u_analytics/spc/

rules.rs

//! Run rules for detecting non-random patterns in control charts.
//!
//! Implements the Western Electric (4 rules) and Nelson (8 rules) run tests
//! for identifying special causes of variation in control chart data. The two
//! sets share three tests and differ in the fourth: a run on one side of the
//! centre line is **eight** points in the Western Electric handbook and
//! **nine** in Nelson's list, so each has its own [`ViolationType`].
//!
//! # Choosing a set
//!
//! Every added test raises the false alarm rate of an in-control process. The
//! supplementary tests help find a shift while a process is being brought into
//! control (Phase I); in routine monitoring (Phase II) the 3-sigma test alone is
//! the conventional choice (ISO 7870-2:2023, 8.2.7). That is why an unspecified
//! set is [`RuleSet::shewhart`].
//!
//! # References
//!
//! - Nelson, L.S. (1984). "The Shewhart Control Chart — Tests for Special Causes",
//!   *Journal of Quality Technology* 16(4), pp. 237-239.
//! - Western Electric (1956). *Statistical Quality Control Handbook*.
//! - NIST/SEMATECH e-Handbook of Statistical Methods, 6.3.2 ("What are the WECO rules").
//! - ISO 7870-2:2023, *Control charts — Part 2: Shewhart control charts*, 8.2.7 and Annex B.
//! - Montgomery, D.C. (2019). *Introduction to Statistical Quality Control*, 8th ed.

use super::chart::{ChartPoint, ControlLimits, ViolationType};

/// Trait for applying run rules to chart data.
///
/// Run rules detect non-random patterns that indicate special causes of
/// variation even when individual points remain within control limits.
pub trait RunRule {
    /// Check points against this rule set and return violations per point index.
    ///
    /// Returns a vector of `(point_index, violation_type)` pairs. A single
    /// point may appear multiple times if it triggers multiple rules.
    fn check(&self, points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)>;
}

/// Western Electric rules (4 rules) -- [`RuleSet::western_electric`].
///
/// The original run tests of the Western Electric *Statistical Quality Control
/// Handbook* (1956):
///
/// 1. Any point beyond 3 sigma (Nelson Rule 1)
/// 2. 2 of 3 consecutive points beyond 2 sigma, same side (Nelson Rule 5)
/// 3. 4 of 5 consecutive points beyond 1 sigma, same side (Nelson Rule 6)
/// 4. **8** consecutive points on the same side of the center line
///    ([`ViolationType::EightOneSide`] -- Nelson's Rule 2 asks for nine)
pub struct WesternElectricRules;

/// Nelson rules (8 rules) -- [`RuleSet::nelson`].
///
/// The full set of eight tests for special causes as defined by
/// Nelson (1984). Rules 1, 5 and 6 are also Western Electric rules; Rule 2
/// (nine points on one side) is a longer run than Western Electric's eight.
///
/// # Examples
///
/// ```
/// use u_analytics::spc::{NelsonRules, RunRule, ChartPoint, ControlLimits};
///
/// let limits = ControlLimits { ucl: 28.0, cl: 25.0, lcl: 22.0 };
/// let points: Vec<ChartPoint> = vec![
///     ChartPoint { value: 25.0, index: 0, violations: vec![] },
///     ChartPoint { value: 29.0, index: 1, violations: vec![] },
/// ];
///
/// let violations = NelsonRules.check(&points, &limits);
/// assert!(!violations.is_empty()); // Rule 1: point beyond UCL
/// ```
pub struct NelsonRules;

// ---------------------------------------------------------------------------
// Internal helpers
// ---------------------------------------------------------------------------

/// Compute 1-sigma and 2-sigma zone boundaries from control limits.
///
/// Returns `(one_sigma, two_sigma)` where `one_sigma = (UCL - CL) / 3`.
fn zone_widths(limits: &ControlLimits) -> (f64, f64) {
    let sigma = (limits.ucl - limits.cl) / 3.0;
    (sigma, 2.0 * sigma)
}

/// Nelson Rule 1: Point beyond control limits.
///
/// A single point falls outside the UCL or LCL.
fn check_rule1(points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
    let mut violations = Vec::new();
    for point in points {
        if point.value > limits.ucl || point.value < limits.lcl {
            violations.push((point.index, ViolationType::BeyondLimits));
        }
    }
    violations
}

