06-reference

commoncog process behaviour charts

Tue Apr 14 2026 20:00:00 GMT-0400 (Eastern Daylight Time) ·reference ·source: Commoncog ·by Cedric Chin

“Process Behaviour Charts: More Than You Need To Know” — @CedricChin

Why this is in the vault

This is Chin’s most complete technical reference on the XmR chart — the exact intellectual parent of RDCO’s MAC 3x6 testing matrix. It is the operator’s manual: what XmR charts are for, the three validity requirements, the exact construction formulas (average and median), the three Western Electric Zone interpretation rules, and the empirical basis for three-sigma limits across ~1,143 real-world distributions. Every one of these constraints translates directly to how MAC cells must be designed and reviewed.

The core argument (paraphrased)

Process behaviour charts exist to separate signal from noise in any time-series metric — and the action taken in response to that signal is where the value lives.

Chin’s reframing of “process”: Shewhart (1931) used the word “phenomenon”, not “process”. XmR charts apply to shopping mall footfall, insurance premiums, asthma peak-flow readings, website visits — anything that is a “sequence of values that are logically comparable” (Wheeler).

Three validity requirements for any XmR chart:

  1. Same system of causes. All points from one predictable, steady-state system. The asthma example: plotting pre-med (X) and post-med (Y) readings on the same chart is invalid — two systems, plot separately. Double-humped histograms = two systems mixed together.
  2. Same measurement method. Every point measured the same way.
  3. Chronological order. It is a time series.

What they are for, in one sentence: “to separate signal from noise.” Payoffs: (1) investigate with confidence when exceptional variation appears; ignore routine variation with equal confidence; (2) know when process improvements actually worked — they show up as exceptional variation; (3) know your next step — a predictable process (routine only) cannot be improved incrementally, it must be redesigned; an unpredictable process (routine + exceptional) must first have its special causes removed before redesign is meaningful.

Construction (average-based XmR):

  1. Plot the time series X.
  2. Plot the moving range mR (absolute difference between successive Xs).
  3. Plot Average(X) as a centreline on the X chart.
  4. Plot Average(mR) as a centreline on the mR chart.
  5. UNPL = Average(X) + 2.66 x Average(mR)
  6. LNPL = Average(X) - 2.66 x Average(mR)
  7. URL = 3.269 x Average(mR)

Median variant (for data with extreme moving ranges): substitute medians and use scaling factors 3.14 and 3.86.

Three interpretation rules (Western Electric Zone, per Wheeler):

  1. Any point outside the natural process limits — strong exceptional cause, investigate immediately.
  2. Three of four consecutive points in the outer 25% band (between centreline and limit) — moderate but sustained exceptional cause.
  3. Eight consecutive points on one side of the centreline — weak but sustained exceptional cause.

Chin’s emphasis: “not designed for precision, but for action.” The chart only estimates three sigma. The magic is in acting on what the chart tells you, not in computing it precisely.

Moving range chart has three uses: (1) a point above the URL signals a process break — recompute limits after it; (2) detects chunky data (failure mode — fewer than three distinct values below URL means XmR is unusable, e.g. spill counts; reframe as “days between spills”); (3) Wheeler argues its presence next to an X chart is a sign limits were computed correctly (three sigma, not three standard deviations).

Sample size. Limits begin to stabilise at 17 points and settle at 24. But “computed limits with just five to six data points are good enough to start acting on.” Wait 5-6 new points after a process change to judge it — this is Deming’s cycle in action, and it requires patience.

No distribution assumption required. XmR was designed for the common case where you can’t know the distribution. Works for any single-humped distribution. Shewhart’s move was to invert the statistical approach: instead of fixing P and deriving A/B for a known f(y,n), choose generic A/B (three sigma) such that for any f(y,n), P is reasonably close to 1.00. Tchebycheff guarantees >89% coverage; in practice Wheeler tested 1,143 real-world probability models and found three-sigma limits give >98% coverage for all mound-shaped and >97.5% for J-shaped distributions — a <2.5% false-alarm rate, better than the 5% used in most statistical procedures.

Why not standard deviation s? “The global standard deviation statistic … assumes the data to be completely homogenous.” XmR’s entire purpose is to test homogeneity. Using s to set limits defeats the point.

Common gotchas: chunky data; autocorrelation above 0.7 (fix: sample no faster than the process can change — not every 15s for boiler temp); too many data points (collect at the frequency the process can actually change).

Closing note. The deeper point is to understand variation, not to fetishise XmR. Amazon’s WBR does not mandate XmR charts, but demands deep understanding of what is normal vs exceptional in every metric. Bryar & Carr: “It’s therefore critical to differentiate normal variation (noise) from some fundamental change or defect in a process (signal).” XmR is one tool for that understanding; it is not the only one.

Mapping against Ray Data Co

This article is high-relevance to MAC’s 3x6 matrix. XmR is the canonical control-chart cell-basis. Five mappings, each tighter than the last:

1. Every cell of the MAC 3x6 matrix is an XmR chart in disguise — and the three validity requirements are hard design constraints. The matrix assumes each cell (e.g. column x temporal, row x rel-source, aggregate x rel-recon) generates logically comparable sequences of values. Chin’s asthma warning is a concrete review question for MAC test design: if a cell mixes pre-transform and post-transform values, combines two upstream feeds, or changes its measurement method between runs, the cell is invalid the same way the combined X/Y asthma chart is invalid. “Same system of causes, same measurement method, chronological order” should be a mandatory checklist when defining any new MAC test.

2. The temporal basis in MAC is literally an XmR chart. The temporal column of the MAC matrix exists to catch exceptional variation over time — which is what an XmR chart does. The three interpretation rules (outside limits / 3-of-4 in outer band / 8-on-a-side) become the Stop/Pause/Go severity tiers for every temporal cell. The agent-deployer (per 2026-04-14-levie-agent-deployer-role-jd) is the operator running this discipline against AI-generated data artifacts instead of factory throughput — MAC is the WBR for agents.

3. “Predictable process needs redesign, unpredictable process needs investigation” = the phData / MG engagement diagnostic. Early in a prospect conversation, place their current data-quality record on a notional XmR chart:

4. “Not designed for precision, but for action” is the rebuttal to over-engineered MAC tests. The temptation is to build extremely tight cells that detect every drift. Chin (via Wheeler) is explicit: XmR charts are conservative by design — they err toward no signal rather than false alarms, because false alarms destroy the operator’s willingness to act. MAC severity tiers should inherit this conservatism. A Stop tier must be rare and trustworthy; if it fires on routine variation, the discipline dies within a month.

5. State-ownership reinforcement — operational definitions must persist client-side. The XmR chart is only valid if “same measurement method” holds over time. That requires the operational definitions (what counts as a row, a null, a match, a reconciliation key) to persist across sessions and across model swaps. That is ../04-tooling/rdco-state-ownership-architecture in miniature: the definitions live in the client-owned vault and skills, not in the model. Every time an agent silently “reinterprets” what a column means, the client’s entire XmR history is invalidated. This is a concrete, testable reason the state-ownership thesis matters — not philosophy, but chart validity.

One additional callout for the coaching curriculum. Chin notes that 5-6 points is enough to start acting, and that limits stabilise at 17-24. That timing discipline (wait for enough points, don’t chase noise, don’t move on too fast) is behavioural, not technical — it belongs in the MAC drip course alongside the formulas. Training patience is part of the engagement.

Mapping strength: strong. This is the methodological parent of MAC. The three validity requirements, three interpretation rules, and the predictable/unpredictable distinction map one-to-one onto RDCO’s testing framework and sales diagnostic.