Glossary

This glossary defines terms used throughout the Numerics.NET SPC documentation and API. Terms are listed in alphabetical order. For the statistical background behind any term, follow the cross-references to the relevant conceptual page.

Terms

Attribute chart: A control chart that monitors a qualitative (classified) characteristic rather than a measured quantity. Attribute charts count defectives or defects per sample period. The four attribute chart types in this API are P, NP, C, and U. See Attribute Charts.
Capability (process capability): A measure of how well a statistically stable process can meet its specification limits using the within-process (short-term) variation as the denominator. The primary indices are $C_{p}$ (potential capability, centered) and $C_{p k}$ (actual capability, accounting for mean offset). Capability indices are only meaningful when the process is first confirmed to be in statistical control. See Capability, Performance, and Assumption Diagnostics.
Center line: The horizontal reference line drawn through the estimated process mean (or rate) on a control chart. It represents the expected value of the plotted statistic when the process is in control. Returned as the CenterLine property on all chart data types. See Result Model and Rendering Semantics.
Common cause variation: The inherent, random variation present in every process that results from many small, unavoidable sources acting simultaneously. A process exhibiting only common cause variation is said to be in statistical control or stable. Reducing common cause variation requires a fundamental change to the process system.
Control limit: A statistically derived boundary, placed at ±3 sigma from the center line, that defines the range of expected variation for a process in statistical control. Points beyond a control limit are signals of special cause variation. Control limits are computed from process data and must not be confused with specification limits, which are set by customer or engineering requirements. See Control Charts and Stability.
CUSUM (Cumulative Sum chart): A time-weighted control chart that accumulates deviations of the process statistic from a target value. The CUSUM is sensitive to small, sustained shifts in the process mean that Shewhart charts may miss. Signals are generated when the cumulative sum exceeds a decision interval h. See Time-Weighted Charts.
Defect: A single nonconformity found on an inspected unit. One unit may contain multiple defects. Defect counts are monitored with C and U charts. Contrast with defective.
Defective: An inspected unit that fails to meet requirements as a whole, regardless of how many individual nonconformities it contains. The binary pass/fail outcome is monitored with P and NP charts. Contrast with defect.
Diagnostic message: An advisory message attached to an analysis result that describes a condition the library detected—such as insufficient data, a violated normality assumption, or an unstable process—that may affect the validity or interpretation of the result. Messages carry a DiagnosticSeverity and a stable code string. See Diagnostics, Exceptions, and Failure Modes.
EWMA (Exponentially Weighted Moving Average): A time-weighted control chart that gives exponentially decreasing weight to older observations via a smoothing parameter $λ$ ∈ (0, 1]. The EWMA is more sensitive than a Shewhart chart to small, sustained process shifts while retaining a reasonable false-alarm rate. See Time-Weighted Charts.
I‑MR (Individuals–Moving Range): A pair of control charts used when only one measurement is taken per time period (subgroup size = 1). The Individuals (X) chart monitors the process level; the Moving Range (MR) chart monitors period-to-period variation. The I‑MR chart is the variables chart for individual measurements. See Variables Charts.
NP chart: An attribute control chart that monitors the number (count) of defective units per sample. Unlike the P chart, the NP chart requires a constant sample size n across all periods so that the plotted statistic is a count rather than a proportion. See Attribute Charts.
P chart: An attribute control chart that monitors the proportion (fraction) of defective units per sample. The P chart accommodates variable sample sizes, making it suitable for high-volume inspection where the number of units inspected varies by period. See Attribute Charts.
Performance (process performance): A measure of how well a process meets its specification limits using the overall (long-term) standard deviation of all observations as the denominator, regardless of stability. The primary indices are $P_{p}$ (potential performance) and $P_{p k}$ (actual performance). Performance indices characterize observed behavior; capability indices characterize the process potential when stable. See Capability, Performance, and Assumption Diagnostics.
Pointwise limits: Control limit vectors of the same length as the Values vector, providing one upper and one lower limit value per plotted period. Pointwise limits arise when the sample size or inspection area varies between periods (P and U charts with variable n) or during the transient phase of EWMA charts. The scalar UpperControlLimit / LowerControlLimit properties hold average values in these cases and should not be used for point-level rendering. See Result Model and Rendering Semantics.
