5.8 APPLICATION PROBLEM Section 5.5.2 contained a description of a filling machi
ID: 3041720 • Letter: 5
Question
5.8 APPLICATION PROBLEM Section 5.5.2 contained a description of a filling machine used to fill a dry soap product. Investigation of the behavior of the four heads of the machine revealed that head 4 was more variable than the others. In addition, contain- ers filled on shift 2 also showed more variation. After discovering this infor- mation, head 4 was found to have a specific malfunction and was overhauled. Investigation of the different levels of variation between the two shifts revealed that shift 2 personnel followed a different procedure in rout- ing bins of material to the filling machine and more short-term variation in density was observed. Maintenance completed work on head 4 and mixing procedures were reviewed on both shifts and standardized. Additional data are reported in Table 5.9, and the new data are plotted in Figure 5.17 a. Is the process in control? b. Does it appear that the process has changed as a result of the work on c. Prepare any additional plots deemed necessary to complete the analysis d. What recommendations should be made for continuing operation of the head 4 and on standardizing procedures? If so, in what respects? of the current behavior of the filling machine. filling machine?Explanation / Answer
Since data is available Head-wise and Shift-wise, analysis is also done like-wise.
Back-up Theory
Control Limits for Xbar-Rchart.
Xbar Chart
Central Line: CL = Xdouble bar = (1/k)[1,k](xibar)
Lower Control Limit: LCL = Xdouble bar – A2.Rbar
Upper Control Limit: UCL = Xdouble bar + A2.Rbar
R Chart
Central Line: CL = R bar = (1/k)[1,k](Ri)
Lower Control Limit: LCL = D3.Rbar
Upper Control Limit: UCL = D4.Rbar
Xibar = mean of the ith sample
Ri = range of ith sample
k = number of samples.
A2, D3 and D4 are Control Chart Constants available in any standard textbook on Quality Control
Calculations
k = 5 for each Head-shift combination
A2(2) = 1.88
D3(2) = 0
D4(2) = 3.267
Details
Head 1
Head 2
Head 3
Head 4
Shift 1
Shift 2
Shift 1
Shift 2
Shift 1
Shift 2
Shift 1
Shift 2
[1,k](xibar)
32.2
32.1
28
28.3
32.9
32.6
28.7
27.1
Xdouble bar
6.44
6.42
6
5.66
6.58
6.52
5.74
5.42
[1,k](Ri)
1.4
0.6
2
2.5
2.8
1.7
1.7
1.9
Rbar
0.28
0.12
0
0.5
0.56
0.34
0.34
0.38
Xbar Chart
CL
6.44
6.42
5.52
5.66
6.58
6.52
5.74
5.42
LCL
5.91
6.19
4.92
4.72
5.53
5.88
5.10
4.71
UCL
6.97
6.65
6.12
6.6
7.63
7.16
6.38
6.13
Rchart
CL
0.28
0.12
0.32
0.5
0.56
0.34
0.34
0.38
LCL
0
0
0
0
0
0
0
0
UCL
0.92
0.39
1.05
1.63
1.83
1.11
1.11
1.24
Viewing the given values of xibar and Ri’s, it is seen that all the values are within the respective control limits implying that all the processes are under control.
DONE
To give answers to the specific questions,
Process is under control
Process has changed for the better as a result of work done on Head 4 and standardizing of procedures.
The recommendation to the management would be to employ the above limits for conrol of the process in future.
Details
Head 1
Head 2
Head 3
Head 4
Shift 1
Shift 2
Shift 1
Shift 2
Shift 1
Shift 2
Shift 1
Shift 2
[1,k](xibar)
32.2
32.1
28
28.3
32.9
32.6
28.7
27.1
Xdouble bar
6.44
6.42
6
5.66
6.58
6.52
5.74
5.42
[1,k](Ri)
1.4
0.6
2
2.5
2.8
1.7
1.7
1.9
Rbar
0.28
0.12
0
0.5
0.56
0.34
0.34
0.38
Xbar Chart
CL
6.44
6.42
5.52
5.66
6.58
6.52
5.74
5.42
LCL
5.91
6.19
4.92
4.72
5.53
5.88
5.10
4.71
UCL
6.97
6.65
6.12
6.6
7.63
7.16
6.38
6.13
Rchart
CL
0.28
0.12
0.32
0.5
0.56
0.34
0.34
0.38
LCL
0
0
0
0
0
0
0
0
UCL
0.92
0.39
1.05
1.63
1.83
1.11
1.11
1.24
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