Statistical Process Control

The Numerics.NET SPC API is a statistical computation engine for Statistical Process Control analysis. It produces chart-ready result objects, control limits, rule-violation records, capability metrics, and diagnostic messages.

What the SPC API provides

The Numerics.NET SPC API provides:

Static, retrospective (Phase I) analysis of process data.
Variables control charts: Individuals–Moving Range (I‑MR), XBar–R, and XBar–S.
Attribute control charts: P, NP, C, and U.
Time-weighted charts: EWMA and CUSUM.
Nelson and Western Electric rule evaluation.
Capability and performance metrics: $C_{p}$ , $C_{p k}$ , $P_{p}$ , $P_{p k}$ , and one-sided variants.
Assumption diagnostics including normality testing.
JSON serialization and round-trip persistence of results.

What the SPC API does not provide

The SPC API is a calculation engine, not a charting control or dashboard framework. It does not include:

UI widgets or chart controls.
Built-in plotting or report generation.
Per-observation incremental (streaming) updates.

Note

Phase II batch monitoring is supported via the Deploy() / Apply(Vector<Double>) lifecycle: fit a chart from Phase I data, deploy it to freeze the control limits, then call Apply(Vector<Double>) on each new batch of observations. Your application layer is responsible for rendering, displaying, and responding to the results.

The chart-centered model

SPC analyses use a chart-centered API. You create a chart object such as IndividualsMovingRangeChartSet, call Analyze() to fit the control limits, then read results directly from the chart's properties (series values, center lines, control limits, rule violations, capability metrics, and diagnostics). Nothing is drawn automatically. Nothing is displayed automatically.

This design keeps statistical computation cleanly separated from presentation, making it straightforward to use the library in desktop applications, web APIs, batch processing pipelines, or reporting services.

Inputs and outputs

Input	Output
Ordered process measurements (Vector<T>, Matrix<T>, or ReadOnlySpan<double>)	Chart points, center line, and control limits
Optional rule set	Rule violations with window start and length
Optional specification limits	Capability and performance metrics
Optional assumption-diagnostics flag	Normality test result and advisory diagnostics

Where to start

Choose the section that matches your current need:

I want a working result as quickly as possible. Start with getting started.
I need to choose the right chart for my data. See choosing the right analysis.
I need to understand inputs and outputs in detail. See the SPC process.
I need capability analysis. See capability, performance, and assumption diagnostics.
I need to integrate results into an application or API. See integration and persistence.

Documentation map

Getting Started with Numerics.NET SPC: quick start and core mental model.
The SPC Process: workflow overview: choosing an analysis, preparing data, consuming results, integrating outputs, and handling failures.
Control Charts and Stability: variables, attribute, and time-weighted charts; rule evaluation.
Capability, Performance, and Assumption Diagnostics: $C_{p}$ / $C_{p k}$ / $P_{p}$ / $P_{p k}$ , sigma estimators, normality testing, confidence intervals.
Worked Examples and Cookbook: realistic end-to-end scenarios.
Common Pitfalls and Misuse Patterns: the most likely mistakes and how to avoid them.
Frequently Asked Questions.
Constraints, Limits, and Support Matrix: implementation limits in table form.
Glossary: key SPC and library terms.
API Surface Map: bridge from the conceptual guide to the generated API reference.