or if no subgroups can be formed - e.g. for long cycle times. EWMA map for small shifts to make them recognizable. In the IATF context, the x̄/R chart is the standard because it is easy to implement and well documented.
What does 'statistical process control (SPC)' mean in contrast to the process performance indicator?
Process performance indicators (Cpk, Ppk etc.) are a snapshot: they tell you how capable the process was over a period of time. SPC is a process monitoring system: it continuously monitors whether the process remains stable and gives signals when special situations occur. SPC without process performance indicator: You know that the process is stable, but not whether it is capable. Process performance indicator without SPC: You know how capable the process was, but not whether it still is. Together they provide complete statistical quality assurance.