Control Limits for X- and R-charts
LCL for X chart =
UCL for X chart =
LCL for R-chart =
UCL for R-chart =
Center line for R-chart: By default, the center line for the ith subgroup (where k is the sigma multiplier) indicates an estimate of the expected value of Ri. This value is computed as: , where is an estimate of σ. If you specify a known value (σ0) for σ, the central line indicates the value of . Note that the central line varies with ni.
Xw = weighted average of subgroup means
σ = process standard deviation
d2(n) is the expected value of the range of n independent normally distributed variables with unit standard deviation
d3(n) is the standard error of the range of n independent observations from a normal population with unit standard deviation
Control Limits for X- and S-charts
LCL for X chart =
UCL for X chart =
LCL for S-chart =
UCL for S-chart =
Center line for S-chart: By default, the center line for the ith subgroup (where k is equal to the sigma multiplier) indicates an estimate of the expected value of si. This value is computed as , where is an estimate of σ. If you specify a known value (σ0) for σ, the central line indicates the value of . Note that the central line varies with ni.
Xw = weighted average of subgroup means
σ = process standard deviation
c4(n) is the expected value of the standard deviation of n independent normally distributed variables with unit standard deviation
c5(n) is the standard error of the standard deviation of n independent observations from a normal population with unit standard deviation
X = the mean of the individual measurements
σ = the process standard deviation
k = the number of standard deviations
d2(n) = expected value of the range of n independent normally distributed variables with unit standard deviation.
d3(n) = standard error of the range of n independent observations from a normal population with unit standard deviation.
LCLi =
UCLi =
w is the span parameter (number of terms in moving average)
k is the number of standard deviations
Xw is the weighted average of subgroup means
k is the number of standard deviations
Xw is the weighted average of subgroup means
p-chart LCL =
p-chart UCL =
np-chart LCL =
np-chart UCL =
p is the average proportion of nonconforming items taken across subgroups
k is the number of standard deviations
u is the expected number of nonconformities per unit produced by process
u is the average number of nonconformities per unit taken across subgroups. The quantity u is computed as a weighted average
N is the number of subgroups
u is the expected number of nonconformities per unit produced by process
u is the average number of nonconformities per unit taken across subgroups. The quantity u is computed as a weighted average
N is the number of subgroups
Levey-Jennings charts show a process mean with control limits based on a long-term sigma. The control limits are placed at 3s distance from the center line.
The standard deviation, s, for the Levey-Jennings chart is calculated the same way standard deviation is in the Distribution platform.