/// `run` consecutive points on the same side of the center line, reported as
/// `rule` -- Nelson Rule 2 (nine) and the Western Electric run rule (eight).
///
/// Indicates a sustained shift in the process mean.
fn check_one_side(
    points: &[ChartPoint],
    limits: &ControlLimits,
    run: usize,
    rule: ViolationType,
) -> Vec<(usize, ViolationType)> {
    let mut violations = Vec::new();
    if points.len() < run {
        return violations;
    }

    let cl = limits.cl;
    // Track consecutive runs above/below center line.
    // +1 = above, -1 = below, 0 = exactly on center (counted as neither side).
    let sides: Vec<i8> = points
        .iter()
        .map(|p| {
            if p.value > cl {
                1
            } else if p.value < cl {
                -1
            } else {
                0
            }
        })
        .collect();

    let mut run_length = 1_usize;
    for i in 1..sides.len() {
        if sides[i] != 0 && sides[i] == sides[i - 1] {
            run_length += 1;
        } else {
            run_length = 1;
        }
        if run_length >= run {
            violations.push((points[i].index, rule));
        }
    }
    violations
}

/// Nelson Rule 3: 6 consecutive points steadily increasing or decreasing.
///
/// Indicates a trend in the process.
fn check_rule3(points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
    let _ = limits; // Not used for trend detection
    let mut violations = Vec::new();
    if points.len() < 6 {
        return violations;
    }

    // Direction: +1 = increasing, -1 = decreasing, 0 = equal
    let dirs: Vec<i8> = points
        .windows(2)
        .map(|w| {
            if w[1].value > w[0].value {
                1
            } else if w[1].value < w[0].value {
                -1
            } else {
                0
            }
        })
        .collect();

    let mut run_length = 1_usize;
    for i in 1..dirs.len() {
        if dirs[i] != 0 && dirs[i] == dirs[i - 1] {
            run_length += 1;
        } else {
            run_length = 1;
        }
        // 5 consecutive same-direction changes = 6 points forming a trend.
        // The violation is reported at the last point of the trend.
        if run_length >= 5 {
            // dirs[i] corresponds to the transition between points[i] and points[i+1],
            // so the last point of the 6-point trend is points[i+1].
            violations.push((points[i + 1].index, ViolationType::SixTrend));
        }
    }
    violations
}

/// Nelson Rule 4: 14 consecutive points alternating up and down.
///
/// Indicates systematic variation (e.g., two alternating streams).
fn check_rule4(points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
    let _ = limits;
    let mut violations = Vec::new();
    if points.len() < 14 {
        return violations;
    }

    // Direction changes: +1 = up, -1 = down, 0 = equal
    let dirs: Vec<i8> = points
        .windows(2)
        .map(|w| {
            if w[1].value > w[0].value {
                1
            } else if w[1].value < w[0].value {
                -1
            } else {
                0
            }
        })
        .collect();

    // Count consecutive alternations
    let mut alt_length = 1_usize;
    for i in 1..dirs.len() {
        if dirs[i] != 0 && dirs[i - 1] != 0 && dirs[i] == -dirs[i - 1] {
            alt_length += 1;
        } else {
            alt_length = 1;
        }
        // 13 consecutive alternating directions = 14 points alternating.
        // dirs[i] corresponds to points[i]→points[i+1],
        // so the last point is points[i+1].
        if alt_length >= 13 {
            violations.push((points[i + 1].index, ViolationType::FourteenAlternating));
        }
    }
    violations
}

/// Nelson Rule 5: 2 out of 3 consecutive points beyond 2 sigma, same side.
///
/// An early warning of a potential shift.
fn check_rule5(points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
    let mut violations = Vec::new();
    if points.len() < 3 {
        return violations;
    }

    let (_, two_sigma) = zone_widths(limits);
    let upper_2s = limits.cl + two_sigma;
    let lower_2s = limits.cl - two_sigma;

    for i in 2..points.len() {
        let window = &points[i - 2..=i];

