Quality and Reliability Methods - SAS

Chapter 5 Shewhart Control Charts 75
Shewhart Control Charts for Variables
Note: When sample sizes are unequal, the Test options are greyed out. If the samples change while the chart
is open and they become equally sized, and the zone and/or test option is selected, the zones and/or tests will
be applied immediately and appear on the chart.
Control Limits for X - and S-Charts
JMP generates control limits for X - and S-charts as follows.
kσˆ
LCL for X chart = X w – --------
n i
kσˆ
UCL for X chart = X w + --------
n i
LCL for S-chart = maxc 4
( n i
)σˆ
– kc 5
( n i
)σˆ
, 0
UCL for S-chart = c 4
( n i
)σ+
kc 5
( n i
)σ
Center line for S-chart: By default, the center line for the i th subgroup (where k is equal to the sigma
multiplier) indicates an estimate of the expected value of s i . This value is computed as c ( 4
n )σ σˆ
i , where
is an estimate of σ. If you specify a known value (σ 0 ) for σ, the central line indicates the value of
c 4
n i . Note that the central line varies with n i .
( )σ 0
The estimate for the standard deviation in an X
/S chart is
σˆ
where
=
s 1
s
--------------- N
+ … + ----------------
c 4
( n 1
) c 4
( n N
)
---------------------------------------------------
N
X w = weighted average of subgroup means
σ = process standard deviation
n i = sample size of i th subgroup
c 4 (n) is the expected value of the standard deviation of n independent normally distributed variables
with unit standard deviation
c 5 (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 whichn i
≥ 2
s i is the sample standard deviation of the i th subgroup