X-bar/R · X-bar/S · Individuals/MR

Control-chart limit arithmetic

Inputs

Chart modeChoose the declared series form to calculate; no mode supplies a control-status conclusion.

Declared subgroup sizenobservationsRequired for X-bar modes only; enter an integer from 2 through 10.

Subgroup 1 meanx̄₁unitFirst declared subgroup mean; enter two through five contiguous subgroup summaries.

Subgroup 1 range / sR₁ or s₁unitEnter range in X-bar/R mode or sample standard deviation in X-bar/S mode.

Subgroup 2 meanx̄₂unitSecond declared subgroup mean.

Subgroup 2 range / sR₂ or s₂unitEnter range in X-bar/R mode or sample standard deviation in X-bar/S mode.

Subgroup 3 meanx̄₃unitOptional third declared subgroup mean; summaries must be contiguous.

Subgroup 3 range / sR₃ or s₃unitOptional variation paired to subgroup 3.

Subgroup 4 meanx̄₄unitOptional fourth declared subgroup mean; summaries must be contiguous.

Subgroup 4 range / sR₄ or s₄unitOptional variation paired to subgroup 4.

Subgroup 5 meanx̄₅unitOptional fifth declared subgroup mean.

Subgroup 5 range / sR₅ or s₅unitOptional variation paired to subgroup 5.

Results

Subgroup summaries entered

subgroups

X-bar chart center line

10.04

unit

X-bar chart upper limit

11.102

unit

X-bar chart lower limit

8.9783

unit

Range chart center line

1.84

unit

Range chart upper limit

3.8916

unit

Range chart lower limit

unit

X-bar limits = x̄̄ ± A2·R̄; R limits = D3/D4·R̄

A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.

Calculation snapshot

Control-chart limit arithmetic

Formula version 1.0.0

Conditions

Chart mode	xbarR
Declared subgroup size	5
Subgroup 1 mean	10.0
Subgroup 1 range / s	1.8
Subgroup 2 mean	10.2
Subgroup 2 range / s	2.0
Subgroup 3 mean	9.9
Subgroup 3 range / s	1.7
Subgroup 4 mean	10.1
Subgroup 4 range / s	1.9
Subgroup 5 mean	10.0
Subgroup 5 range / s	1.8
Individual 1	10.0
Individual 2	10.2
Individual 3	9.9
Individual 4	10.1
Individual 5	10.0

Calculated response

Subgroup summaries entered	5 subgroups
X-bar chart center line	10.04 unit
X-bar chart upper limit	11.102 unit
X-bar chart lower limit	8.9783 unit
Range chart center line	1.84 unit
Range chart upper limit	3.8916 unit
Range chart lower limit	0 unit

Method

X-bar limits = x̄̄ ± A2·R̄ · R limits = D3/D4·R̄

Source

NIST Shewhart variables-control-chart guidance: https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc321.htm

Boundaries

User supplies compatible subgroup summaries or sequence
Subgroup size is 2 through 10
Conventional listed chart constants
No control-status conclusion

This printout is a record of displayed inputs and deterministic formula output. It is not an approval, certification, or engineering conclusion.

Nearby: ISO 286 fits · Tolerance stack · Position deviation · MMC bonus & virtual condition

Method

Formula, when it applies, and when it does not

Calculate central lines and conventional limit arithmetic from up to five subgroup summaries or sequential individual observations.

X-bar limits = x̄̄ ± A2·R̄; R limits = D3/D4·R̄

When

User supplies compatible subgroup summaries or sequence
Subgroup size is 2 through 10
Conventional listed chart constants
No control-status conclusion

Don’t

This reports conventional X-bar/R or X-bar/S limit arithmetic from user-entered subgroup summaries. It does not recreate subgroup observations, test normality, independence, rational subgrouping, data integrity, special-cause signals, trends, rules, capability, process control, process acceptance, or a control decision.

NIST Shewhart variables-control-chart guidance