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Module rules

fdars_core::spm

Module rules 

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Runs and zone rules for control chart analysis.

Implements Western Electric (WE) and Nelson rules for detecting non-random patterns in control chart data. These rules supplement T²/SPE alarm logic by detecting non-random patterns (trends, runs, stratification) that may indicate process shifts even when individual points remain within control limits.

§Theoretical ARL₀ (independent normal data)

RuleARL₀
WE1 (3σ)370.4
WE2 (2/3 beyond 2σ)122.0
WE3 (4/5 beyond 1σ)90.7
WE4 (8 same side)119.7
Nelson5 (6 monotone)360.0
Nelson6 (14 alternating)182.0
Nelson7 (15 within 1σ)44.1
All WE combined~46

§Assumptions

These rules assume observations are independent and identically distributed under in-control conditions. When applied to autocorrelated data (e.g., EWMA-smoothed statistics), false alarm rates may be inflated.

§Computational complexity

All rules evaluate in O(n·W) time where W is the maximum window size (1 for WE1, 15 for Nelson7). Memory usage is O(W) per rule.

§NaN handling

NaN values in the input are not handled specially; comparisons involving NaN return false, so NaN points will not trigger WE1–WE3 or Nelson5–Nelson6 violations but may affect WE4/Nelson7 (which check all-same-side or all-within conditions).

§References

  • Western Electric Company (1956). Statistical Quality Control Handbook. Western Electric Co., Indianapolis. Chapter 4, pp. 25–28.
  • Nelson, L.S. (1984). The Shewhart control chart — tests for special causes. Journal of Quality Technology, 16(4), 237-239, p. 238.
  • Nelson, L.S. (1985). Interpreting Shewhart X̄ control charts. Journal of Quality Technology, 17(2), 114-116, p. 115.

§False Alarm Rates

For false alarm rate estimation under these rules with independent data, the theoretical ARL₀ for WE1 alone is ~370 (at 3σ). Combining multiple rules increases sensitivity but reduces ARL₀; empirical calibration via arl0_t2 or simulation is recommended when using multiple rules simultaneously.

Structs§

RuleViolation
A detected rule violation.

Enums§

ChartRule
A control chart pattern rule.

Functions§

evaluate_rules
Evaluate a set of chart rules against a sequence of values.
nelson_rules
Apply Nelson rules 5-7 (in addition to WE rules which cover Nelson 1-4).
western_electric_rules
Apply all four Western Electric rules.