Median Charts
Preparing Median Charts
The primary reason for using medians is that it is easier to do on the shop floor because
no arithmetic must be done. The person doing the charting can simply order the data
and pick the center element. For simplicity, odd numbers of samples are chosen 3, 5, 7,
etc. The major disadvantage of using a median chart is that it is less sensitive
(powerful) in detecting process changes when extreme values occur.
Traditionally, all subgroup values are plotted, and only the median values are
connected by line segments. One must be careful when interpreting the chart that the
"out of control" rules are only applied to the median elements.
Steps in Constructing a Median Chart
1. Either an R chart or s chart is developed as shown on the respective XBAR-r or
XBAR-s charts and the process variation is shown to be in statistical control.
2. If an R chart was used, the control limits are as follows:
3. If an s chart was used, the control limits are as follows:
Table of A(6) and A(7)
n
A(6)
A(7)
n
A(6)
A(7)
2
3
4
5
1.880
1.187
.796
.691
1.880
1.067
.796
.660
6
7
8
9
.549
.509
.434
.412
.580
.521
.477
.444
The centerline is XDBLBAR. Note that it is the subgroup MEANS
that determine
both the centerline and the control limits.
4. Plot the centerline XDBLBAR, LCL, UCL, and the subgroup medians.
5. Interpret the data using the following guidelines to determine if the process is
in control:
a.
b.
one pount outside the 3 sigma control limits
eight successive points on the same side of the centerline
c. six successive points that increase or decrease
d. two out of three points that are on the same side of the
centerline,
both at a distance exceeding 2 sigmas from the centerline
e. four out of five points that are on the same side of the
centerline,
four at a distance exceeding 1 sigma from the centerline
f. using an average run length (ARL) for determining process
anomolies
Example:
The following data consists of 20 sets of three measurements of the diameter of an
engine shaft. An R-Chart will be used to examine variability followed by a Median
Chart.
n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
meas#1
2.0000
1.9998
1.9998
1.9997
2.0003
2.0004
1.9998
2.0000
2.0005
1.9995
2.0002
2.0002
2.0000
2.0000
1.9994
1.9999
2.0002
2.0000
1.9997
2.0003
meas#2
1.9998
2.0003
2.0001
2.0000
2.0003
2.0003
1.9998
2.0001
2.0000
1.9998
1.9999
1.9998
2.0001
2.0002
2.0001
2.0003
1.9998
2.0001
1.9994
2.0007
meas#3
2.0002
2.0002
2.0005
2.0004
2.0002
2.0000
1.9998
2.0001
1.9999
2.0001
2.0001
2.0005
1.9998
2.0004
1.9996
1.9993
2.0004
2.0001
1.9998
1.9999
Range
0.0004
0.0005
0.0007
0.0007
0.0001
0.0004
0.0000
0.0001
0.0006
0.0006
0.0003
0.0007
0.0003
0.0004
0.0007
0.0010
0.0006
0.0001
0.0004
0.0008
2.574*.0005 =
0 * .0005
=
0.001287
0.00
XBAR
2.0000
2.0001
2.0001
2.0000
2.0003
2.0002
1.9998
2.0001
2.0001
1.9998
2.0001
2.0002
2.0000
2.0002
1.9997
1.9998
2.0001
2.0001
1.9996
2.0003
Median
2.0000
2.0002
2.0001
2.0000
2.0003
2.0003
1.9998
2.0001
2.0000
1.9998
2.0001
2.0002
2.0000
2.0002
1.9996
1.9999
2.0002
2.0001
1.9997
2.0003
RBAR CHART LIMITS:
RBAR = 0.0005
UCL
LCL
=
=
D(4)*RBAR
D(3)*RBAR
=
=
XBAR CHART LIMITS:
XDBLBAR = 2.0000
UCL
LCL
=
XDBLBAR + A(6)*RBAR
= XDBLBAR - A(6)*RBAR
R Chart:
= 2.000+1.187*.0005
= 2.000-1.187*.0005
= 2.0005935
= 1.9994065
Median - Chart: