Struct XBarRChart 

pub struct XBarRChart { /* private fields */ }

X-bar and Range (X-bar-R) control chart.

Monitors the process mean (X-bar chart) and process variability (R chart) using subgroup ranges. Accepts subgroup sizes MIN_SUBGROUP_SIZE..=MAX_SUBGROUP_SIZE; above about n = 10 the range discards enough of each subgroup’s information that XBarSChart is the usual choice.

Algorithm

1. For each subgroup, compute the mean (X-bar) and range (R).
2. Compute the grand mean (X-double-bar) and average range (R-bar).
3. X-bar chart limits: CL = X-double-bar, UCL/LCL = CL +/- A2 * R-bar.
4. R chart limits: CL = R-bar, UCL = D4 * R-bar, LCL = D3 * R-bar.

Examples

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

let mut chart = XBarRChart::new(5).expect("subgroup size is in range");
chart.add_sample(&[25.0, 26.0, 24.5, 25.5, 25.0]).unwrap();
chart.add_sample(&[25.2, 24.8, 25.1, 24.9, 25.3]).unwrap();
chart.add_sample(&[25.1, 25.0, 24.7, 25.3, 24.9]).unwrap();

let limits = chart.control_limits().expect("should have limits after 3 samples");
assert!(limits.ucl > limits.cl);
assert!(limits.cl > limits.lcl);

Reference

Montgomery, D.C. (2019). Introduction to Statistical Quality Control, 8th ed., Chapter 6: Control Charts for Variables.

Implementations

impl XBarRChart

pub fn with_rules(self, rules: RuleSet) -> Self

Apply only the given run tests when computing limits.

Defaults to RuleSet::shewhart – the 3-sigma test alone; the supplementary tests raise the false alarm rate and are asked for here. Existing points are re-evaluated, so the call may be made at any time.

Examples

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

let chart = XBarRChart::new(5).expect("5 is within range")
    .with_rules(RuleSet::nelson().without(ViolationType::FourteenAlternating));

pub fn rules(&self) -> RuleSet

The run tests this chart applies.

pub fn new(subgroup_size: usize) -> Result<Self, ControlChartError>

Create a new X-bar-R chart with the given subgroup size.

Errors

Returns ControlChartError::SubgroupSizeOutOfRange when subgroup_size is outside MIN_SUBGROUP_SIZE..=MAX_SUBGROUP_SIZE. The size is data in most callers – it comes from the measurements a user supplied – so rejecting it is an ordinary outcome rather than a contract violation, and a boundary that cannot unwind (WebAssembly, C) needs it as a value.

pub fn sigma_hat(&self) -> Option<f64>

Short-term (within-subgroup) sigma estimated from this chart: sigma-hat = R-bar / d2(n).

This is the quantity a capability study needs for Cp/Cpk, and it cannot be recovered from a flat measurement vector — it depends on the subgroup structure the chart already holds. Returning it here is what lets a caller feed crate::capability::ProcessCapability::compute without reimplementing the d2 table.

Returns None if there is not enough data for control limits.

Examples

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

let mut chart = XBarRChart::new(5).expect("subgroup size is in range");
for g in [[9.9, 10.1, 10.0, 9.8, 10.2], [10.3, 9.7, 10.0, 10.1, 9.9]] {
    chart.add_sample(&g).unwrap();
}
let sigma = chart.sigma_hat().expect("limits available");
assert!(sigma > 0.0);

pub fn sigma_hat_df(&self) -> Option<f64>

Degrees of freedom of sigma_hat – what CapabilityIndices::intervals takes as within_df for Cp/Cpk intervals.

R-bar of m subgroups of n has squared coefficient of variation (d3/d2)^2 / m; David’s (1951) approximation turns it into the degrees of freedom of a sample standard deviation with the same precision – fewer than the m (n - 1) a pooled standard deviation would have, the price of using the range. d3/d2 is (D4 - 1) / 3.

Returns None if there is not enough data for control limits.

Examples

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

let mut chart = XBarRChart::new(5).expect("subgroup size is in range");
for g in [[9.9, 10.1, 10.0, 9.8, 10.2], [10.3, 9.7, 10.0, 10.1, 9.9]] {
    chart.add_sample(&g).unwrap();
}
let df = chart.sigma_hat_df().expect("limits available");
assert!(df > 7.0 && df < 8.0); // two ranges of five: fewer than 2 x 4

pub fn r_limits(&self) -> Option<ControlLimits>

Get the R chart control limits, or None if insufficient data.

pub fn r_points(&self) -> &[ChartPoint]

Get the R chart points.

Trait Implementations

impl Clone for XBarRChart

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl ControlChart for XBarRChart

fn add_sample(&mut self, sample: &[f64]) -> Result<(), ControlChartError>

Add a subgroup sample. The sample length must equal the chart’s subgroup size.

fn control_limits(&self) -> Option<ControlLimits>

Get the computed control limits, or None if insufficient data.

fn is_in_control(&self) -> bool

Check if the process is in statistical control.

fn violations(&self) -> Vec<Violation>

Get all violations detected across all chart points.

fn points(&self) -> &[ChartPoint]

Get all chart points.

impl Debug for XBarRChart

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.