        // Check upper side: count points above CL + 2σ
        let above_count = window.iter().filter(|p| p.value > upper_2s).count();
        if above_count >= 2 {
            violations.push((points[i].index, ViolationType::TwoOfThreeBeyond2Sigma));
            continue;
        }

        // Check lower side: count points below CL - 2σ
        let below_count = window.iter().filter(|p| p.value < lower_2s).count();
        if below_count >= 2 {
            violations.push((points[i].index, ViolationType::TwoOfThreeBeyond2Sigma));
        }
    }
    violations
}

/// Nelson Rule 6: 4 out of 5 consecutive points beyond 1 sigma, same side.
///
/// Indicates a small sustained shift.
fn check_rule6(points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
    let mut violations = Vec::new();
    if points.len() < 5 {
        return violations;
    }

    let (one_sigma, _) = zone_widths(limits);
    let upper_1s = limits.cl + one_sigma;
    let lower_1s = limits.cl - one_sigma;

    for i in 4..points.len() {
        let window = &points[i - 4..=i];

        // Check upper side: count points above CL + σ
        let above_count = window.iter().filter(|p| p.value > upper_1s).count();
        if above_count >= 4 {
            violations.push((points[i].index, ViolationType::FourOfFiveBeyond1Sigma));
            continue;
        }

        // Check lower side: count points below CL - σ
        let below_count = window.iter().filter(|p| p.value < lower_1s).count();
        if below_count >= 4 {
            violations.push((points[i].index, ViolationType::FourOfFiveBeyond1Sigma));
        }
    }
    violations
}

/// Nelson Rule 7: 15 consecutive points within 1 sigma of center line.
///
/// Indicates stratification — reduced variation suggesting mixed streams.
fn check_rule7(points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
    let mut violations = Vec::new();
    if points.len() < 15 {
        return violations;
    }

    let (one_sigma, _) = zone_widths(limits);
    let upper_1s = limits.cl + one_sigma;
    let lower_1s = limits.cl - one_sigma;

    let mut run_length = 0_usize;
    for point in points {
        if point.value >= lower_1s && point.value <= upper_1s {
            run_length += 1;
        } else {
            run_length = 0;
        }
        if run_length >= 15 {
            violations.push((point.index, ViolationType::FifteenWithin1Sigma));
        }
    }
    violations
}

/// Nelson Rule 8: 8 consecutive points beyond 1 sigma on either side.
///
/// Indicates a mixture pattern — points avoid the center zone.
fn check_rule8(points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
    let mut violations = Vec::new();
    if points.len() < 8 {
        return violations;
    }

    let (one_sigma, _) = zone_widths(limits);
    let upper_1s = limits.cl + one_sigma;
    let lower_1s = limits.cl - one_sigma;

    let mut run_length = 0_usize;
    for point in points {
        // Point is beyond 1σ on either side (not within CL ± σ)
        if point.value > upper_1s || point.value < lower_1s {
            run_length += 1;
        } else {
            run_length = 0;
        }
        if run_length >= 8 {
            violations.push((point.index, ViolationType::EightBeyond1Sigma));
        }
    }
    violations
}

// ---------------------------------------------------------------------------
// Selectable rule sets
// ---------------------------------------------------------------------------

/// A chosen subset of the run tests.
///
/// Each test reports exactly one [`ViolationType`], so a rule is named by what
/// it would report rather than by a parallel enum that would have to be kept in
/// step with this one.
///
/// Three sets have names -- [`shewhart`](RuleSet::shewhart) (the 3-sigma test
/// alone, the default), [`western_electric`](RuleSet::western_electric) and
/// [`nelson`](RuleSet::nelson) -- and [`RuleSet::named`] looks them up by the
/// names a wire request uses; any other combination is built from the tests a
/// process actually warrants. A rule that a process is known to
/// trigger for a benign reason -- a deliberately drifting tool, a bimodal
/// fixture -- otherwise has to be filtered out downstream, after it has already
/// been counted as an out-of-control signal.
///
/// # Examples
///
/// ```
/// use u_analytics::spc::{RuleSet, RunRule, ChartPoint, ControlLimits, ViolationType};
///
/// // Only the 3-sigma test, and nothing else.
/// let rules = RuleSet::from_iter([ViolationType::BeyondLimits]);
///
/// let limits = ControlLimits { ucl: 28.0, cl: 25.0, lcl: 22.0 };
/// let points: Vec<ChartPoint> = (0..12)
///     .map(|i| ChartPoint { value: 26.0, index: i, violations: vec![] })
///     .collect();
///
/// // Twelve points above the centre line would trip Nelson rule 2, but that
/// // test is not in this set.
/// assert!(rules.check(&points, &limits).is_empty());
/// assert!(RuleSet::nelson().check(&points, &limits).len() > 0);
/// ```
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct RuleSet {
    mask: u16,
}

fn bit_of(v: ViolationType) -> u16 {
    let position = ViolationType::ALL
        .iter()
        .position(|&r| r == v)
        .expect("ViolationType::ALL lists every variant");
    1 << position
}

impl RuleSet {
    /// The names [`RuleSet::named`] takes, in the order a refusal lists them.
    pub const NAMES: [&'static str; 3] = ["shewhart", "western_electric", "nelson"];

    /// The 3-sigma test alone -- Shewhart's criterion, and the default.
    ///
    /// In routine monitoring each added test raises the false alarm rate of an
    /// in-control process (ISO 7870-2:2023, 8.2.7), so the supplementary tests
    /// are chosen, not assumed.
    pub fn shewhart() -> Self {
        Self::from_iter([ViolationType::BeyondLimits])
    }

    /// Nelson's eight tests (1984).
    pub fn nelson() -> Self {
        Self::from_iter([
            ViolationType::BeyondLimits,
            ViolationType::NineOneSide,
            ViolationType::SixTrend,
            ViolationType::FourteenAlternating,
            ViolationType::TwoOfThreeBeyond2Sigma,
            ViolationType::FourOfFiveBeyond1Sigma,
            ViolationType::FifteenWithin1Sigma,
            ViolationType::EightBeyond1Sigma,
        ])
    }

    /// The four Western Electric tests (1956): Nelson rules 1, 5 and 6, and
    /// eight points in a row on one side of the centre line.
    pub fn western_electric() -> Self {
        Self::from_iter([
            ViolationType::BeyondLimits,
            ViolationType::TwoOfThreeBeyond2Sigma,
            ViolationType::FourOfFiveBeyond1Sigma,
            ViolationType::EightOneSide,
        ])
    }

    /// The set a name in [`RuleSet::NAMES`] stands for.
    pub fn named(name: &str) -> Option<Self> {
        match name {
            "shewhart" => Some(Self::shewhart()),
            "western_electric" => Some(Self::western_electric()),
            "nelson" => Some(Self::nelson()),
            _ => None,
        }
    }

    /// The empty set: no run test is applied.
    ///
    /// Useful as a base to add to, and as the honest way to say "limits only".
    pub fn none() -> Self {
        Self { mask: 0 }
    }

    /// Whether this set applies the test that reports `rule`.
    pub fn contains(&self, rule: ViolationType) -> bool {
        self.mask & bit_of(rule) != 0
    }

    /// This set with `rule` added.
    #[must_use]
    pub fn with(mut self, rule: ViolationType) -> Self {
        self.mask |= bit_of(rule);
        self
    }

    /// This set with `rule` removed.
    #[must_use]
    pub fn without(mut self, rule: ViolationType) -> Self {
        self.mask &= !bit_of(rule);
        self
    }

    /// The tests in this set, in the order of [`ViolationType::ALL`].
    pub fn iter(&self) -> impl Iterator<Item = ViolationType> + '_ {
        ViolationType::ALL.into_iter().filter(|&r| self.contains(r))
    }

    /// How many tests this set applies.
    pub fn len(&self) -> usize {
        self.mask.count_ones() as usize
    }

