spc_xbar_r — SPC `chart` op

• Data kinds: matrix → table

• Call: import fullseye as fs; fs.ledger.spc_xbar_r(subgroups) (to call the implementation directly, import spc; spc.spc_xbar_r(subgroups); from the registry, opsspc.get("spc_xbar_r"))

Usage

Shewhart Xbar-R control chart from subgroup measurements.

`subgroups is a 2-D array of shape (m, n) — m subgroups of n`

measurements each, `2 <= n <= 10` (the range chart is only calibrated for

small subgroups). For each subgroup `j` the plotted statistics are the mean

`Xbar_j and the range R_j = max - min`. The centre lines are the grand

mean `Xbarbar and the mean range Rbar`, and with the ISO 8258 constants

`(A2, D3, D4) for that n`::

xbar_ucl = Xbarbar + A2*Rbar xbar_lcl = Xbarbar - A2*Rbar

r_ucl = D4*Rbar r_lcl = D3*Rbar

Returns a dict (a "table") with the per-subgroup `xbar / r` arrays, the

six limits and three centre lines, the integer indices `out_of_control` of

subgroups outside either chart, and `in_control` (True when that list is

empty). The constants are fixed by `n: for n=5` they are exactly

`A2=0.577, D3=0.000, D4=2.115` (pinned in the tests).

Raises `ValueError`: a non-2-D / empty *subgroups*, a subgroup size

outside `[2, 10]`, or non-finite / mislabelled input.

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• poc_spc — py -3.11 examples/poc_spc.py

Ops the type connects to (they accept `table` as input)

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Same category (`chart`)

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*Provenance: spc.py — SPC operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

spc_xbar_r — SPC chart op