solve using EXCEL (screen shot cell formulas and values) 9 85.8 156.3 119.7 96.2
ID: 3050312 • Letter: S
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solve using EXCEL (screen shot cell formulas and values)
9 85.8 156.3 119.7 96.2 153.0 122.2 70.6 10107.4 148.7 127.4 125.0 127.5 127.2 41.3 2.9 3.2 5.26 Parts manufactured by an injection modeling molding process are subjected to a compressive strength test. Twenty samplesof 4 parts each are collected, and the s.3 2.2 ompressive strengths (in psi) are shown in Table 5E.6. a. Establish X and R control charts for compressive strength using these data. Is the process in statis- tical control? b. After establishing the control charts in part (a), 15 new subgroups were collected; the compressive strengths are shown in Table 5E.7. Plot the X and R values against the control limits from part (a) and draw conclusions. le 5E.6 .0 .9 .8 .8 .0 Part Strength Data for Problem 5.26 Sample Number x 1 83.0 81.2 78.7 75.7 77.0 79.1 7.3 2 88.6 78.3 78.8 71.0 84.2 80.2 17.6 3 85.7 75.8 84.3 75.2 81.0 80.4 10.4 4 5 83.4 78.4 82.6 78.2 78.9 80.3 5.2 80.8 74.4 82.5 74.1 75.7 77.5 8.4 Exercises 225Explanation / Answer
XBAR-R CHART
Back-up Theory
Let there be n measurements on a quality characteristic taken at k equally-spaced intervals. Let xij represent the jth measurement at the ith interval, i = 1, 2, …., k and j = 1, 2, …., k.
The Xbar part of Xbar-R Chart has:
Central line: CL = Xdouble bar
Lower Control Limit: LCL = Xdouble bar – A2Rbar
Upper Control Limit: UCL = Xdouble bar + A2Rbar;
The R part of Xbar-R Chart has:
Central line: CL = Rbar
Lower Control Limit: LCL = D3Rbar
Upper Control Limit: UCL = D4Rbar, where
Xdouble bar = (1/k)(i = 1, k)xibar, xibar = (1/n)(i = 1, n)xij
Rbar = (1/k)(i = 1, k)Ri, Ri = Max(xij) - min(xij)
A2, D3, D4 are constants which can be directly obtained from standard Control Chart Constants Table.
Now, to work out the solution,
Part 5.26(a)
Xboublebar
79.52
Rbar
8.73
n
5
k
20
A2
0.577
D3
0
D4
2.114
Xbar Chart
CL
79.52
LCL
74.48279
UCL
84.55721
Rchart
CL
8.73
LCL
0
UCL
18.45522
By visual examination all Xibar and Ri’s are found to be within the respective control limits. Hence, the process is under control. ANSWER
Part 5.26(b)
The following points are found to be out of respective limits:
Points 4, 11, 14 – xbar is out of control.
Points 5, 6, 7, 11, 13, 14, 15 – R is out of control. ANSWER
Xboublebar
79.52
Rbar
8.73
n
5
k
20
A2
0.577
D3
0
D4
2.114
Xbar Chart
CL
79.52
LCL
74.48279
UCL
84.55721
Rchart
CL
8.73
LCL
0
UCL
18.45522
By visual examination all Xibar and Ri’s are found to be within the respective control limits. Hence, the process is under control. ANSWER
Part 5.26(b)
The following points are found to be out of respective limits:
Points 4, 11, 14 – xbar is out of control.
Points 5, 6, 7, 11, 13, 14, 15 – R is out of control. ANSWER
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