Statistical process control / X̄–R

Separate normal process variation from a real stability signal.

The Mechatrovich X̄–R SPC Kit converts rational subgroup measurements into readable control charts—so unusual movement is visible before it becomes routine output.

Try the limited chartUnderstand X̄–R first
Both X̄ and R chartsEditable subgroup setupAutomatic control limitsOffline engineering workflow
01 / The problem

A process can meet specification and still be statistically unstable.

Specification limits describe acceptable product. Control limits describe the process behaviour observed over time. Mixing the two answers the wrong question: an in-spec point can still signal a process change, while a stable process can still be incapable of meeting specification.

Use the charts in sequence: check the R chart first to confirm within-subgroup variation is stable, then interpret the X̄ chart for movement in the process average.
Specification limitsCome from design or customer requirements. They define acceptable output.
Control limitsAre calculated from process data. They identify statistically unusual behaviour.
02 / Method

One subgroup produces two signals.

The X̄ chart tracks the average of each subgroup. The R chart tracks the range within each subgroup. For subgroup sizes from 2 to 10, standard SPC constants convert the grand average and average range into control limits.

01Collect rational subgroupsMeasurements should represent a short, meaningful window of process output.
02Check range stabilityAn unstable R chart makes the estimated process variation unreliable.
03Check process averageInterpret X̄ signals only after within-subgroup variation is understood.
03 / Working trial

Build both control charts from subgroup data.

Enter one subgroup per line. The trial calculates subgroup averages, ranges, center lines and control limits using the correct constants for the detected subgroup size.

X̄–R STABILITY CHECK / SPC-02LIVE LIMITED VERSION
One subgroup per line; 2–5 values per subgroup. Maximum 6 subgroups.
Trial boundary: six equal-size subgroups and basic limit checks. The complete kit handles larger datasets, configurable sampling and complete rule evaluation.
STABILITY ASSESSMENT

Ready to calculate

X̄̄—
R̄—
Subgroup n—
Signals—
R CHART / WITHIN-SUBGROUP VARIATIONCheck this chart first
X̄ CHART / PROCESS AVERAGEInterpret after the R chart
What was checked

Run the calculation to generate an interpretation.

A short trial cannot establish long-term statistical control. Use enough rational subgroups and follow your organization’s approved SPC procedure for production decisions.

04 / Interpretation

A point beyond a limit is only the first rule.

Rule 1One point beyond either control limit indicates an immediate special-cause signal.
RunsSeveral points on the same side of the center line can indicate a sustained process shift.
TrendsA consistent rise or fall can indicate drift before any individual point crosses a limit.

The limited trial checks control-limit violations. The complete kit can show the broader rule set and preserve the evidence in the report.

05 / Complete product

Move from a small demonstration to a repeatable SPC study.

The complete kit manages subgroup configuration, the complete measurement table, X̄ and R control charts, signal-rule evaluation and the stability report as one offline workflow.

MECHATROVICH / X̄–R SPC WORKSPACE

Process stability report

SUBGROUPS25
SUBGROUP SIZE5
ACTIVE SIGNALS2
R CHART / VARIATION STABILITY
X̄ CHART / PROCESS AVERAGE
SIGNAL LOG
SG 14  X̄ above UCL  · Rule 1
SG 19  8 points one side · Run rule
R chart  No active signal
STABILITYINVESTIGATE
Complete SPC workspace preview

Full subgroup tables, both control charts, extended signal rules, investigation log and stability-report export are included.

See what is included
06 / Product scope

The trial proves the calculation. The complete kit manages the study.

SPC functionTrialFull SPC Kit
SubgroupsUp to 6Complete study
Editable subgroup size2–5Configurable
X̄ and R chartsYesYes
Control-limit calculationYesYes
Beyond-limit checkYesYes
Extended signal rules—Yes
Subgroup summary and signal log—Yes
Saved study and report export—Yes

Build the complete stability study.

Offline X̄–R SPC Kit · Complete file package · No subscription.

Buy Full Version

Purchase and file delivery are handled securely through Gumroad. Engineering acceptance criteria remain subject to your approved quality procedures.