Control Limits for X and Rcharts
LCL for X chart =
UCL for X chart =
LCL for Rchart =
UCL for Rchart =
Center line for Rchart: 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.
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
N is the number of subgroups for which
Control Limits for X and Scharts
LCL for X chart =
UCL for X chart =
LCL for Schart =
UCL for Schart =
Center line for Schart: 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.
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
N is the number of subgroups for which
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.
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
LeveyJennings charts show a process mean with control limits based on a longterm sigma. The control limits are placed at 3s distance from the center line.
The standard deviation, s, for the LeveyJennings chart is calculated the same way standard deviation is in the Distribution platform.
Based on this approximation, approximate upper and lower control limits can be determined. For a nominal level αType 1 error probability in one direction, an approximate upper control limit is a limit UCL such that:
Likewise, an approximate lower control limit is a limit LCL for a nominal level αType 1 error probability is a limit such that:
is the upper (lower) percentile of the chisquare distribution with
v = 2u/(1+uk) degrees of freedom. Negative lower control limits can be set to zero.
v = 2u/(1+uk) degrees of freedom. Negative lower control limits can be set to zero.
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