Friday, August 21, 2015

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, UCLR = R̄ + 3CR̄
= (1 + 3C)R̄ = D4
LCLR =  R̄ - 3CR̄
= (1 - 3C)R̄ = D3
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.

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