How PGM-Q is validated

PGM LLC · Last updated 26 September 2026 · Version 1.0.1

If you are going to put a Cpk in front of a customer, you are entitled to ask where the number came from. This page says exactly that.

The approach. Every statistical routine in PGM-Q has automated tests that compare its output against an independent implementation — SciPy 1.17.1 and NumPy 2.4.4 — on synthetic datasets committed alongside the code. The expected values were computed once in Python and written into the repository as fixtures. The tests run on every change, and a drift beyond the stated tolerance fails the build. A further 28 tests are regression locks rather than comparisons: they pin the simulation's output for fixed models and seeds, so a refactor cannot quietly change an answer a saved scenario has already been given. None of their expected values has ever been re-recorded.

Test counts in this build

25 capability engine
38 simulation engine
28 regression and migration locks
20 timeline layout
220 application
331 total

Methods, references and tolerances

Method	Published reference	Asserted tolerance
Control-chart constants (d2, c4, A2, D3, D4)	NIST/SEMATECH e-Handbook of Statistical Methods §6.3.2	Sigma estimates to `1e-6` of the reference
Cp, Cpk, Pp, Ppk; PPM; sigma level; yield	Standard definitions; reference values from SciPy 1.17.1	Indices `1e-4`; PPM `0.5` parts per million
Normal CDF	Abramowitz & Stegun 7.1.26	Round-trip against the inverse to `1e-6`
Inverse normal CDF	Acklam's algorithm	Round-trip to `1e-6` across p = 0.001 … 0.999
Anderson–Darling normality	Stephens (1974); p-value adjustment D'Agostino & Stephens (1986)	A² and A*² to `1e-4`; p-value to `1e-3`
Non-normal capability, percentile method	ISO 22514-4 — indices from the fitted 0.135% and 99.865% points	See the three fits below
Box-Cox transform, λ by maximum likelihood	Box & Cox (1964); golden-section search on the log-likelihood	λ `2e-3`; μ `5e-3`; σ `2e-3`; percentiles `2e-4`
Lognormal fit, maximum likelihood	Standard MLE, n-denominator, as SciPy	μ and σ to `1e-6`; percentiles `1e-6`
Weibull fit, 2-parameter maximum likelihood	Standard MLE; shape by bisection on the likelihood equation	Shape `1e-3`; scale `1e-5`; percentiles `1e-5`
Random number generator	xoshiro128** and SplitMix — Blackman & Vigna, public domain	Uniform mean `0.005`; normal mean and standard deviation `0.01`
Gamma sampler (used for PERT)	Marsaglia & Tsang (2000)	Moments against analytic values, `0.03`–`0.5`
Beta-PERT distribution	Malcolm et al. (1959); Vose	Mean `0.04`, variance `0.5` over 200,000 draws
Percentiles	NumPy linear interpolation method	`1e-9`
Spearman rank correlation (tornado ordering)	Standard rank correlation, ties averaged	`1e-6`

Test data

The fixtures are synthetic and generated with a fixed seed, so anyone can reproduce them. The capability fixture is 25 subgroups of 4 drawn from a normal distribution (numpy.random.seed(42), mean 10.005, standard deviation 0.02, rounded to four decimals). The non-normal fixture is lognormal data with seed 11, representing a flatness characteristic. No real part data from any customer is used anywhere in the tests.

What PGM-Q does not do

Being straight about the boundaries is part of the validation:

No gauge R&R. Measurement system analysis is not implemented. PGM-Q assumes your gage is capable and your data are what you say they are.
No attribute data. There are no p, np, c or u charts — variable data only.
No Johnson or Pearson transforms. The non-normal analysis offers Box-Cox, lognormal and Weibull. A dataset that none of those fit well will not be flagged as unfittable; check the reported Anderson–Darling statistic for the chosen fit and judge it yourself.
Quick assumes normality. The Quick tab computes from a mean and a sigma you supply and has no data to test, so a skewed characteristic will read better there than it should. Run a Study from the raw measurements for anything that matters.
No stability test gates the indices. The X̄-R chart flags out-of-control subgroups and a warning appears, but capability is still computed. Capability on an unstable process is a number without a meaning; that judgement stays with you.
Confidence intervals are not reported for capability indices in this version.

On comparisons with other software

PGM-Q agrees with independent implementations to the tolerances stated above. That is a different claim from being equivalent to any particular commercial package: other tools make their own choices about estimator conventions, percentile definitions and transform selection, and small differences in those choices produce small differences in the result. Where a number matters, compare it against your own reference and satisfy yourself.

Reporting a discrepancy

If you find a result you believe is wrong, send the input data and what you expected to support@phasegatemanager.com. A reproducible numerical defect is treated as the most serious kind of bug in this application.