u-analytics

Statistical process control, process capability analysis, Weibull reliability, and change-point detection for industrial quality engineering.

Features

Statistical Process Control (SPC)

Control charts for monitoring process stability:

Variables charts: X̄-R, X̄-S, Individual-MR
Attributes charts: P, NP, C, U
Run rules: Nelson (8 rules), Western Electric (4 rules)

use u_analytics::spc::{XBarRChart, ControlChart};

let mut chart = XBarRChart::new(5);
chart.add_sample(&[25.0, 26.0, 24.5, 25.5, 25.0]);
chart.add_sample(&[25.2, 24.8, 25.1, 24.9, 25.3]);
chart.add_sample(&[25.1, 25.0, 24.7, 25.3, 24.9]);

if chart.is_in_control() {
    println!("Process is stable");
}

Process Capability

Capability indices quantifying process performance against specifications:

Short-term: Cp, Cpk, Cpu, Cpl
Long-term: Pp, Ppk, Ppu, Ppl
Taguchi: Cpm
Sigma level: PPM ↔ sigma conversion (1.5σ shift convention)

use u_analytics::capability::{ProcessCapability, sigma_to_ppm};

let spec = ProcessCapability::new(Some(220.0), Some(200.0)).unwrap();
let data = [210.0, 209.5, 210.2, 209.8, 210.1, 210.3, 209.7, 210.0];
let indices = spec.compute(&data, 0.15).unwrap();

println!("Cp = {:.2}, Cpk = {:.2}", indices.cp.unwrap(), indices.cpk.unwrap());
println!("6σ PPM = {:.1}", sigma_to_ppm(6.0)); // 3.4

Weibull Reliability

Parameter estimation and reliability engineering metrics:

MLE: Maximum Likelihood Estimation (Newton-Raphson)
MRR: Median Rank Regression (Bernard's approximation)
Reliability: R(t), hazard rate, MTBF, B-life

use u_analytics::weibull::{weibull_mle, ReliabilityAnalysis};

let failure_times = [150.0, 200.0, 250.0, 300.0, 350.0, 400.0];
let fit = weibull_mle(&failure_times).unwrap();

let ra = ReliabilityAnalysis::from_mle(&fit);
println!("R(200h) = {:.1}%", ra.reliability(200.0) * 100.0);
println!("MTBF = {:.0}h", ra.mtbf());
println!("B10 life = {:.0}h", ra.b_life(0.10).unwrap());

Change-Point Detection

Algorithms for detecting process mean shifts:

CUSUM: Cumulative Sum chart (Page, 1954)
EWMA: Exponentially Weighted Moving Average (Roberts, 1959)

use u_analytics::detection::Cusum;

let cusum = Cusum::new(10.0, 1.0).unwrap();
let data = [10.1, 9.9, 10.0, 10.2, 12.0, 12.1, 11.9, 12.3];
let signals = cusum.signal_points(&data);

Dependencies

u-numflow -- statistics, special functions, probability distributions

References

Montgomery, D.C. (2019). Introduction to Statistical Quality Control, 8th ed.
Nelson, L.S. (1984). "The Shewhart Control Chart -- Tests for Special Causes"
Abernethy, R.B. (2006). The New Weibull Handbook, 5th ed.
Page, E.S. (1954). "Continuous Inspection Schemes", Biometrika
Roberts, S.W. (1959). "Control Chart Tests Based on Geometric Moving Averages"

u-numflow -- Mathematical optimization primitives
u-metaheur -- Metaheuristic algorithms
u-geometry -- Computational geometry
u-schedule -- Scheduling framework

License

MIT

u-analytics 0.1.0