    /// Whether no test is applied.
    pub fn is_empty(&self) -> bool {
        self.mask == 0
    }
}

impl Default for RuleSet {
    /// [`RuleSet::shewhart`] -- the 3-sigma test alone.
    fn default() -> Self {
        Self::shewhart()
    }
}

impl FromIterator<ViolationType> for RuleSet {
    fn from_iter<I: IntoIterator<Item = ViolationType>>(iter: I) -> Self {
        let mut mask = 0u16;
        for v in iter {
            mask |= bit_of(v);
        }
        Self { mask }
    }
}

impl RunRule for RuleSet {
    fn check(&self, points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
        let mut results = Vec::new();
        for rule in self.iter() {
            results.extend(match rule {
                ViolationType::BeyondLimits => check_rule1(points, limits),
                ViolationType::NineOneSide => {
                    check_one_side(points, limits, 9, ViolationType::NineOneSide)
                }
                ViolationType::EightOneSide => {
                    check_one_side(points, limits, 8, ViolationType::EightOneSide)
                }
                ViolationType::SixTrend => check_rule3(points, limits),
                ViolationType::FourteenAlternating => check_rule4(points, limits),
                ViolationType::TwoOfThreeBeyond2Sigma => check_rule5(points, limits),
                ViolationType::FourOfFiveBeyond1Sigma => check_rule6(points, limits),
                ViolationType::FifteenWithin1Sigma => check_rule7(points, limits),
                ViolationType::EightBeyond1Sigma => check_rule8(points, limits),
            });
        }
        results.sort_by_key(|&(idx, _)| idx);
        results
    }
}

// ---------------------------------------------------------------------------
// RunRule implementations
// ---------------------------------------------------------------------------

impl RunRule for WesternElectricRules {
    /// Apply the 4 Western Electric run rules.
    fn check(&self, points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
        RuleSet::western_electric().check(points, limits)
    }
}

impl RunRule for NelsonRules {
    /// Apply all 8 Nelson run rules.
    fn check(&self, points: &[ChartPoint], limits: &ControlLimits) -> Vec<(usize, ViolationType)> {
        RuleSet::nelson().check(points, limits)
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    // --- RuleSet ---

    /// Twelve points above the centre line: rule 2 fires, rule 1 does not.
    /// The distinguishing case for "did the selection actually take effect".
    fn nine_on_one_side() -> (Vec<ChartPoint>, ControlLimits) {
        let limits = ControlLimits {
            ucl: 28.0,
            cl: 25.0,
            lcl: 22.0,
        };
        let points = (0..12)
            .map(|i| ChartPoint {
                value: 26.0,
                index: i,
                violations: vec![],
            })
            .collect();
        (points, limits)
    }

    #[test]
    fn ruleset_applies_only_the_tests_it_holds() {
        let (points, limits) = nine_on_one_side();

        // Nelson catches the run; a set without that test does not.
        assert!(!RuleSet::nelson().check(&points, &limits).is_empty());
        assert!(RuleSet::nelson()
            .without(ViolationType::NineOneSide)
            .check(&points, &limits)
            .is_empty());

        // And a set holding only that test still catches it -- so the empty
        // result above is the selection working, not the data failing to trip.
        assert!(!RuleSet::from_iter([ViolationType::NineOneSide])
            .check(&points, &limits)
            .is_empty());
    }

    #[test]
    fn ruleset_empty_reports_nothing_even_beyond_limits() {
        let limits = ControlLimits {
            ucl: 28.0,
            cl: 25.0,
            lcl: 22.0,
        };
        let points = vec![ChartPoint {
            value: 99.0,
            index: 0,
            violations: vec![],
        }];
        assert!(!RuleSet::nelson().check(&points, &limits).is_empty());
        assert!(RuleSet::none().check(&points, &limits).is_empty());
    }

    #[test]
    fn named_sets_match_their_definitions() {
        assert_eq!(RuleSet::nelson().len(), 8);
        assert_eq!(RuleSet::western_electric().len(), 4);
        for r in [
            ViolationType::BeyondLimits,
            ViolationType::TwoOfThreeBeyond2Sigma,
            ViolationType::FourOfFiveBeyond1Sigma,
            ViolationType::EightOneSide,
        ] {
            assert!(RuleSet::western_electric().contains(r), "{r:?} missing");
        }
        for r in [
            ViolationType::NineOneSide,
            ViolationType::SixTrend,
            ViolationType::FourteenAlternating,
            ViolationType::FifteenWithin1Sigma,
            ViolationType::EightBeyond1Sigma,
        ] {
            assert!(!RuleSet::western_electric().contains(r), "{r:?} present");
        }
        assert!(RuleSet::none().is_empty());
    }

