Bayesian Cpk Calculator

Bayesian Cpk treats process capability as a probability distribution rather than a single number. Instead of "Cpk = 1.34," you get a posterior that says "median Cpk is 1.34 with a 95% credible interval of [1.18, 1.52], and there is a 62% probability that Cpk exceeds 1.33." This accounts for sampling uncertainty — with 30 measurements your uncertainty is large; with 500 it's tight.

Traditional Cpk gives you a point estimate with no uncertainty attached. A Cpk of 1.34 from 30 measurements could easily be 1.1 or 1.6 in reality — you have no way to tell. Bayesian Cpk quantifies that uncertainty directly. It also eliminates the 1.5σ shift assumption used to convert between short-term and long-term capability. The posterior naturally accounts for what you know and don't know.

Bayesian Cpk works with any sample size — even 10–15 observations give meaningful results. The credible interval width tells you how much to trust the result. With small samples, the interval is wide (honest about uncertainty). With 100+ observations, it tightens considerably. The calculator shows you exactly how much uncertainty remains.

P(Cpk > 1.33) is the posterior probability that your process is truly capable at the 4-sigma level, given your data. If P(Cpk > 1.33) = 0.85, there's an 85% chance your process meets the requirement. This is a direct answer to the question practitioners actually care about — unlike a p-value or confidence interval that requires mental gymnastics to interpret.

This calculator uses a non-informative (Jeffreys) prior: the standard reference prior for Normal mean and variance. This means the data drives the result. With enough data (n > 20), the prior has negligible influence. The full Svend platform supports informative priors from historical process data.

The calculator draws samples from the posterior distribution of (μ, σ) using the conjugate Normal-Inverse-Gamma model. For each (μ, σ) draw, it computes Cpk = min((USL − μ)/(3σ), (μ − LSL)/(3σ)). The collection of Cpk values forms the posterior distribution of capability. 10,000 samples gives stable quantiles; increase to 50,000+ for smoother histograms.