X-bar R vs X-bar S Control Charts

Both X-bar & R and X-bar & S charts monitor process mean and variation for subgroup data. The choice depends on subgroup size and how tightly you need to track variability.

Comparison table

	X-bar & R	X-bar & S
Subgroup size	n = 2 to 8 (some say ≤ 10)	n > 8 (or n ≥ 10)
Variation stat	Range R = max − min	Sample std dev s
Efficiency	Range uses only 2 of n values	s uses all n values — more efficient
Control constants	A₂, D₃, D₄	A₃, B₃, B₄
Simplicity	Easier to calculate by hand	Requires calculator for s

Control limits

X-bar & R: UCL_x = x̄̄ + A₂R̄ LCL_x = x̄̄ − A₂R̄ UCL_R = D₄R̄ LCL_R = D₃R̄ X-bar & S: UCL_x = x̄̄ + A₃s̄ LCL_x = x̄̄ − A₃s̄ UCL_s = B₄s̄ LCL_s = B₃s̄ For n = 5: A₂ = 0.577, D₃ = 0, D₄ = 2.114

CQE exam tips

For small subgroups (n ≤ 8), the range is a reliable estimator of σ; for larger subgroups, s is statistically superior.
D₃ = 0 for n ≤ 6, meaning there is no lower control limit on the R chart for small subgroups.
Both chart types monitor the same process mean using the same X-bar chart structure.

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