Question

An electronic firm manufactures circuits to produce 30 amps. The UCL and LCL on the mean of the
circuits for samples of size 4 were computed to be LCL = 27.15 and UCL = 33.04. The UCL and LCL for
the sample range were estimated to be LCL = 0 and UCL = 5.75. These control limits were used to
monitor the circuits produced for 13 time periods, yielding the following data:
Time Period Sample amp measurements
1
2
3
4
5
6
7
8
9
10
11
12
13

30.9 30.1 32.9 32.1
31.8 32.4 27 28.6
29 27.2 28 30
26.8 29.8 27.4 32.1
26.8 27.6 31.4 29.2
30.4 30.4 34.5 30.1
31.6 30.8 29 30.6
28.4 29.4 30.3 28.5
31.5 23.5 37 21
25.5 33.4 31 20.1
34.5 29 32.1 28.3
22 29.5 24.5 23.5
29.5 28.5 32.5 33

a) Plot the sample means on the X̅ chart for 13 time periods. Discuss the quality of the process with
respect to the mean
b) Plot the sample ranges on R chart for the 13 time periods. Discuss the quality of the process with
respect to the variability

without using mathlab

Answer 1

SOLUTION-

(a) Plot the sample man on the chart for the 13 time periods.

Starting iwth MINITAB procedure:

steps to follow

Step 1: First Choose Stat > Control Charts > Variables Charts for Subgroups > Xbar.

Step 2: Choose All observations for a chart are in one column and then enter column of 1, 2, 3, 4.

Step 3: In Subgroup sizes, enter a 4.

Step 4: Click OK.

.

MINITAB output

From the MINITAB output the lower control limit for chart LCL 24.39 , upper control limit for UCL is 34.27 .

Yes, all values are lies between (24.39 , 34.27).

(b)

Plot the sample man on the R chart for the 13 time periods.

MINITAB procedure:

steps to follow

Step 1: Choose Stat > Control Charts > Variables Charts for Subgroups > R.

Step 2: Choose All observations for a chart are in one column and then enter column of 1, 2, 3, 4.

Step 3: In Subgroup sizes, enter a 4.

Step 4: Click OK.

MINITAB output:

From the MINITAB output the lower control limit for Rchart LCL , upper control limit for R UCL is 15.47

Yes, all R values are lies between .

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