    /// The named unit structs delegate to `RuleSet`, so they must still agree
    /// with it -- otherwise the delegation quietly changed public behaviour.
    #[test]
    fn named_unit_structs_agree_with_their_rule_sets() {
        let (points, limits) = nine_on_one_side();
        assert_eq!(
            NelsonRules.check(&points, &limits),
            RuleSet::nelson().check(&points, &limits)
        );
        assert_eq!(
            WesternElectricRules.check(&points, &limits),
            RuleSet::western_electric().check(&points, &limits)
        );
    }

    /// Helper: create chart points from a slice of values.
    fn make_points(values: &[f64]) -> Vec<ChartPoint> {
        values
            .iter()
            .enumerate()
            .map(|(i, &v)| ChartPoint {
                value: v,
                index: i,
                violations: Vec::new(),
            })
            .collect()
    }

    // --- Rule 1: Beyond limits ---

    #[test]
    fn test_rule1_point_above_ucl() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let points = make_points(&[25.0, 31.0, 25.0]);
        let violations = check_rule1(&points, &limits);
        assert_eq!(violations.len(), 1);
        assert_eq!(violations[0].0, 1);
        assert_eq!(violations[0].1, ViolationType::BeyondLimits);
    }

    #[test]
    fn test_rule1_point_below_lcl() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let points = make_points(&[25.0, 19.0, 25.0]);
        let violations = check_rule1(&points, &limits);
        assert_eq!(violations.len(), 1);
        assert_eq!(violations[0].0, 1);
    }

    #[test]
    fn test_rule1_on_limit_is_not_violation() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let points = make_points(&[30.0, 20.0]);
        let violations = check_rule1(&points, &limits);
        assert!(violations.is_empty());
    }

    // --- Rule 2: 9 on same side ---

    #[test]
    fn test_rule2_nine_above() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        // 9 points above center line
        let values: Vec<f64> = (0..9).map(|_| 26.0).collect();
        let points = make_points(&values);
        let violations = check_one_side(&points, &limits, 9, ViolationType::NineOneSide);
        assert_eq!(violations.len(), 1);
        assert_eq!(violations[0].1, ViolationType::NineOneSide);
    }

    #[test]
    fn test_rule2_eight_not_enough() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let values: Vec<f64> = (0..8).map(|_| 26.0).collect();
        let points = make_points(&values);
        let violations = check_one_side(&points, &limits, 9, ViolationType::NineOneSide);
        assert!(violations.is_empty());
    }

    #[test]
    fn test_rule2_nine_below() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let values: Vec<f64> = (0..9).map(|_| 24.0).collect();
        let points = make_points(&values);
        let violations = check_one_side(&points, &limits, 9, ViolationType::NineOneSide);
        assert_eq!(violations.len(), 1);
    }

    // --- Western Electric run rule: 8 on one side ---

    /// Eight points above the centre line: the Western Electric set signals at
    /// the eighth point, Nelson's (nine) does not -- the one test where the two
    /// sets disagree.
    #[test]
    fn western_electric_run_is_eight_points_nelson_is_nine() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let points = make_points(&[26.0; 8]);

        let we = RuleSet::western_electric().check(&points, &limits);
        assert_eq!(we, vec![(7, ViolationType::EightOneSide)]);
        assert!(RuleSet::nelson().check(&points, &limits).is_empty());
        assert_eq!(WesternElectricRules.check(&points, &limits), we);

        // Seven is not a run for either.
        let seven = make_points(&[26.0; 7]);
        assert!(RuleSet::western_electric()
            .check(&seven, &limits)
            .is_empty());
    }

    /// The default set is the 3-sigma test alone: a run that both named sets
    /// flag is not a signal until a set asks for it.
    #[test]
    fn default_set_is_the_three_sigma_test() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let mut values = vec![26.0; 12];
        values.push(31.0);
        let points = make_points(&values);

        assert_eq!(RuleSet::default(), RuleSet::shewhart());
        assert_eq!(
            RuleSet::default().check(&points, &limits),
            vec![(12, ViolationType::BeyondLimits)]
        );
        assert!(RuleSet::nelson().check(&points, &limits).len() > 1);
    }

