1. 1) The following data represents individual observations of molecular weight taken hourly
from a chemical process
Observation x Observation x Observation x Observation x
no no no no
1 1045 6 1008 11 1139 16 1125
2 1055 7 1050 12 1169 17 1163
3 1037 8 1087 13 1151 18 1188
4 1064 9 1125 14 1128 19 1146
5 1095 10 1146 15 1238 20 1167
The target value of the molecular weight is 1050 and process standard deviation is
thought to be 25.setup a tabular CUSUM for the mean of this process. Design CUSUM to
detect a shift of about 1.0 times standard deviation in the process mean.
2) A Shewhart X bar chart has centre line at 10 with UCL = 16, and LCL = 4. Suppose you
wish to supplement this chart with an EWMAcontrol chart using /(lambda) =0.1 and the
same control limit width in Sigma units as employed on the X bar chart. What are the
values of the study state upper and lower control limits on the EWMA chart
3) Analysis the data using a Moving average control chart with w = 5,
sample No x sample No x
1 8.00 13 8.05
2 8.01 14 8.04
3 8.02 15 8.03
4 8.01 16 8.05
5 8.00 17 8.06
6 8.01 18 8.04
7 8.06 19 8.05
8 8.07 20 8.06
9 8.01 21 8.04
10 8.04 22 8.02
11 8.02 23 8.03
12 8.01 24 8.05
4) The data shown here come from a production process with two observable quality
characteristics x1, x2. The data are sample means of each quality characteristic, based on
the samples of size n=25. Assume that mean value of the quality characteristics and the
co variance matrix were computed from 50 preliminary samples.
X
2. Observation no X1 X2 Observation no X1 X2
1 58 32 9 46 25
2 60 33 10 50 29
3 50 27 11 49 27
4 54 31 12 57 30
5 63 38 13 58 33
6 53 30 14 75 45
7 42 20 15 55 27
8 55 31
Means values of X1 and X2 are 55 and 30 respectively.
S= 200 130
130 120
Construct a T2 control chart using this data. Use the phase 2 control limits.
