Algorithm Lab

Collection of numerical distribution functions (normal, χ², t, F) — the foundation of all hypothesis tests.

Generation of pseudo-random numbers from over 20 continuous and discrete distributions using the Mulberry32 PRNG.

Measures process spread relative to the tolerance width, ignoring centering.

Measures how well a process fits within specification limits, accounting for centering.

Overall process capability based on total variation (population σ, ddof = 0).

Tests whether a sample comes from a normally distributed population.

Tests whether a sample comes from a normally distributed population — especially sensitive in the distribution tails.

Asymptotic normality test based on skewness and kurtosis (chi-squared with 2 degrees of freedom). Reliable for large samples (n > 30).

Omnibus normality test: Combines Z-scores from skewness and kurtosis into a χ²(2) test statistic. Requires n ≥ 20.

Tests whether the population variance equals a hypothesized value (one-sample variance test).

Tests whether two normally distributed populations have equal variances.

Robust test for equality of variances of two samples, insensitive to non-normality.

Tests whether the population mean equals a hypothesized value.

Compares the means of two independent samples assuming equal variances.

Compares the means of two independent samples without assuming equal variances.

Nonparametric alternative to the one-sample t-test for the median.

Nonparametric alternative to the two-sample t-test for independent samples.

Compares the means of k independent, normally distributed samples.

Nonparametric alternative to one-way ANOVA for k samples.

Parametric test for equality of variances of k ≥ 2 normally distributed samples.

Identifies a single outlier in normally-distributed data.

Outlier test for very small samples (n = 3..30) based on range ratios.

Iterative test that identifies up to k outliers simultaneously, avoiding masking.

Distribution-free outlier flagging via boxplot whisker fences.

Robust Z-score replacement using median and MAD — resistant to masking.

Flags points with |Z| > threshold using mean and standard deviation.

Robust Z-score variant by Iglewicz & Hoaglin (1993) — based on median and MAD.

Decomposes total variation of the response into explained (regression) and unexplained (residual) components.

Tests the significance of individual regression coefficients via t-test and determines confidence intervals.

Computes Pearson r, Spearman ρ and Kendall τ including p-values and confidence intervals.

Models a binary response (0/1) as a function of predictors using the logistic link function and IRLS estimation.

Generalized linear model for count data with log link function and Poisson distribution.

Regression model for overdispersed count data using a log link and negative binomial distribution.

Computes the ROC curve (Receiver Operating Characteristic) and the Area Under the Curve (AUC) for binary classification.

Tests the goodness of fit of a logistic regression model using groups of predicted probabilities.

Checks for overdispersion in count data models using the Pearson χ²/df ratio.

Compares model mis-specification against pure noise from replicated design points.

Maps a categorical factor with k levels onto k − 1 indicator columns; the intercept becomes the grand mean.

Wald-form F-test for a group of related model-matrix columns — typically the n − 1 indicators that encode one categorical factor.

Evaluates the repeatability of a measurement instrument: How large is the spread of repeated measurements relative to the tolerance?

Evaluates repeatability and systematic deviation (bias) of a measurement instrument in a single index.

Decomposes measurement variation into repeatability (EV), reproducibility (AV), and part-to-part variation using two-factor crossed ANOVA with interaction.

Control chart core values (CL, UCL, LCL, σ̂) for I-MR, X̄-R and X̄-S plus Nelson Rule evaluation and capability from σ̂.

Control chart core values (CL, UCL, LCL, σ̂) for p, np, c, u charts plus reduced Nelson rule evaluation.

Median plus four runs tests (clustering, mixtures, trends, oscillation) with p-values from a normal approximation.

EWMA and tabular CUSUM with transient/fixed control limits for small drifts.

g chart (Benneyan) and t chart (Nelson 1/3.6 transform) for rare events.

Hotelling T² for individual observations with Phase II UCL from the F distribution.

Standardised I-MR across multiple parts with different targets/spreads.

Box-Cox transform with auto λ via Anderson-Darling, I-MR on the transformed scale, back-transformed limits.

Evaluates the quality of an experimental design using three criteria: D-efficiency (determinant), A-efficiency (trace), and G-efficiency (leverage).

Generates structural experimental designs: full 2^k, fractional 2^(k-p), CCD and Box-Behnken.

Measures multicollinearity between model terms in an experimental design.

Generates the Cartesian product of all level combinations when factors have different level counts (e.g. 2 × 3 × 4).

Orthogonal array with 18 runs and one 2-level plus seven 3-level columns — the classic mixed-level screening design.

Extends the classical central composite design to plans with mixed continuous/categorical factors — every categorical level combination gets a full CCD over the continuous factors.

Extends the Box-Behnken design to mixed factors — continuous get the classical 3-level RSM plan, categorical are Cartesian-crossed alongside.

D-optimal search that constrains categorical factors to their discrete levels — continuous factors keep the 5-level grid for quadratic models.

Maps a response value y onto a dimensionless desirability d ∈ [0, 1] — the building block of multi-response optimisation.

Blends several individual desirabilities d_i into a single composite D ∈ [0, 1] via the weighted geometric mean.

Filters a set of points down to the non-dominated solutions — the Pareto frontier of a multi-objective optimisation.

Optimises models with mixed factors: enumerates the Cartesian product of categorical level combinations and runs a continuous multi-start Nelder–Mead inside each cell.