Struct XBarSChart

Source

pub struct XBarSChart { /* private fields */ }

Expand description

X-bar and Standard Deviation (X-bar-S) control chart.

Monitors the process mean (X-bar chart) and process variability (S chart) using subgroup standard deviations. Preferred over X-bar-R for larger subgroups where range is a less efficient estimator.

§Algorithm

For each subgroup, compute the mean (X-bar) and sample standard deviation (S).
Compute the grand mean (X-double-bar) and average S (S-bar).
X-bar chart limits: CL = X-double-bar, UCL/LCL = CL +/- A3 * S-bar.
S chart limits: CL = S-bar, UCL = B4 * S-bar, LCL = B3 * S-bar.

§Reference

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

Implementations§

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impl XBarSChart

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

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

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pub fn rules(&self) -> RuleSet

The run tests this chart applies.

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

Create a new X-bar-S 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.

Source

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

Short-term (within-subgroup) sigma estimated from this chart: sigma-hat = S-bar / c4(n).

The S-chart counterpart of XBarRChart::sigma_hat, and the estimator preferred for larger subgroups. Returns None if there is not enough data for control limits.

§Examples

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

let mut chart = XBarSChart::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);

Source

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

Degrees of freedom of sigma_hat, for Cp/Cpk intervals: S-bar of m subgroups has squared coefficient of variation (1 - c4^2) / (m c4^2), turned into degrees of freedom by David’s approximation – a little under the m (n - 1) of a pooled standard deviation.

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

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