Control Limits for R-Chart

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3 - σ control limits for R-chart are given by -
E (R) + 3σR
E (R) is estimated by R̄ (R-bar) and σR from
σR = C.E (R) = CR̄
where C is the constant depending on n.
So, UCL_R = R̄ + 3CR̄
= (1 + 3C)R̄ = D₄R̄
LCL_R =  R̄ - 3CR̄
= (1 - 3C)R̄ = D₃R̄
The values D₃ = (1-3C) and D₄ = (1 +3C) have been tabulated for different values of n from 2 to 25.
However, the control limits for R-chart can be obtained directly from the assumed or known value of σ as follows:
UCLR = D₂σ
LCLR = D₁σ
Where, D₁ and D₂ are tabulated for different values of n from 2 to 25.