1.The formula of the x-bar and r-charts are as follows:
x-bar:
`barX = (sum(barX_1 ... barX_k))/k`
Where k = subgroups
r-chart:
`barR = (sum(R_1 ... R_k))/k`
Where k = subgroups
From the above equations, k (subgroups) is common in both equations.
2.The control lower limit formula for r-chart is as follows:
`LCL_R = D_3 * barR`
As seen in the attachment, there are no D_3 values for subgroup size for 6 and...
1.The formula of the x-bar and r-charts are as follows:
x-bar:
`barX = (sum(barX_1 ... barX_k))/k`
Where k = subgroups
r-chart:
`barR = (sum(R_1 ... R_k))/k`
Where k = subgroups
From the above equations, k (subgroups) is common in both equations.
2.The control lower limit formula for r-chart is as follows:
`LCL_R = D_3 * barR`
As seen in the attachment, there are no D_3 values for subgroup size for 6 and below.
On the r-chart the line the line for the lower limit is dotted of the subgroup size is atleast 7
3. If your x-bar and r-charts are out of control, are your capability calculations unreliable?
When the r-chart is out of control, the values for the r-bar are not meaningful. The process variation therefore becomes unstable. Because the r-chart values are not meaningful, the control limits of the x-bar chart will not be meaningful. Likewise, if the x-bar chart is out of control then the process location becomes unstable and cannot be estimated by a single average value.
Since the capability calculations depend on the x-bar and r-chart, if these charts are out of control, the capability calculations become unreliable.
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