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For Students · Quality Control (SPC)

Quality Control (SPC) for a Bayesian update

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a Bayesian update live below — adjust the inputs and watch it respond, right in your browser.

Control Chart

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SPC Control ChartLive

in control or not?

Controls

Speed1×

Presets

Process shift

Statistical process control watches a process over time against control limits set at three standard deviations from the target. Points inside are normal random variation — leave them alone. A point beyond the limits, or a run trending one way, signals a real change worth investigating. Nudge the process shift and watch points breach the limits.

▶ Run in Python

Data Inspector

Center line50

Control limits±3σ (44–56)

Out of control0

Governing equation

UCL, LCL = μ \pm 3 σ = 50 \pm 3 (2) = 56, 44

Reading this result: The process is centered on target: points scatter randomly inside the ±3σ limits, so every point is just noise — reacting now would only add variation (tampering).

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↓

Process Capability

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Process Capability (Cp / Cpk)Live

how good is the process?

Controls

Presets

Process mean

Process σ

Spec width (USL−LSL)

Cp compares the spec width to the process spread — can the process fit inside the tolerances at all? Cpk also accounts for how well-centered it is. A Cpk of 1.33 is the usual bar for capable; 2.0 is Six Sigma quality with just 3.4 defects per million. Widen the spread or push the mean off-center and defects climb fast.

▶ Run in Python

Data Inspector

Cp1.00

Cpk1.00

Defects2700 ppm

Ratingmarginal

Sigma level4.5σ

Capability indices

C_{p} = \frac{U S L - L S L}{6 σ} = \frac{53.0 - 47.0}{6 ( 1.0 )} = 1.00, C_{p k} = min (\frac{U S L - μ}{3 σ}, \frac{μ - L S L}{3 σ}) = 1.00

Reading this result: Centered and capable at Cpk 1.00, comfortably above the 1.33 industry bar.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Hypothesis Test

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Hypothesis Test (z-test)Live

p-values & rejection regions

Controls

Presets

Sample mean x̄

Null mean μ₀

Std deviation s

Sample size n

Two-tailed test

A hypothesis test asks whether a sample mean is far enough from the null value to be surprising by chance alone. The test statistic z measures that distance in standard errors; if it falls in the red rejection region (p below 0.05) we reject the null. Larger samples shrink the standard error and sharpen the test.

▶ Run in Python

Data Inspector

Standard error1.265

z-statistic1.581

p-value0.1138

Decisionfail to reject

Governing equation

z = \frac{x ˉ - μ _{0}}{σ / n} = \frac{52 - 50}{8/ 40} = 1.58

Reading this result: The statistic sits in the white central zone, so the gap between x̄ and μ₀ is within ordinary sampling noise and you fail to reject H₀.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Also for:Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders General version →

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Frequently asked questions

Is this good for students?: Yes — this version of "Quality Control (SPC) for a Bayesian update" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.