Ppk process performance

Under the conventional normal model, Ppk is the smaller one-sided index calculated using overall observed SD. Its scope depends on the collection window and conditions. Minitab normal capability interpretation

In the dimensional example, the mean is 10.020 mm and the upper limit is 10.100 mm. Overall SD of 0.020 mm gives Ppk = 1.333, controlled by the upper side. With a separately justified within-subgroup SD of 0.010 mm, the same mean and limits give Cpk = 2.667.

Formula and quantities

For a normal analysis using the conventional six-standard-deviation reference spread:

• PPU = (USL − mean) / (3s)
• PPL = (mean − LSL) / (3s)
• Ppk = min(PPU, PPL)
• Pp = (USL − LSL) / (6s)

Here s is the overall sample standard deviation, and USL/LSL are specification limits. The indices are dimensionless when consistent units are used. Minitab’s formula documentation identifies an overall standard deviation and a configurable sigma-tolerance multiplier, with 6 as the default. Record that setting instead of assuming every software output uses the same convention. Minitab overall capability formulas

Pp describes spread relative to the specification width; Ppk also responds to the mean’s position. A large Pp with a smaller Ppk can indicate an off-center process. A negative one-sided index occurs when the mean lies beyond the corresponding specification limit. Do not replace it with zero or reinterpret it as a percentage. The index identifies the limiting side, so inspect both tails and the actual observations. JMP process capability definitions

Ppk versus Cpk

JMP distinguishes Cpk’s within-subgroup estimator from Ppk’s overall estimator. These are estimation choices, not interchangeable labels. Rational subgroups and the chosen within estimator matter to the comparison. A gap can indicate between-subgroup shifts or drift, but does not by itself identify the physical cause. JMP within and overall sigma

Minitab’s current options also support different naming conventions, study stages, and calculation methods. Its Six Sigma labels and AIAG/VDA labels do not map simply by reading the letters alone; .Z and .G identify different calculation approaches. Preserve the software version, study purpose, estimator, and calculation settings when comparing reports. Minitab capability-analysis options

Establish what the data represent

Collect continuous measurements over conditions relevant to the intended claim, including appropriate time coverage and sources of variation. Keep time order and identifiers such as machine, cavity, setup, material lot, and shift where relevant. Minitab recommends sufficient data over a sufficiently long period and rational subgroups of similar items produced under the same conditions. Its suggested 100 total observations is guidance for that analysis, not a universal contractual sample-size rule. Minitab data considerations

Assess the measurement process too. Minitab’s measurement-system guidance distinguishes variation introduced by the measurement system from variation in the production process. Poor discrimination, repeatability, or operator effects can change the observed spread; systematic bias can affect location. A calibration sticker alone does not quantify those effects in the actual collection method. Minitab measurement-system analyses

Stability and distribution limits

Use time-ordered plots or suitable control charts to assess stability. NIST describes stability in terms of constant mean, variance, and distribution over time. A histogram can conceal a sequence of shifts. Ppk can still be computed numerically from unstable data, but that historical summary does not establish predictable ongoing capability. Investigate and describe instability before using the result to predict future production. NIST process stability

The normal formulas do not automatically produce reliable tail probabilities for skewed, bounded, mixed, or otherwise nonnormal data. Minitab’s nonnormal analysis can calculate Ppk using a fitted-distribution Z-score method and also offers other methods. Thus “Ppk” on a nonnormal report need not be the simple mean-and-standard-deviation calculation above. Identify the model and check its suitability, especially near specification tails. Minitab nonnormal overall capability

Illustrative calculation

Assume a hypothetical dimensional study has LSL = 9.900 mm, USL = 10.100 mm, mean = 10.020 mm, and overall s = 0.020 mm. Then:

• PPU = 0.080 / 0.060 = 1.333.
• PPL = 0.120 / 0.060 = 2.000.
• Ppk = 1.333, controlled by the upper side.
• Pp = 0.200 / 0.120 = 1.667.

If a separately justified within-subgroup estimate were 0.010 mm, the corresponding conventional Cpk would be 2.667. That contrast illustrates the effect of the denominator; it does not prove that within variation can be achieved across production simply by recentering. These assumed values demonstrate arithmetic, not a validated study or acceptance threshold. Formula basis

Report the result with its limits

Report the specification/revision, sampling window, observations and exclusions, time plots, distribution assessment, mean, variation estimator, Pp/Ppk and one-sided indices, and software settings. Include confidence intervals or an agreed lower confidence bound where required. Minitab provides both one- and two-sided capability bounds; the chosen confidence level and sample size affect their width. A point estimate barely exceeding a threshold is not equivalent to its lower bound exceeding that threshold. Minitab confidence-interval options

Separate observed out-of-specification counts from fitted-distribution estimates and from a customer’s required performance criterion. Although 1.33 is a commonly cited benchmark, use the actual agreed requirement and rule. Ppk is a process statistic, not an individual-part inspection result or authorization to release nonconforming product. Minitab interpretation and benchmark guidance

Related reference

Inspection and quality documents