Page 310 - Six Sigma Demystified

290 Six SigMa DemystifieD

UCL, LCL (upper and lower control limit):

UCL = x + 3σ (normal distribution)
x x

LCL = x – 3σ (normal distribution)
x x
where x is the average and σ is the process sigma.
x
Note: Some authors prefer to write this as:

UCL = x + E MR
2
x
LCL = x – E MR
x
2
For nonnormal distributions, the UCL is defined at the 99.865 percentile of
the fitted curve, and the LCL is defined at the 0.135 percentile of the fitted
curve.

Moving-Range Chart Calculations
Plotted statistic: The moving ranges between successive subgroups in an individ-
ual-X chart (i.e., the difference between the current observation and the obser-
vation immediately prior):

MR = x − x
j j −1
Centerline:

1 m
MR = ∑ MR j
m − 1 j =1

where m is the total number of subgroups included in the analysis, and MR is
j
the moving range at subgroup j.
UCL, LCL (upper and lower control limit):

UCL MR = MR + 3d σ (all distributions)
3 x

LCL MR = max(0, MR – 3d σ ) (all distributions)
3 x
where MR is the average of the moving ranges, σ is the process sigma, and d
x 3
is a function of n (tabulated in Appendix 6).