    #[test]
    fn named_sets_round_trip_and_names_round_trip() {
        for name in RuleSet::NAMES {
            assert!(RuleSet::named(name).is_some(), "{name}");
        }
        assert_eq!(RuleSet::named("weco"), None);
        for v in ViolationType::ALL {
            assert_eq!(ViolationType::from_name(v.name()), Some(v));
        }
        let all: RuleSet = ViolationType::ALL.into_iter().collect();
        assert_eq!(all.len(), ViolationType::ALL.len());
    }

    // --- Rule 3: 6 trending ---

    #[test]
    fn test_rule3_six_increasing() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let points = make_points(&[20.0, 21.0, 22.0, 23.0, 24.0, 25.0]);
        let violations = check_rule3(&points, &limits);
        assert_eq!(violations.len(), 1);
        assert_eq!(violations[0].1, ViolationType::SixTrend);
    }

    #[test]
    fn test_rule3_six_decreasing() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let points = make_points(&[30.0, 29.0, 28.0, 27.0, 26.0, 25.0]);
        let violations = check_rule3(&points, &limits);
        assert_eq!(violations.len(), 1);
    }

    #[test]
    fn test_rule3_five_not_enough() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let points = make_points(&[20.0, 21.0, 22.0, 23.0, 24.0]);
        let violations = check_rule3(&points, &limits);
        assert!(violations.is_empty());
    }

    // --- Rule 4: 14 alternating ---

    #[test]
    fn test_rule4_fourteen_alternating() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        // Create alternating pattern: 24, 26, 24, 26, ...
        let values: Vec<f64> = (0..14)
            .map(|i| if i % 2 == 0 { 24.0 } else { 26.0 })
            .collect();
        let points = make_points(&values);
        let violations = check_rule4(&points, &limits);
        assert_eq!(violations.len(), 1);
        assert_eq!(violations[0].1, ViolationType::FourteenAlternating);
    }

    #[test]
    fn test_rule4_thirteen_not_enough() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let values: Vec<f64> = (0..13)
            .map(|i| if i % 2 == 0 { 24.0 } else { 26.0 })
            .collect();
        let points = make_points(&values);
        let violations = check_rule4(&points, &limits);
        assert!(violations.is_empty());
    }

    // --- Rule 5: 2 of 3 beyond 2σ ---

    #[test]
    fn test_rule5_two_of_three_above() {
        let limits = ControlLimits {
            ucl: 28.0, // σ = (28-25)/3 ≈ 1.0, 2σ = 2.0
            cl: 25.0,
            lcl: 22.0,
        };
        // 2σ line upper = 25 + 2 = 27, lower = 25 - 2 = 23
        // Two of three points above 27
        let points = make_points(&[27.5, 25.0, 27.5]);
        let violations = check_rule5(&points, &limits);
        assert_eq!(violations.len(), 1);
        assert_eq!(violations[0].1, ViolationType::TwoOfThreeBeyond2Sigma);
    }

    #[test]
    fn test_rule5_two_of_three_below() {
        let limits = ControlLimits {
            ucl: 28.0,
            cl: 25.0,
            lcl: 22.0,
        };
        // Two of three below CL - 2σ = 23
        let points = make_points(&[22.5, 25.0, 22.5]);
        let violations = check_rule5(&points, &limits);
        assert_eq!(violations.len(), 1);
    }

    // --- Rule 6: 4 of 5 beyond 1σ ---

    #[test]
    fn test_rule6_four_of_five_above() {
        let limits = ControlLimits {
            ucl: 28.0, // σ = 1.0
            cl: 25.0,
            lcl: 22.0,
        };
        // 1σ upper = 26. Four of five points above 26.
        let points = make_points(&[26.5, 26.5, 25.0, 26.5, 26.5]);
        let violations = check_rule6(&points, &limits);
        assert_eq!(violations.len(), 1);
        assert_eq!(violations[0].1, ViolationType::FourOfFiveBeyond1Sigma);
    }

