Batch phase 2: online Nomikos-MacGregor monitoring

[kgdunn]

Summary

• Adds BatchPCA.predict_online: projection to the model plane (PMP) for a partially-observed batch. At each time sample the future trajectory columns are treated as missing and the score is the least-squares fit of the observed columns onto the loadings (t = pinv(P_obs) @ x_obs); initial conditions, known from the batch start, are always observed. At full observation it matches BatchPCA.diagnose exactly.
• Adds BatchMonitor: builds time-varying Hotelling's T2 and SPE control limits by running every good batch through predict_online at each sample and summarising the good-batch spread (spe_calculation per sample; the analytical F-based T2 limit). monitor() tracks a new batch sample-by-sample and flags the samples where each statistic exceeds its limit.
• Adds online_monitoring_plot: the online SPE/T2 chart, drawing the batch trace over the time-varying limit and the mean good-batch trace, with alarm samples marked.

This is Phase 2 of the batch modernization plan (online monitoring). It builds on the offline BatchPCA from Phase 1.

Note on base branch: this PR is stacked on claude/process-improve-library-review-9h1fn2 (Phase 1, #459), since predict_online is a method on BatchPCA which isn't merged yet. GitHub will retarget the base to main automatically once #459 merges. Review #459 first.

Test plan

• tests/batch/test_batch_monitor.py: PMP matches diagnose at full observation; upto_k bounds; limit shapes; a good training batch stays mostly in-limit; a large injected fault in a real nylon batch trips SPE in the fault window; upto_k truncation; initial-conditions threaded end-to-end
• tests/batch/test_batch_plots.py: online monitoring plot builds for SPE and T2; bad-statistic guard
• Full batch suite: 111 passed; ruff check . and mypy src/process_improve clean (142 files)

Checklist

• Version bumped in pyproject.toml (MINOR: 1.55.0 -> 1.56.0) and CITATION.cff synced
• Tests added or updated where relevant
• ruff check . passes
• CHANGELOG.md updated

🤖 Generated with Claude Code

https://claude.ai/code/session_01SyEpexCyqHn1rwTMYQSiP6

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Generated by Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 90.17857% with 11 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/process_improve/batch/_batch_pca.py	83.33%	3 Missing and 3 partials ⚠️
src/process_improve/batch/_batch_monitor.py	94.11%	2 Missing and 1 partial ⚠️
src/process_improve/batch/_batch_plots.py	91.66%	1 Missing and 1 partial ⚠️

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