Struct IndividualMRChart 

pub struct IndividualMRChart { /* private fields */ }

Individual and Moving Range (I-MR) control chart.

Monitors individual observations (subgroup size = 1) using the moving range of consecutive observations to estimate process variability.

Algorithm

1. Compute moving ranges: MR_i = |x_i - x_{i-1}| for i >= 1.
2. Compute the mean of individual observations (X-bar) and the average moving range (MR-bar).
3. I chart limits: CL = X-bar, UCL/LCL = X-bar +/- E2 * MR-bar.
4. MR chart limits: CL = MR-bar, UCL = D4 * MR-bar, LCL = 0.

Examples

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

let mut chart = IndividualMRChart::new();
for &x in &[25.0, 25.2, 24.8, 25.1, 24.9, 25.3, 25.0, 24.7] {
    chart.add_sample(&[x]).unwrap();
}

let limits = chart.control_limits().expect("should have limits after 2+ observations");
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 IndividualMRChart

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::{IndividualMRChart, ControlChart, RuleSet, ViolationType};

let chart = IndividualMRChart::new()
    .with_rules(RuleSet::nelson().without(ViolationType::FourteenAlternating));

pub fn rules(&self) -> RuleSet

The run tests this chart applies.

pub fn new() -> Self

Create a new Individual-MR chart.

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

Short-term sigma estimated from this chart: sigma-hat = MR-bar / d2(2).

The moving range of consecutive observations is a range of two, so d2(2) = 2/sqrt(pi) is the unbiasing constant. This is the within sigma a capability study of individual observations uses, and the counterpart of XBarRChart::sigma_hat for subgroups of one.

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

Examples

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

let mut chart = IndividualMRChart::new();
for x in [1.0, 3.0, 2.0] {
    chart.add_sample(&[x]).unwrap();
}
// MR-bar = (2 + 1) / 2 = 1.5
let sigma = chart.sigma_hat().expect("limits available");
assert!((sigma - 1.5 / (2.0 / std::f64::consts::PI.sqrt())).abs() < 1e-12);

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

Degrees of freedom of sigma_hat, for Cp/Cpk intervals: 0.62 (N - 1) for N observations. Successive moving ranges share a value, so they are not independent and no range-distribution formula applies; the factor is Wheeler’s empirical one (as JMP uses it).

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

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

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

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

Get the MR chart points.

Trait Implementations

impl Clone for IndividualMRChart

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 IndividualMRChart

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

Add a single observation. The sample slice must contain exactly one element.

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 IndividualMRChart

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

Formats the value using the given formatter.

impl Default for IndividualMRChart

fn default() -> Self

Returns the “default value” for a type.