I — Datum

Classical vs Bayesian SPC
Two frameworks for the same question: is this process capable? Classical SPC gives you confidence intervals. Bayesian SPC gives you probability statements. Sometimes they agree. When they don't, the sample size and the stakes determine which one you should trust.
Ref: Shewhart (1931) · Box & Tiao · ISO 22514-2 · AIAG SPC Manual

II — The Classical Framework

Classical (frequentist) SPC treats process parameters as fixed but unknown. Control limits are computed from a baseline period. A 95% confidence interval for Cpk means: if you repeated the sampling 100 times, about 95 of those intervals would contain the true value. It does not mean there is a 95% probability the true Cpk is in this particular interval. This distinction matters when the plant manager asks "what's the probability we meet spec?"

SVEND's Cpk calculator computes classical indices with confidence intervals.

III — The Bayesian Framework

Bayesian SPC treats parameters as random variables with probability distributions. After observing data, the posterior distribution for Cpk directly answers: P(Cpk > 1.33 | data) = 0.82. This is the statement most practitioners actually want. A 95% credible interval means there is a 95% posterior probability the parameter falls within the interval—the intuitive interpretation people incorrectly apply to confidence intervals.

SVEND's Bayesian Cpk calculator computes the full posterior with credible intervals and exceedance probabilities.

IV — When They Diverge

For large samples (n > 100), the two methods give numerically similar results. The difference emerges with small samples (n < 50) and borderline results (Cpk near the acceptance threshold). A classical point estimate of Cpk = 1.33 with 35 observations might look like a pass. The Bayesian posterior might report P(Cpk > 1.33) = 0.43—less than a coin flip. The method changes the decision.

For a deeper treatment with worked examples, see the whitepaper: Bayesian vs. Frequentist SPC: When the Prior Matters.

V — SVEND's Approach

SVEND provides both. Use classical indices for contractual compliance (PPAP, AIAG). Use Bayesian posteriors for internal decision-making when samples are small or results are borderline. Run both side by side. When they agree, report either. When they disagree, the Bayesian posterior tells you what the classical point estimate is hiding.