Rational subgroup: A set of consecutive process outputs collected under conditions that are as homogeneous as possible within the group but allow meaningful comparisons between groups. The rational subgroup principle, attributed to Walter Shewhart, is the foundation of XBar‑R and XBar‑S chart design: all within-subgroup variation should reflect only common cause variation so that special causes appear as between-subgroup differences.
Rule violation: A detection of a specific control rule pattern in a chart series, indicating a possible special cause. Each violation records the chart series, the rule that fired, the index of the triggering point, and the window of contributing points. Represented by RuleViolation. See Rule Evaluation and Stability Interpretation.
Rule violation window: The contiguous sequence of plotted points that collectively constitute a rule violation. For a single point-beyond-limit rule the window contains only the violating point. For run rules (e.g., 8 consecutive points on one side of the center line) the window contains all 8 contributing points. The window bounds are exposed on RuleViolation as WindowStart and WindowLength.
Sigma estimator: The method used to estimate within-process variation (σ) for computing control limits. Common estimators are the moving range (for individuals data), the average subgroup range $\bar{R}$ (for XBar‑R), and the average subgroup standard deviation $\bar{S}$ (for XBar‑S). The choice of estimator affects both the numerical value of the limits and their interpretation. Controlled via the SigmaEstimator enum.
Specification limit: A threshold defined by customer requirements, engineering standards, or regulatory bodies that separates conforming from nonconforming product. Specification limits are not derived from process data and must not be confused with control limits. Process capability indices ( $C_{p}$ , $C_{p k}$ , $P_{p}$ , $P_{p k}$ ) relate specification limits to the observed process spread. See Capability, Performance, and Assumption Diagnostics.
Special cause variation: Variation attributable to a specific, identifiable source that is not part of the normal process system. Special cause variation appears as signals on a control chart: points beyond control limits, unusual runs, or other non-random patterns. Also called assignable cause variation. Eliminating special causes is the goal of the control-chart phase of SPC.
Stability (statistical): The property of a process whose variation is explained entirely by common causes, exhibiting no trends, shifts, or other non-random patterns over time. A statistically stable process is said to be in statistical control. Stability is a prerequisite for meaningful capability analysis. See Control Charts and Stability.
Subgroup: A set of measurements collected together in a single sampling period, treated as a homogeneous unit for computing a plotted statistic. For XBar‑R and XBar‑S charts the subgroup is the group of n individual measurements from which the subgroup mean and dispersion are calculated. For attribute charts the subgroup is the set of inspected items in one period. See also rational subgroup.
U chart: An attribute control chart that monitors the average number of defects per inspection unit (u = c / n, where c is the count of defects and n is the number of inspection units). The U chart accommodates variable inspection areas (n) between periods, unlike the C chart. See Attribute Charts.
Variables chart: A control chart that monitors a measured (continuous) quality characteristic. Variables charts provide more statistical power than attribute charts for detecting process shifts. The three variables chart families supported by this API are I‑MR, XBar‑R, and XBar‑S. See Variables Charts.
Western Electric rules: A set of supplemental run rules originally published in the Western Electric Statistical Quality Control Handbook (1956) for detecting non-random patterns in Shewhart control charts. The standard set includes rules based on zones defined at 1σ and 2σ from the center line as well as the 3σ limit. Available via ControlRuleSets. See Rule Evaluation and Stability Interpretation.
XBar‑R chart: A pair of variables control charts for subgrouped data where subgroup size is between 2 and 8. The XBar chart monitors the subgroup mean; the R (range) chart monitors within-subgroup variation via the subgroup range. The range is used as the dispersion estimator because it is computationally simple and efficient for small subgroups. See Variables Charts.
XBar‑S chart: A pair of variables control charts for subgrouped data of any size ≥ 2. The XBar chart monitors the subgroup mean; the S (standard deviation) chart monitors within-subgroup variation via the subgroup standard deviation, which is more statistically efficient than the range for subgroup sizes larger than about 4. Also supports variable subgroup sizes. See Variables Charts.

Glossary

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