    // --- Rule 7: 15 within 1σ ---

    #[test]
    fn test_rule7_fifteen_within() {
        let limits = ControlLimits {
            ucl: 28.0, // σ = 1.0
            cl: 25.0,
            lcl: 22.0,
        };
        // 15 points within CL ± σ = [24, 26]
        let values: Vec<f64> = (0..15).map(|i| 24.5 + (i as f64 % 3.0) * 0.25).collect();
        let points = make_points(&values);
        let violations = check_rule7(&points, &limits);
        assert_eq!(violations.len(), 1);
        assert_eq!(violations[0].1, ViolationType::FifteenWithin1Sigma);
    }

    // --- Rule 8: 8 beyond 1σ on either side ---

    #[test]
    fn test_rule8_eight_beyond() {
        let limits = ControlLimits {
            ucl: 28.0, // σ = 1.0
            cl: 25.0,
            lcl: 22.0,
        };
        // 8 points beyond CL ± σ (alternating sides is fine)
        let points = make_points(&[27.0, 23.0, 27.0, 23.0, 27.0, 23.0, 27.0, 23.0]);
        let violations = check_rule8(&points, &limits);
        assert_eq!(violations.len(), 1);
        assert_eq!(violations[0].1, ViolationType::EightBeyond1Sigma);
    }

    #[test]
    fn test_rule8_seven_not_enough() {
        let limits = ControlLimits {
            ucl: 28.0,
            cl: 25.0,
            lcl: 22.0,
        };
        let points = make_points(&[27.0, 23.0, 27.0, 23.0, 27.0, 23.0, 27.0]);
        let violations = check_rule8(&points, &limits);
        assert!(violations.is_empty());
    }

    // --- Western Electric Rules ---

    #[test]
    fn test_western_electric_combines_four_rules() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        // A point beyond limits triggers WE rules
        let points = make_points(&[25.0, 31.0, 25.0]);
        let we = WesternElectricRules;
        let violations = we.check(&points, &limits);
        assert!(!violations.is_empty());
        assert!(violations
            .iter()
            .any(|(_, v)| *v == ViolationType::BeyondLimits));
    }

    // --- Nelson Rules ---

    #[test]
    fn test_nelson_detects_trend() {
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let points = make_points(&[20.0, 21.0, 22.0, 23.0, 24.0, 25.0]);
        let nelson = NelsonRules;
        let violations = nelson.check(&points, &limits);
        assert!(violations
            .iter()
            .any(|(_, v)| *v == ViolationType::SixTrend));
    }

    #[test]
    fn test_nelson_no_violations_in_random_data() {
        let limits = ControlLimits {
            ucl: 28.0,
            cl: 25.0,
            lcl: 22.0,
        };
        // A short random-looking sequence should not trigger
        let points = make_points(&[25.5, 24.8, 25.2, 24.9, 25.1]);
        let nelson = NelsonRules;
        let violations = nelson.check(&points, &limits);
        assert!(violations.is_empty());
    }

    #[test]
    fn test_nelson_rule2_continuation() {
        // If 10 points on same side, rules fire at point 8 (index) and 9
        let limits = ControlLimits {
            ucl: 30.0,
            cl: 25.0,
            lcl: 20.0,
        };
        let values: Vec<f64> = (0..10).map(|_| 26.0).collect();
        let points = make_points(&values);
        let violations = check_one_side(&points, &limits, 9, ViolationType::NineOneSide);
        // Should fire at index 8 and 9
        assert_eq!(violations.len(), 2);
        assert_eq!(violations[0].0, 8);
        assert_eq!(violations[1].0, 9);
    }

    #[test]
    fn test_rule5_not_triggered_mixed_sides() {
        let limits = ControlLimits {
            ucl: 28.0,
            cl: 25.0,
            lcl: 22.0,
        };
        // One point above 2σ upper (>27), one below 2σ lower (<23) — different sides
        // Rule 5 requires 2 of 3 on the SAME side, so this should not trigger
        let points = make_points(&[27.5, 25.0, 22.5]);
        let violations = check_rule5(&points, &limits);
        assert!(violations.is_empty());
    }

    #[test]
    fn test_rule7_fourteen_not_enough() {
        let limits = ControlLimits {
            ucl: 28.0,
            cl: 25.0,
            lcl: 22.0,
        };
        let values: Vec<f64> = (0..14).map(|_| 25.5).collect();
        let points = make_points(&values);
        let violations = check_rule7(&points, &limits);
        assert!(violations.is_empty());
    }
}